Goldman sachs Aptitude
IMPORTANTS ARE: Goldman Sachs important Questions
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1. At what percentage above the cost price must an article be marked, so as to gain 33% after allowing the customer a discount of 5%?
A. 33%
B. 45%
C. 40%
D. 51%
Answer: Option C
Explanation:
Let us assume the C.P of the article as Rs. 100
It is mentioned that the gain is 33%
So, S.P = 100 + 33%(C.P) = 100 + 33 = Rs. 133
This is the S.P after allowing 5% discount.
100% (M.P) - 5%(M.P) = S.P
95%(M.P) = 133
M.P = 133/0.95
M.P = 140
Therefore, Mark up % = [(M.P - C.P)/C.P] * 100
= [(140 - 100)/100] * 100
= 40%
2. How many three-digit numbers which are divisible by 7 can be formed using the first three prime numbers (without repetition)?
A. 1
B. 2
C. 4
D. 6
Answer: Option
Explanation:
The first three prime numbers are 2, 3, and 5.
Three-digit numbers that can be formed with the help of 2, 3 and 5 without repetition are 235, 253, 325, 352, 523, 532.
Let's divide all the above numbers with 7 and check whether the number is exactly divisible by 7.
235/7 = R(4)
253/7 = R(1)
325/7 = R(3)
352/7 = R(2)
523/7 = R(5)
532/7 = R(0)
Only 532 is exactly divisible by 7.
Q3. How many 6-digit numbers divisible by 2 can be formed by the first six whole numbers, with repetition allowed?
A. 10 * 2 * 64
B. 15 * 64
C. 10 * 65 * 2
D. 15 * 65
Answer: Option B
Explanation:
The first six whole numbers are 0, 1, 2, 3, 4, 5
We need to find 6-digit numbers divisible by 2 that can be formed by 0, 1, 2, 3, 4 and 5 with repetition allowed.
The number should be divisible by 2. The last number can be 0 or 2 or 4. So, the last place will have 3 ways.
0 cannot come in the first place because if 0 comes in the first place, it will be a five-digit number.
First place will have 5 ways i.e 1 or 2 or 3 or 4 or 5
Second place will have 6 ways i.e 0 or 1 or 2 or 3 or 4 or 5
Third place will have 6 ways i.e 0 or 1 or 2 or 3 or 4 or 5
Fourth place will have 6 ways i.e 0 or 1 or 2 or 3 or 4 or 5
Fifth place will have 6 ways i.e 0 or 1 or 2 or 3 or 4 or 5
So, the total number of ways = 5 * 6 * 6 * 6 * 6 * 3 = 15 * 64
Q4. The ratio of the ages of 'A' and 'B' is 3:5, that of 'C' and 'D' is 2:5 and that of 'D' and 'B' is 1:2 respectively. 'E' is 8 years old and the ratio of the ages of 'E' and 'C' is 4:5. Find the sum of the ages of 'A' and 'D'.
A. 50 years
B. 80 years
C. 75 years
D. 55 years
Answer: Option D
Explanation:
Given, Age of E = 8 years.
The ratio of ages of E and C = 4 : 5 = 4x : 5x
4x = 8 years => x = 2 years
Age of C = 5x = 5*2 = 10 years
The ratio of ages of C and D = 2 : 5 = 2y : 5y
2y = 10 years => b = 5
Age of D = 5y = 5*5 = 25 years
The ratio of ages of D and B = 1 : 2 = 1z : 2z
1z = 25
Age of B = 2z = 2*25 = 50 years
The ratio of ages of A and B = 3 : 5 = 3p : 5p
5p = 50 => p = 10
Age of A = 3p = 3*10 = 30
Therefore, the sum of ages of A and D = 30 + 25 = 55 years
Q5. A bullet train can cover 550 km in 3 hours. If the speed of the train is decreased by 23 1/3 km/hr, how much time will it take to cover a distance of 480 km?
A. 4 hours
B. 5 hours
C. 2 hours
D. 3 hours
Answer: Option D
Explanation:
Given, a bullet train covers 550 km in 3 hours.
Speed of bullet train = Distance/Time = 550/3 kmph
Given, the speed of the train decreases by 23 1/3 kmph
New speed = Speed - 23 1/3 = 550/3 - 70/3 = 480/3 kmph
Time taken to cover 4880 km with new speed = 480/(480/3) = 3 hours
Q6. Avik starts running on a circular track of length 600 metres. He completes the first round in 2 min 24 sec. For all subsequent rounds, his speed decreases by 10% of his previous round's speed. What will be Avik's speed when he is running the third round?
A. 12.15 km/hr
B. 20.25 km/hr
C. 14.58 km/hr
D. 16.2 km/hr
Answer: Option A
Explanation:
Given, Avik runs 600 meters in 2 min 24 sec i.e 144 sec
Speed = 600/144 m/sec
Speed = (600/144)*(18/5) kmph = 15 kmph
This is the speed for the first round.
Given, his speed decreases by 10% of his previous round's speed
Speed for the second round = 15*0.9 = 13.5 kmph
Speed for the third round = 13.5*0.9 = 12.15 kmph
Q7. A team of five members is formed from 9 boys and 8 girls. Find the probability that at least one girl is included in the team.
A. 409/442
B. 417/442
C. 421/442
D. 433/442
Answer: Option D
Explanation:
Probability of having at least one girl in the team = 1 - Probability of no girl in the team
Sample Space = 17C5
Number of ways of selecting a team of five members with no girl in the team = 9C5
Probability of selecting a team of five members with no girl in the team = 9C5/17C5 = 9/442
So, the probability of selecting a team of five members with at least one girl in the team = 1 - 9/442 = 443/442
Q8. Town A's population last year was 70,000. This year its population became 74,725. The male population increased by 5% and the female population increased by 7%. How many males were there last year in town A?
A. 12565
B. 9245
C. 61250
D. 8750
Answer: Option D
Explanation:
Let us assume,number of male as M and number of female as F in the previous year.
Given, M + F = 70,000 --- (1)
This year its population is 74,725.
The male population is increased by 5% and the female population is increased by 7%
1.05M + 1.07F = 74,725 --- (2)
Multiply the eq (1) with 1.07
1.07M + 1.07F = 74,900 --- (3)
Subtract (3) and (2)
=> 0.02M = 175
M = 8,750
Q9. The average money a mango seller earned during a month comprising 31 days was Rs. 110 per day. His average earnings during the first 15 days was Rs. 98 per day, and his average earnings during the last 15 days was Rs. 100 per day. What were his earnings on the 16th day?
