divelab/Sys2Bench huggingface dataset:
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
A. 65
Options:
A)28 sec
B)89 sec
C)85 sec
D)16 sec
E)15 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10
= 89 sec.
Answer:B
Answer: B
Question: Susan, John, Tim,and Kim need to be seated in 4 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Options:
A)A)12
B)B)120
C)C)80
D)D)240
E)E)60
Rationale: Total number of arrangements = 4! = 24
In exactly half, Susan will be to the left of Tim, which gives us 12 arrangements
Option (A)
Answer: A
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 24, what is the sum of the first 15 terms of the progression?
Options:
A)300
B)240
C)220
D)200
E)180
Rationale: 4th term + 12th term = 24
i.e., (a+3d)+(a+11d) = 24
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 24 --------------- From (1)
=180
Answer : E
Answer: E
Question: Find the least number must be added to 228712 so that remaining no.is divisible by 9?
Options:
A)5
B)3
C)1
D)6
E)2
Rationale: On dividing 228712 by 9 we get the remainder 4, so 5 should be subtracted
A
Answer: A
Question: If n = 2.0563 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
Options:
A) -0.0053
B) -0.0003
C) 0.0007
D) 0.0037
E) 0.0153
Rationale: n*=2.06
n*-n=2.06-2.0563
0.0037
Answer: D
Answer: D
Question: 8^9 - 8^2 is approximation of which of the following?
Options:
A)9^7
B)9^8
C)9^9
D)9^11
E)8^9
Rationale: => Since 8^2 is a small number compared to 8^9, it can be disregarded. Thus, 8^9-8^2=8^9 is derived and the answer is E.
Answer: E
Question: A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 80 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
Options:
A)3/16,000
B)1/8,100
C)1/600
D)1/90
E)2/45
Rationale: Solution provided by stanford2012 is correct: 80/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=80/800*1/600=1/6,000.
Answer: C.
Answer: C
Question: Caitlin bought three puppies for Rs. 200, Rs. 350 and Rs.450 and she sold that to George for Rs. 250, Rs. 300 and Rs.600.
What is the percentage of profit Caitlin got?
Options:
A)10
B)12
C)18
D)15
E)20
Rationale: Cost of buying=200+350+450=Rs.1000
Cost of selling=250+300+600=Rs. 1150
profit=1150-1000=Rs.150
profit%= (150/1000)x100=15%
Answer:D
Answer: D
Question: Ritesh and Co. generated revenue of Rs. 1,800 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
Options:
A)17.36%
B)20%
C)25%
D)50%
E)None of these
Rationale: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,800 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1800 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1800.
=>14,400.
Hence, the total revenue by end of 2007 is Rs. 14,400. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/14400)×100.
=>17.36%.
Answer : A
Answer: A
Question: If 5a + 7b = g, where a and b are positive integers, what is the largest possible value of g for which exactly one pair of integers (a, b) makes the equation true?
Options:
A)35
B)48
C)69
D)70
E)74
Rationale: 5*a1 + 7*b1 = g
5*a2 + 7*b2 = g
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 from a and add 5 to b respectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer
Answer: D
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
Options:
A)11 1/8%
B)11 1/3%
C)11 1/9%
D)11 1/6%
E)11 1/4%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer: C
Answer: C
Question: There is a school were 60% are girls and 35% of the girls are poor. Students are selected at random, what is the probability of selecting a poor girl out of total strength?
Options:
A)21/100
B)22/100
C)23/100
D)24/100
E)26/100
Rationale: Let take 100 students
outoff 100 60 are girls
among girls poor girls are =35% 0f 60=21
pbt of selecting poor girl in total strength=21/100
ANSWER:A
Answer: A
Question: A boy has six trousers and 8 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)99
B)38
C)28
D)48
E)271
Rationale: The boy can select one trouser in six ways.
The boy can select one shirt in 8 ways.
The number of ways in which he can select one trouser and one shirt is 6 * 8
= 48 ways.
Answer: D
Answer: D
Question: We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $397. How many math books did we buy?
Options:
A)47
B)53
C)56
D)61
E)64
Rationale: Let M be the number of math books and let H be the number of history books.
M+H=90.
H=90-M.
4M+5H=397.
4M+5(90-M)=397.
-M+450=397.
M=450-397=53.
The answer is B.
Answer: B
Question: A train running at the speed of 90 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150 meter
B)145 meter
C)140 meter
D)135 meter
E)225 meter
Rationale: Explanation:
Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train(Distance) = Speed * Time
=25*9=225 meter
Option E
Answer: E
Question: How many 5 digit even numbers with distinct digits can be formed using the digits 1, 2, 5, 5, 4 ?
Options:
A)16
B)36
C)24
D)48
E)58
Rationale: The 5 digit even numbers can be formed out of 1, 2, 5, 5, 4 by using either 2 or 4 in the unit’s place. This can be done in 2 ways.
Corresponding to each such arrangement, the remaining 4 places can be filled up by any of the remaining four digits in 4! / 2! = 12 ways. Hence, the total number of words = 2 x 12 = 24.
ANSWER:C
Answer: C
Question: Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen.
Options:
A)23
B)34
C)25
D)26
E)27
Rationale: 1 pen cost x,let 1 pencil cost y
2x+3y=86, ...y=(86-2x)/3
again,
4x+y=112
4x+(86-2x)/3=112
12x+86-2x=336
10x=250
x=25
ANSWER:C
Answer: C
Question: If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
Options:
A)1098
B)1000
C)1628
D)1098
E)1094
Rationale: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x
1 = 1/10 * 1/10 * 1/10 * x
=> x = 1000
Answer: B
Answer: B
Question: If |20x-10| = 110, then find the product of the values of x?
Options:
A)-45
B)50
C)-62
D)35
E)-30
Rationale: |20x-10| = 110
20x-10 = 110 or 20x-10 = -110
20x = 120 or 20x = -100
x = 6 or x = -5
product = -5*6 = -30
Answer is E
Answer: E
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
Options:
A)25%
B)10% or 