A. Rs. 390
B. Rs. 420
C. Rs. 440
D. Rs. 480
Answer: Option C
Explanation:
We know that, Average = Sum/Number of days
The average money a mango seller earned during a month comprising 31 days was Rs. 110 per day.
Avg of 31 days = Sum of the money earned for 31 days/31
Sum of the money earned for 31 days = 110*31 = 3410 --- (1)
His average earnings during the first 15 days was Rs. 98 per day
Sum of first 15 days earnings = 15*98 = 1470 --- (2)
His average earnings during the last 15 days was Rs. 100 per day
Sum of last 15 days earnings = 15*100 = 1500 --- (3)
Earnings on the 16th day = (1) - (2) - (3) = 3410 - 1470 - 1500 = Rs. 440
Q10. The average price of 16 apples is Rs. 32 while the average price of 14 of these apples is Rs. 22. Of the remaining two apples, if the price of one apple is 40% more than the other, what is the price of each of these two apples?
A. Rs. 125 and Rs. 89
B. Rs. 119 and Rs. 85
C. Rs. 133 and Rs. 95
D. Rs. 111 and Rs. 79
Answer: Option B
Explanation:
Given, the average price of 16 apples is Rs. 32
Sum of price of 16 apples = 16*32 = Rs. 512 --- (1)
The average price of 14 of these apples is Rs. 22
Sum of price of 14 apples = 14*22 = Rs. 308 --- (2)
Of the remaining two apples, if the price of one apple is 40% more than the other
Let's assume the price as x and y respectively.
So, x is 40% more than y
x = 1.4y --- (3)
From (1), (2) and (3)
Sum of price of 16 apples = Sum of price of 14 apples + x + y
512 = 308 + 1.4y + y
2.4 y = 204
y = Rs. 85
So, x = 1.4 (85) = Rs. 119
11. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
A. Rs. 9,423
B. Rs. 10,250
C. Rs. 12,500
D. Rs. 10,500
Explanation:
Simran=50000*3=150000
Nanda = 80000*2.5=200000
So, Ratio = 150000/200000=3:4
Simran's share = (3/7) * 24500 = 10500.
12. There are 200 pupils in total, out of which 125 like pizza,115 like burger, then how many like both?
A. 80
B. 40
C. 45
D. 60
Explanation:
n(A U B)=n(A) + n(B) - n(A n B)
200 = 125 + 115 - BOTH
BOTH = 240 - 200 = 40.
13. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:
A. 100/7% gain
B. 15% gain
C. 100/7% loss
D. 15 % loss
Explanation:
c.p of 100 oranges = 350
100 oranges = 100/12 = 8 dozen + 4 oranges
1 dozens s.p = 48
8 dozens s.p = 48*8=384
4 0ranges s.p = 48/12*4 = 16
100 oranges sp = 400;
profit = 50
profit% = 50/350*100 = 100/7%.
14. A father has 8 children; he takes 3 at a time to a zoo. What is the probability of a child going to the zoo?
A. 1/2
B. 3/8
C. 1/4
D. 5/8
Explanation:
the total number of children is 8.
* 3 children can go to the zoo at one time.
* But the probability of a child going to zoo is= here one child should be going to zoo.
so, remaining two members selected from remaining 7 children.
=1*(7C2) / 8C3 = 3/8.
15. A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?
A. 154
B. 150
C. 160
D. none
Explanation:
9 friends: 5 Girls and 4 Boys.
Use permutation concept,
Selecting exactly 3 girls out of 5: 5c3 = 5! / (5-3)! *3! = 10 ways.
Selecting boys: 4C0 + 4C1 + 4C2 + 4C3 + 4C4 = 16 ways.
Total ways = 10*16 = 160.
16. I bought 5 pens, 7 pencils and 4 erasers Rs. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I had paid. What percent of the total amount paid by me was paid for the pens?
A. 61.25%
B. 61%
C. 62.5%
D. 60%
Explanation:
Assume P is Cost of one pen, C is cost of one Pencil & E is cost of one Eraser.
Let cost of 5 pens, 7 pencils and 4 erasers be X
5P+7C+4E=X --------(i)
Rajan has bought 6 pens, 14 pencils and 8 erasers at 1.5x cost (half more than mine)
6P+14C+8E=1.5X ------------(ii)
Multiplying Equation 1 by 2 and subtracting 2nd equation from it:
10P+14C+8E=2X
6P+14C+8E=1.5X
-----------------
4P = 0.5X
-----------------
=> P = 0.5X/4
Total amount paid by me for pens = 5P= 0.5X/4 * 5 = 2.5X/4
Percent of the total amount paid by me for the pens = {(2.5X/4)/X}* 100 = 62.5%.
17. A box contains 90 mts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is:
A. 10 kg
B. 10.5 kg
C. 11 kg
D. 11.5 kg
E. None of the above
Explanation:
A box contains 90 mts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., and the weight of the empty box is x,
Then,
=> 90*0.100 + 100*0.150 +x = 35.5
=> 9.0+ 15.0 +x = 35.5
=> x = 11.5 kg.
18. Syllogism:
Statements:
All papers are books;
Some papers are files.
Conclusions:
(I)Some files are books
(II) Some books are files
A. Only conclusion I is followed.
B. Only conclusion II is followed.
C. Both conclusion I & II are followed.
D. Neither conclusion I nor II follow
Answer: D.
19. Analogy:
SLIPPER:17 : : LOTUS:7 : : PEACE:?
A. 20
B. 10
C. 14
D. 24
Explanation:
slipper=19,12,9,16,16,5,18 according to their respective positions. Now to get 17 we must subtract sum of last three i.e. (16+5+18) from first four i.e. (19+12+9+16).
Now lotus= 12,15,20,21,19 to get 7 we subtract sum of last two i.e. (21+19) from first three (12+15+20) just like the previous case and we get 7.
So in case of peace we subtract(c+e) from(p+e+a) and we get 14.
20. If in a certain code, TWENTY is written as 863985 and ELEVEN is written as 323039, how is TWELVE written in that code?
A. 863203
B. 863584
C. 863903
D. 863063
Explanation:
The alphabets are coded as shown:
T W E N Y L V
8 6 3 9 5 2 0
So, In TWELVE,
T is coded as 8,
W as 6,
E as 3,
L as 2,
V as 0.
Thus, the code for TWELVE is 863203.
21. Find the odd man out:
1, 8, 27, 64, 125, 196, 216, 343
A. 64
B. 196
C. 216
D. 1
Explanation:
The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3.
196 is not a perfect cube.
22. In a certain code, BOXER is written as AQWGQ. How VISIT is written in that code?
A. UKRKU
B. UKRKS
C. WKRKU
D. WKRKS
E. None of these
Explanation:
Letters at the odd places have been written one letter back, and letters at the even places have been written two letters ahead in the coded word as their positions in the alphabet
23. The cost price of item A, Item A was sold at a profit of 10% and Item B was sold at a loss of 20%. If the respective ratio of selling price of items A and B is 11:12, what is the cost price of item B?
a)Rs.450/-
b)Rs.420/-
c)Rs.400/-
d)Rs.350/-
e)Rs.480/-
Answer: Option A
The cost price of item B is Rs. 150/- more than the Let us assume cost price of A= X
So that Cost price of B= X+150.
SP of A= X*1.1
SP of B=(X+150)*0.8
Given that
SPA: SPB
11:12
So that 1.1X/(X+150)*0.8= 11/12
X=300
CP of B= 300+150=450
Answer is 450.
24. A sum of Rs 731 is divided among A, B and C such that 'A' receive 25% more than 'B' and 'B' receive 25% less than 'C'. What is C's share in the amount?
a)Rs. 172
b)Rs. 200
c)Rs. 262
d)Rs. 258
None of these
Answer: Option E
A + B + C = 731 ..... (i)
A = 1.25B, gives A = 1.25 * 0.75 C = 0.9375 C....(ii)
B = 0.75C....(iii)
Using (ii) and (iii) in (i) we get
0.9375C + 0.75C + C = 731, gives C = 272.
So option E is the answer.
25. In how many different ways can letters of the word "PRAISE" be arranged?
a)720
b)610
c)360
d)210
None of these
Answer: Option A
As total number of alphabets in PRAISE are 6, so total no. of ways is 6!=720 So option A is the answer
26. If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 300%, the resultant fraction is [5/18]. What is original fraction?
a)4/9
b)4/5
c)8/9
d)8/11
None of these
Answer: Option A
Let the fraction be [n/d] & after that it becomes [2.5n/4d]=5/18 . So we get the result as [4/9]
27. A car covers the first 30 km of its journey in 45 minutes and the remaining 25 km in 30 minutes. What is the average speed of the car?
a)60
b)64
c)49
d)48
None of these
Answer: Option E
Total distance/Total time =(30+25)/[(3/4)+(1/2)]
Average Speed=44kmph
28. Four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day. For how many hours a day would 2 examiners have to work in order to examine twice the number of answer papers in 20 days?
a)8
b)7.5
c)10
d)8.5
None of The above
Answer: Option C
Examiners Days Hours/Day Papers
4 10 5 x
2 20 ? 2xSo, we required number of hours = so optionC is the answer
Using chain rule,
(4×10×5)/X= (2×20×Y)/2X
X=10 hrs/day
29. A student got twice as A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly? many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly?
a)12
b)16
c)18
d)24
Answer: b
Solution:
Suppose the boy got x sums right and 2x sums wrong. Then, x + 2x = 48 3x = 48 x = 16.
30. A man fixed an appointment to meet the manager, Manager asked him to come two days after the day before the day after tomorrow. Today is Friday. When will the manager expect him?
a)Friday
b) Monday
c)Tuesday
d)Sunday
Answer: b
Solution:
Don’t confuse it with Tuesday.the correct answer is Monday
31.There is a merry-go-round race going on.One person says,”1/3 of those in front of me and 3/4 of those behind me, give the total number of children in the race”. Then the number of children took part in the race?
a)12
b)11
c)13
d)14
Answer: 3
Solution:
Assume there are x participants in the race. In a round race, number of participants in front of a person wil be x-1 and that behind him wil be x-1. i.e, 1/3(x-1) + 3/4(x-1) = x solving x = 13
32. Find the value of X,Y and Z in the following
X XXX
Y YYY
Z ZZZ
…………….
Y X XX Z
a)X=9 , Y=2; Z=8
b)X=9 , Y=1; Z=9
c)X=8 , Y=1; Z=8
d)X=9 , Y=1; Z=8
Answer: d
33. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is?
a)1008
b)1015
c)1022
d)1032
Answer: b
Solution:
Required number = (L.C.M. of 12,16, 18, 21, 28) + 7 = 1008 + 7 = 1015
34. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is?
a)12
b)16
c)24
d)48
Answer: d
Solution:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.
35. The ratio of number of girls to boys in a class is 3:1. If 50% of the girls and 75% of the boys are above 5 feet, then the percentage of students in the class who are 5 feet or below is
A. 44.25
B. 48.25
C. 47.5
D. 43.75
Answer: Option D
Explanation:
Given, the ratio of number of girls to boys in a class is 3:1
Let's assume the total number of students = 400
So, number of girls = 300
The number of boys = 100
50% of the the girls are above 5 feet
Number of girls above 5 feet = 50%(300) = 150
So, the number of girls 5 feet or below = 300 - 150 = 150
75% of boys are above 5 feet
Number of boys above 5 feet = 75%(100) = 75
Number of boys 5 feet or below = 100 - 75 = 25
Number of students 5 feet or below = 150 + 25 = 175
Percentage of students who are 5 feet or below = (175/400)*100 = 43.75
36. On the opening ceremony of a bakery, Raju sold chocolate cake at a profit of 20%. After a few days he gets 10% discount on its ingredients, making its cost price equivalent to 90% of its initial cost price. But even then he decides to sell it at Rs. 18 more than the previous selling price, making him a gain of 40%. Find the initial cost price of chocolate cake.
A. Rs. 180
B. Rs. 330
C. Rs. 220
D. Rs. 300
Answer: Option D
Explanation:
Let us assume the C.P of the cake as x
Raju sold chocolate cake at a profit of 20%
S.P of the cake = 1.2x
After a few days he gets 10% discount on its ingredients, making its cost price equivalent to 90% of its initial cost price.
New C.P = 0.9x
He decides to sell it at Rs. 18 more than the previous selling price
New S.P = 1.2x + 18 --- (1)
He made a profit of 40%
New S.P = 1.4(0.9x) --- (2)
Equate (1) and (2)
1.2x + 18 = 1.4(0.9x)
0.06x = 18
x = 300
C.P of the cake = Rs. 300
37. A man spends exactly Rs. 810 for buying caps and gloves at Rs. 30 and Rs. 70 respectively. What is the ratio of number of gloves to that of caps, if he purchased maximum possible number of gloves ?
A. 3 : 2
B. 4 : 5
C. 2 : 3
D. 5 : 4
Answer: Option A
Explanation:
Given, the total amount spent = Rs. 810
Cost of a cap = Rs. 30
Cost of a glove = Rs. 70
Let's assume the number of caps as x and number of gloves as y
30x + 70y = 810 --- (1)
It is given that the man purchased maximum possible number of gloves.
So, this indicates he purchased minimum number of caps.
The minimum of caps won't be equal to 0, 1 , 2, 3, 4 and 5 because eq (1) won't be satisfied as we will get a decimal value for y.
So, the minimum value for x = 6
From (1), 70y = 810 - 180
70y = 630
y = 9
So, the ratio of number of gloves to that of caps = y : x = 9 : 6 = 3 : 2
38. A sum of money amounts to Rs. 5120 in 3 years and to Rs. 7290 in 6 years at certain rate of compound interest, compounded annually. Find the rate of interest.
A. 7.5 %
B. 12.5 %
C. 10 %
D. 15 %
Answer: Option B
Explanation:
Given,
A sum of money amounts to Rs. 5120 in 3 years and to Rs. 7290 in 6 years at certain rate of compound interest, compounded annually.
We know that
A = P[1 + R/100]n
Amount after 3 years = 5120
P[1 + R/100]3 = 5120 --- (1)
Amount after 6 years = 7290
P[1 + R/100]6 = 7290 --- (2)
Divide (2) with (1)
[1 + R/100]3 = 729/512
1 + R/100 = 9/8
R/100 = 1/8
R = 12.5%
39. If x = 1 - 1/x , find the value of (x6+2x3+1)
A. 3
B. 1
C. 8
D. 0
Answer: Option D
Explanation:
Given,
x = 1 - 1/x
x + 1/x = 1 -- (1)
Cubing on both sides
(x+1/x)3 = 1
x3+1/x3+ 3(x)(1/x)(x+1/x) = 1
x3+ 1/x3 + 3 = 1 [From (1)]
(x6+ 1 + 2x3)/x3 = 0
(x6+ 1 + 2x3) = 0
40.If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15 students?
A.10 days
B.12 days
C.11 days
D.None of these
Answer & Explanation
Answer: Option 3
Required number of days = 9 X 5/15 X 66/18 = 11 days
41.A man rows 8 km/hr in still water. If the river is running at 2 km/hr, it takes 32 minutes to row to a place and back. How far is the place?
A.1.5 km
B.2.5 km
C.2 km
D.3 km
Answer & Explanation
Answer: Option 3
Upstream speed = 8 – 2 = 6 km/h,
Downstream speed = 8 + 2 = 10 km/h
D/10 + D/6 = 32/60
, solving we get D = 2 km.
OR simply checking by the options
42.A person on tour has Rs. 360 for his daily expenses. He decides to extend his tour programme by 4 days which leads to cutting down daily expenses by Rs. 3 a day. The number of days of his tour programme is
A.15
B.20
C.18
D.16
Answer & Explanation
Answer: Option 1
On checking the options we find that if the tour is for 20 days then the daily expenses will be Rs 18. To extend the tour by 4 days would make the tour for 24 days and the
daily expense will become Rs 15, so the total bill will be Rs 24×15 = Rs 360, the same as before.
43.The tax on a commodity is diminished by 10 % and its consumption increased by 10 %. The effect on the revenue derived from it changes by K %. Find the value of K.
A.1
B.2
C.-1
D.-2
Answer & Explanation
Answer: Option 3
Directly using the formula, when a value is increased by R% and then decreased by R%, then net there is R2/100% decrease.
Putting R = 10, we get 1 % decrease.
44.Out of 80 students in a class, 25 are studying commerce, 15 mathematics and 13 physics. 3 are studying commerce and mathematics, 4 are studying mathematics and physics and 2 are studying commerce and physics. 1 student is studying all the three subjects together. How many students are not studying any of the three subjects?
A.35
B.40
C.20
D.15
Answer & Explanation
Answer: Option 1
n(CMP) = n(C) + n (M) + n (P)
– n (CM) – n (MP) – n (CP) + n (CMP)
= 25 + 15 + 13 – 3 – 4 – 2 + 1 = 45 students.
So the number of students not studying any subject = 80 – 45 = 35.
45.A portion of a 30 m long tree is broken by a tornado and the top strikes the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to
A.30/√3 m
B.10 m
C.30√3 m
D.60 m
Answer & Explanation
Answer: Option 2
The height of the tree = 30m.
So, x + y = 30m
Also sin30∘ 1/2 = x/y x = 2y.
So 3x = 30,
x = 10 m.
46.. 252 can be expressed as a product of primes as?
a)2 x 2 x 3 x 3 x 7
b)2 x 2 x 2 x 3 x 7
c)3 x 3 x 3 x 3 x 7
d)2 x 3 x 3 x 3 x 7
Answer: a
Solution:
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
47. 21, 9, 21, 11, 21, 13, 21, …….
a)14
b)15
c)21
d)23
Answer: b
Solution:
In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.
48) Ram &Shyam started from a point X and Y respectively and started moving towards each other. After they met Ram took 4 hours to reach Y and Shyam took 16 hours to reach X. Rams speed is 48 kmph. What is the speed of Shyam?
a)24kmph
b)56kmph
c)32kmph
d)12kmph
e)24kmph
Solution:
Let the speed of Shyam be 'x'kmph, then the ratio of speed of Ram and Shyam = Square root of (Time taken by Shyam to Reach X after they meet / Time taken by Ram to Reach Y after they meet)
= 48/x = Sqrt(16/4)
= 48/x = 2
x = 24
49) A train leaves Meerut at 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Meerut at 10.30 a.m. At what time do the two trains travel in order to cross each other?
a)7.56 AM.
b)7.26 AM.
c)6.26 AM.
d)none
Solution:
The first train takes 4 hours and the second train takes 3.5 hours.
Time ratio is 8:7. Therefore, the speed ratio will be 7:8.
Let the speeds be 7x and 8x, and distance is 28x ( 4x7 or 3.5x8).
At 7 AM, the first train must have covered a distance of 14x. Therefore, at 7 A.M. the distance between the two trains is 28x-14x=14x.
Time taken to meet = 14x/(7x+8x)=14/15 hour or 56 minutes.
Hence, the two trains meet at 7.56 AM.
50) A man reaches his office 20 min late if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house?
a)20 km
b)16 km
c)14 km
d)10 km
Solution:
Let distance = x km.
Time taken at 3 kmph :dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30-(-20) = 50 mins = 50/60 hours.
x/3- x/4 = 50/60
x/12 = 5/6
x =10 km.
51) Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
a)30%
b)33.33%
c)35%
d)44%
Solution:
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs. 5/6 x 30 = Rs. 25.
S.P. of 30 articles = Rs. 6/5 x 30 = Rs. 36.
Gain % = 11/25 x 100 % = 44%.
52) How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs.7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
a)36
b)42
c)54
d)63
Solution:
S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.
C.P. of 1 kg of mixture = Rs. (100/110) x 9.24 = Rs. 8.40
By the rule of alligation, we have:
Ratio of quantities of 1st and 2nd kind = 14:6 = 7 : 3.
Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27
x = (7 x 27)/3 = 63 kg.
53) In an Exhibition seven cars of different companies - Chevrolet, Aston, Fiat, Maruti, Mercedes, Bedford and Ferrari are standing facing to east in the following order :
Chevrolet is next to right of Ferrari.
Ferrari is fourth to the right of Fiat.
Maruti car is between Aston and Bedford.
Fiat which is third to the left of Aston, is at one end.
54) Which of the cars are on both the sides of Chevrolet car ?
a) Aston and Maruti
b) Maruti and Fiat
c) Ferrari and Mercedes
d) Aston and Ferrari
Answer: Option c
F B M A Fe C Me
Ferrari and Mercedes are on both the sides of the Chevrolet car.
55) Which of the following statement is correct?
a) Maruti is next left of Aston.
b) Bedford is next left of Fiat.
c) Bedford is at one end.
d) Fiat is next second to the right of Maruti.
Answer: Option a
F B M A Fe C Me
Therefore, Maruti is next left of Aston.
56 Which one of the following statements is correct?
a) Ferrari car is in between Aston and Fiat.
b) Chevrolet is next left to Mercedes car.
c) Ferrari is next right of Chevrolet.
d) Maruti is fourth right of Mercedes.
Answer: Option b
F B M A Fe C Me
Therefore, Chevrolet is next left to Mercedes car.
57) Which of the following groups of cars is to the right of Aston?
a) Chevrolet, Ferrari and Maruti
b) Mercedes, Chevrolet and Ferrari
c) Maruti, Bedford and Fiat
d) Bedford, Chevrolet and Ferrari
Answer: Option b
F B M A Fe C Me
Mercedes, Chevrolet and Ferrari cars are to the right of Aston.
58) Which one of the following is the correct position of Mercedes?
a) Next to the left of Chevrolet
b) Next to the left of Bedford
c) Between Bedford and Ferrari
d) Fourth to the right of Maruti.
Answer: Option D
F B M A Fe C Me
The correct position of Mercedes is fourth to the right of Maruti.
59) Eleven friends A, B, C, D, E, F, G, H, I, J and K are sitting in the first row of the stadium watching a cricket match.
H is to the immediate left of D and third to the right of I.
J is the immediate neighbor of A and B and third to the left of G.
A is the second to the right of E, who is at one of the ends.
F is sitting next to the right of D and D is second to the right of C.
Who is sitting in the center of the row?
a) B
b) C
c) G
d) I
Answer: Option d
The arrangement of the persons is E K A J B I G C H D F. So I is sitting in the center of the row.
60) Which of the following people are sitting to the right of G?
a) CHDE
b) CHDF
c) IBJA
d) ICHDF
Answer: Option b
The arrangement of the persons is E K A J B I G C H D F. Hence CHDF are sitting to the right of G.
61) Which of the following statements is true with respect to the above arrangement?
a) There are three persons sitting between D and G
b) K is between A and J.
c) B is sitting between J and I
d) G and C are neighbors sitting to the immediate right of H
Answer: Option c
The arrangement of the persons is E K A J B I G C H D F. Hence B is sitting between J and I.
62) Lalit marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000 gm for 800 gm. What is his net profit percentage?
(a) 57.5%
(b) 57%
(c) 61%
(d) 62.5%
Ans: 57.5%
Explanation
Let us assume his CP/1000 gm = Rs 100
The SP/kg (800 gm) = Rs 126
So, his CP/800 gm = Rs 80
So, profit = Rs 46
So, profit percentage = 46/80 x 100 = 57.5%
63) In a bag, there are a certain number of toy-blocks with alphabets A, B, C and D written on them. The ratio of blocks A:B:C:D is in the ratio 4:7:3:1. If the number of A blocks is 50 more than the number of C blocks, what is the number of B blocks?
(a) 120
(b) 350
(c) 240
(d) 210
Ans: 350
Explanation
Let the number of the blocks A,B,C,D be 4x, 7x, 3x and 1x respectively
4x = 3x + 50 ? x = 50. So the number of B blocks is 7*50 = 350.
64) If 60 ml of water contains 12% of chlorine, how much water must be added in order to create a 8% chlorine solution?
(a) 10ml
(b) 35ml
(c) 20ml
(d) 30ml
Ans: 30ml
Explanation
Let x ml of chlorine be present in water.
Then, 12/100 = x/60 ? x = 7.2 ml
Therefore, 7.2 ml is present in 60 ml of water.
In order for this 7.2 ml to constitute 8% of the solution, we need to add extra water. Let this be y ml, then 8/100 of y = 7.2ml ? y = 90 ml.
So in order to get 8% chlorine solution, we need to add 90-60 = 30 ml of water.
65) If a : b = 7 : 5 and c : d = 2a : 3b, then ac : bd is :
(a) 14:15
(b) 50:147
(c) 98:75
(d) 15:14
Ans: 98:75
Explanation
Since a and b are in the ratio 7:5. Then, let a = 7x and b = 5x.
c = 2a = 2 * 7x = 14x and d = 3b = 3 * 5x = 15x.
c : d = 14 : 15 ac : bd = 14 * 7 : 15 * 5 = 98 : 75
66) The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.
(a) 33.25
(b) 33.5
(c) 34.25
(d) 35
Ans: 34.25
Explanation
Total sum of last 4 matches = (1038.9)(642)
=389252=137
Average = 137/4 = 34.25
67) A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs.6500?
(a) 4991
(b) 5467
(c) 5987
(d) 6453
Ans: Rs. 4991
Explanation
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009) = Rs. 4991.
68) The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
(a) 4
(b) 8
(c) 12
(d) 16
Ans: 8
Explanation
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 61.
Or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
69) A car travels at a speed of 60 km/h and returns with a speed of 40 km/h, calculate the average speed for the whole journey.
(a) 48 kmph
(b) 38kmph
(c) 32 kmph
(d) 16 kmph
Ans: 48 kmph
Explanation:
Since equal distances are covered at 60 kmph and 40 kmph, we can apply the formula 2xy/(x+y). Average speed = (24060) / (40 + 60) = 48 kmph
Capgemini Aptitude Questions - set 2
70) A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.
(a) 3 kmph
(b) 3.5 kmph
(c) 2 kmph
(d) 4 kmph
Ans: 4 kmph
Explanation:
Speed of boat in still water = x = 5 km/hr.
Let rate of flow of river = y km/hr.
Therefore, speed of u/s = 5- y and speed of d / s = 5 + y
Hence, 90/(5+y) + 90/(5-y) = 100 ? y = 4 km/hr.
71) How many numbers between 11 and 90 divisible by 7?
(a) 10
(b) 11
(c) 12
(d) 13
Ans: 11
Explanation:The required numbers are 14, 21, 28, 84
This is an A.P with a = 14, d = (21-14) = 7
Let the number of terms be n, then Tn= 84 a + (n-1) d = 84
14 + (n-1) * 7 = 84
n = 11
72. 50 g of an alloy of gold and silver contains 80% gold (by weight). The quantity of gold, that is to be mixed up with this alloy, so that it may contain 95% gold, is
a.150gm
b.120gm
c.130gm
d.none
Solution:
In 50 gms, Gold and Silver in the ratio = 80:20
So, Gold = 40 gms
Silver = 10 gms
Let ua tit of gold e ied up e
SO,
(40+x)/(50+x) = 95/100
X = 150 gms
73. Two planes move along a circle of circumference 1.2 kms with constant speeds. When they move in different directions, they meet every 15 seconds and when they move in the same direction one plane overtakes the other every 60 seconds. Find the speed of the slower plane:
a.0.05km/sec
b.0.88km/sec
c.0.54km/sec
d.none
Solution:
Let the speeds of fast plane and slow planes be x and y m/sec respectively D = s × t
If they move in opposite direction
15 (x + y) = 1200 ⇒ + = /se ... i
If they move in same direction, relative speed = x – y m/sec
Time = 60 i.e. 4 times
∴ Speed is (1/4)th x – = /se ... ii
Solving (i) and (ii),
y = 50 m/sec = 0.05 km/sec
74) The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay?
(a) Rs. 1200
(b) Rs. 2400
(c) Rs. 4800
(d) None
Ans: Rs. 2400
Explanation
Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i) and x + 6y = 1600 .... (ii).
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
---------------------
4y = 800
---------------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
75.Anil is at present one-fourth the age of his father. After 16 years he will be one-half of the age of his father. Find the present age of Anil's father.
A.40 years
B.36 years
C.32 years
D.28 years
Answer & Explanation
Answer: Option 3
Let the present ages of Anil and his father be A and F respectively.
Given A = 1/4 F Also A+16 = 1/2 (F+16),
Solving we get F = 32 years.
OR checking by options.
If Anil’s father’s present age is 32, then Anil’s age is one fourth i.e. 8.
After 16 years, Anil would be 24 years and father will be 48 years old, so Anil’s age is half of his father.
76 .A man sitting in a train travelling at the rate of 50 km/hr observes that it takes 9 sec for a goods train travelling in the opposite direction to pass him. If the goods train is 187.5 m long, find its speed.
A.25 km/hr
B.40 km/hr
C.35 km/hr
D.36 km/hr
Answer & Explanation
Answer: Option 1
Let required speed be x.
187.5/(x+50)5/18 = 9
x = 25 km/hr
77.A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs. 5,100 more. The sum is
A.Rs. 1,70,000
B.Rs. 1,50,000
C.Rs. 1,25,000
D.Rs. 1,20,000
Answer & Explanation
Answer: Option 1
Let the principal = p.
Time = 3 years.
So 1% of p for 3 years = Rs 5100.
p = Rs 170,000.
78.Fill pipe A is 3 times faster than second Fill pipe B and takes 32 minutes less than Fill pipe B. When will the cistern be full if both pipes are opened together?
A.25 minutes
B.24 minutes
C.30 minutes
D.2 minutes
Answer & Explanation
Answer: Option 4
Let the time taken by A to fill the pipe is = A min.
So the time taken by B to fill the pipe B is = B min.
According to the given condition B = 3A;
and given that B – A = 32 min.
So solving we get A = 16 min, B = 48 min.
Let the total work be 48 units.
So time taken by them together is 48/4 = 12 min.
79. What comes next in the series 8, 15, 12, 19, 16, 23?
A. 30
B. 20
C. 26
D. 31
Ans. B
80. A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
A. 4.8 hr
B. 2.4 hr
C. 3.6 hr
D. 1.8 hr
Ans. A
Explanation:
Solution 1
Part filled by first tap in 1 hour =1/3 part
Part emptied by second tap 1 hour =1/8 part
Net part filled by both these taps in 1 hour =1/3−1/8=5/24 part
i.e, the cistern gets filled in 24/5 hours =4.8 hours.
81. A shopkeeper has two items A & B. A was sold at a profit of 25% and B was sold at a loss of 15%. If the cost price of A is 15% more than that of B, what is the overall profit/ loss % to the shopkeeper?
A. 20.65
B. 19.65
C. 18.65
D. 20
Ans. B
82. The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A. 15 kmph
B. 12 kmph
C. 10 kmph
D. 5 kmph
Ans. A
Distance = speed x time
Speed= 90 km/hr
Time = 10/60=1/6 h
D= 90 x 1/6 = 15 km
83. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs. 5,100 more. The sum is :
A. Rs. 1,70,000
B. Rs. 1,50,000
C. Rs. 1,25,000
D. Rs. 1,20,000
Ans. A
Description for Correct answer:
Simple interest for 1 yr = 5100351003 = Rs.1700
1% of sum 1700
Therefore, Sum = 1700×10011700×1001
= Rs.170000
84. Fill pipe A is 3 times faster than second Fill pipe B and takes 32 minutes less than Fill pipe B. When will the cistern be full if both pipes are opened together?
A. 25 minutes
B. 24 minutes
C. 30 minutes
D. 12 minutes
Ans. D
Explanation:
Let pipe A takes p min to fill
Then,
pipe B takes 3p min to fill
=> 3p - p = 32
=> p = 16 min => 3p = 48 min
Required, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min
85. The tax on a commodity is diminished by 10 % and its consumption increased by 10 %. The effect on the revenue derived from it changes by K %. Find the value of K.
A. 1
B. 2
C. -1
D. -2
Ans. C
Description for Correct answer:
Net % effect on revenue
=−10+10−10×10100=−10+10−10×10100
=−1%=−1%
Hence % reduction in
Revenue = 1%
86. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
A. 70 km
B. 80 km
C. 50 km
D. 56 km
Ans. C
Solution
Let the actual distance travelled be x km.
Then,x10=x+2014
⇒14x=10x+200
⇒4x=200⇒x=50km
87.The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is
A) 10
B) 46
C) 70
D) 90
Answer: A) 10
Explanation:
Let the numbers be x and (100-x).
Then,x(100−x)=5*495×100-x=5*495
=> x2−100x+2475=0x2-100x+2475=0
=> (x-55) (x-45) = 0
=> x = 55 or x = 45
The numbers are 45 and 55
Required difference = (55-45) = 10
88.The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
A) 12
B) 48
C) 84
D) 108
Answer: C) 84
Explanation:
Let the numbers be x and 4x. Then, x×4x=84×21 ⇔ x2=84×214⇔ x=21x×4x=84×21 ⇔ x2=84×214⇔ x=21
Hence Larger Number = 4x = 84
89.The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275 , then the other is
A) 279
B) 283
C) 308
D) 318
Answer: C) 308
Explanation:
Other number = (11×7700275)11×7700275= 308.
90.Two number , both greater than 27,have hcf 27 and lcm 162 The sum of the number is
a)1
b)162
c)135
d)81
Answer:C)135
Explanation:
H.C.F*l.C.M= product of two no.
162*27=4374
now find out the factors of 4374
ANd find out the suitavlefactors.I.e 54*81=4374 which have h.cf=27 and L.c.m-162.
therefore 54+81=135
91.Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
A.127
b. 132
c. 114
d. 108
Answer:A
Explanation: Hence, make the dividend completely divisible by the divisor. This is possible, if we subtract remainder from the dividend.
Therefore,
1657 – 6 = 1651
2037 – 5 = 2032
H.C.F. of 1651 and 2032 is 127. 127 is the common factor.
127 × 13 = 1651
Thus by adding 6, we get 1651 + 6 = 1657
127 is the correct answer
92.A five-digit number is formed by using digits 1,2,3,4 and 5 without repetition. What is the probability that the number is divisible by 4?
A)1/5
B)2/5
C)3/5
D)4/5
Answer:A
Solution:
A number divisible by 4 formed using the digits 1,2,3,4 and 5 has to have the last two digits 12 or24 or 32 or 52.
In each of these cases, the five digits number can be formed using the remaining 3 digits in 3! = 6 ways.
A number divisible by 4 can be formed in 6×4=24 ways.
Total number that can be formed using the digits 1,2,3,4 and 5 without repetition
=5!=120
Required probability = 24/120 = 1/5
93.A rectangular courtyard 4.55 meters long and 5.25 meters wide is paved exactly with square tiles of same size. Find the largest size of the tile used for this purpose?
A. 25 cm
b. 45 cm
c. 21 cm
d. 35 cm
Correct Option: (d)
Explanation:
Here, we are asked to find the largest size of tile. Therefore, calculate H.C.F.
Step 1: Covert numbers without decimal places i.e 455 cm and 525 cm
Step 2: Find the H.C.F. of 455 and 525
H.C.F. of 455 and 525 = 35 cm
Hence, the largest size of the tile is 35 cm.
94.John, Smith and Kate start at same time, same point and in same direction to run around a circular ground. John completes a round in 250 seconds, Smith in 300 seconds and Kate in 150 seconds. Find after what time will they meet again at the starting point?
A. 30 min
b. 25 min
c. 20 min
d. 15 min
Correct Option: (b)
Explanation:
L.C.M. of 250, 300 and 150 = 1500 sec
Dividing 1500 by 60 we get 25, which mean 25 minutes.
John, Smith and Kate meet after 25 minutes.
95.Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
A) 4
B) 10
C) 15
D) 16
Answer: D) 16
Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes,they will together (30/2)+1=16 times
96.The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
A) 1677
B) 1683
C) 2523
D) 3363
Answer: B) 1683
Explanation:
L.C.M of 5, 6, 7, 8 = 840
Therefore, Required Number is of the form 840k+3.
Least value of k for which (840k+3) is divisible by 9 is k = 2
Therefore, Required Number = (840 x 2+3)=1683
97.A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
A) 107
B) 117
C) 127
D) 137
Answer: B) 117
Explanation:
Let us calculate both the length and width of the room in centimeters.
Length = 6 meters and 24 centimeters = 624 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48
Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117
98.Find the largest number of four digits exactly divisible by 12,15,18 and 27.
A)9720
B)6580
C)4578
D)1023
Answer:A
Explanation:
The Largest number of four digits is 9999.
Required number must be divisible by L.C.M. of 12,15,18,27 i.e. 540.
On dividing 9999 by 540,we get 279 as remainder .
Required number = (9999-279) = 9720.
99.Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder .
A)1683
B)1982
C)2001
D)none
Ans:A
Sol. L.C.M. of 5,6,7,8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 X 2 + 3)=1683
100. The number of prime factors of (3 x 5)^12 * (2 x 7)^10 * (10)25 is:
A): 47
B): 60
C): 72
D): None of these
Correct Answer : D
Explanation: The equation can be facorize as 3*5*3*2*2*2*7*2*5*2*5*5*5 or 2^5*3^2*5^5*7^1 total no of prime factor =(5+1)*(5+1)*(2+1)*(1+1)=216
101. What least value must be assigned to * so that the number 63576*2 is divisible by 8?
A): 1
B): 2
C): 3
D): 4
Correct Answer :C
Explanation: The test for divisibility by 8 is that the last 3 digits of the number in question have to be divisible by 8.
So, 6*2 has to be divisibile by 8.
I know 512 is divisible by 8.
Also 592 is divisible by 8.
So, 632 is divisible by 8.
So * is 3.
102 The smallest number, which is a perfect square and contains 7936 as a factor is:
A): 251664
B): 231564
C): 246016
D): 346016
Correct Answer :C
Explanation:
7936 => 2^2 * 2^2 * 2^2 * 2^2 * 31^1
To make it as a perfect square, we have to multiply 7936 with 31…
Hence the reqd no. is 7936*31 = 246016
103.A portion of a 30 m long tree is broken by a tornado and the top strikes the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to
A. 30/√3 m
B. 10 m
C. 30√3 m
D. 60 m
Ans. B
104. How many cubes one colored silver on one face, orange or pink on another face and have four uncolored faces ?
A. 8
B. 10
C. 12
D. 16
Ans. A
Solution
Since the cube is divided into 125 pieces then u can imagine it as cut into 5 slices horizontally and vertically resulting in 5x(5x5) pieces.
Suppose Brown is B, Orange is O, Pink is P and Silver is S.
n(P + S) = 4
n(O + S) = 4
Total is 8. Hence, the correct answer is (A).
105. a, b, c and d are four numbers in arithmetic progression. The mean of these four numbers is 20. The common difference between the numbers is 5.
Find the product of first and last numbers.
A. 133.76
B. 343.75
C. 442.25
D. 124
Ans. B
Solution:
Common difference is 5
Mean of 4 numbers is 20
Let four numbers be
X X+ 5 X+10 X+15
Sum of 4 numbers = 4X+30
Mean of 4 numbers =( 4X+30 )/4
Given mean of 4 numbers is 20
Hence 4X+30 =4×20
4X = 80-30=50
X=50/4=12.5
Product of last and first numbers is X × X+15
=12.5 ×(15+12.5)
12.5 × 27.5 =343.75
106. Two numbers are in the ratio xy,when 2 is added to both the numbers.the ratio becomes 1:2.when 3 is subtracted from both the numbers. The ratio becomes 1:3.Find the sum of x and y.
A. 27
B. 24
C. 28
D. 26
Ans. D
Solution:
X and Y, when is added it becomes 1 : 2
Numbers = ( x + 2 ) ÷ ( y + 2 ) = ( 1 ÷ 2 )
Cross multiply
2 x + 4 = y + 2
2 x - y = - 2 --------------------------- ( 1 )
Now, 3 is subtracted from both the numbers
( x - 3 ) ÷ ( y - 3 ) = ( 1 ÷ 3 )
Cross multiply
3 x - 9 = y - 3
3 x - y = 6 ---------------------------- ( 2 )
Now, let us subtract equation 2 from equation 1
2 x - y = - 2
- ( 3 x - y ) = - ( 6 )
---------------------------
2 x - y = - 2
- 3 x + y = - 6
Now , add the two equations
- y and + y get cancelled
- x = - 8
x = 8
Now, substitute x in any equation and find out y
( 2 ) ( 8 ) - y = - 2
16 - y = - 2
- y = - 2 - 16
- y = - 18
y = 18
x = 8
y = 18
x + y = 18 + 8
x + y = 26
The sum of the two numbers is 26
107. The distance between two cities P and Q is 300km. A train starts from station P at 10 am with speed 80 km/hr towards Q. Another train starts from Q towards P with speed 40km/hr at 11 am. At what time do they meet.
A. 12:50 pm
B. 1 pm
C. 12:20 pm
D. 12:40 pm
Ans. A
First train starts at 10am so in one hour it covers 80 km in one hour. Now distance b/w P and Q is 220. Suppose at some’ x’ km they meet. So,
x/80 = (220-x)/40
x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
108. If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15 students?
A. 10 days
B. 12 days
C. 11 days
D. None of these
Ans. C
Solution:
5 students - 18 pencils -9 days
1 student - 18 penicils -45 days (i.e., 9x5)
1 student- 1 pencil- (45/18) days
1 student- 66 pencils - (45/18) x 66 days
15 students- 66 pencils - (45/18) x (66/15)
which is equal to 11 days.
109. Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
A. 18
B. 24
C. 30
D. 28
Answer: Option A
Explanation:
S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
110. Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
A. 3:8
B. 9:31
C. 8:21
D. 10:27
Answer: Option B
Explanation:
1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
111. If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
A. 2:3:3
B. 1:2:6
C. 1/6:1/2:1/3
D. 9:6:4
Answer: Option D
Explanation:
A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
112. Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
A. Rs.600
B. Rs.525
C. Rs.375
D. Rs.0
Answer: Option C
Explanation:
A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
113. Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
A. Rs.260
B. Rs.270
C. Rs.360
D. Rs.540
Answer: Option D
Explanation:
A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
114. Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is:
A. 36
B. 27
C. 18
D. 30
Answer: Option A
Explanation:
(3x-9):(5x-9) = 9:17
x = 12 => 3x = 36
115. From a point A on the ground, the angle of elevation of a tower is 45˚. A ship moving at 20 m/sec started moving from point A to point B in 45 seconds. The angle of elevation from point B is 60˚. Find the height of the tower.
A. 1350 +450√3
B. 1350√3 + 450
C. 1800
D. None of the above
Ans. A
116. A man rows 8 km/hr in still water. If the river is running at 2 km/hr, it takes 32 minutes to row to a place and back. How far is the place?
A. 1.5 km
B. 2.5 km
C. 2 km
D. 3 km
Ans. C
Speed of the man in still water =8 kmph.
Speed of the river =2 kmph
Downstream =8+2=10 kmph
Upstream =8−2=6 kmph
⇒10x+6x=6048
⇒8x=24
⇒x=3 km
117. A set contains all numbers from 1 to 250. If a number is picked at random, what is the probability that it is a multiple of 3?
A. 82/250
B. 83/250
C. 80/250
D. 1/3
Ans. A
118. A person on tour has Rs. 360 for his daily expenses. He decides to extend his tour program by 4 days which leads to cutting down daily expenses by Rs. 3 a day. The number of days of his tour program is
A. 15
B. 20
C. 18
D. 16
Ans. B
119. Anil is at present one-fourth the age of his father. After 16 years he will be one-half of the age of his father. Find the present age of Anil’s father.
A. 40 years
B. 36 years
C. 32 years
D. 28 years
Ans. C
120. A man sitting in a train travelling at the rate of 50 km/hr observes that it takes 9 sec for a goods train travelling in the opposite direction to pass him. If the goods train is 187.5 m long, find its speed.
A. 25 km/hr
B. 40 km/hr
C. 35 km/hr
D. 36 km/hr
Ans. A
Correct option is C)
Let the speed of the goods train be x km/hr
Relative speed =(50+x) km/hr =(50+x)×185 m/s
Therefore, (50+x)×5/18187.5=9
⇒250+5x187.5×18=9
⇒250+5x=187.5×2=375
⇒5x=375−250=125
⇒x=25 km/hr
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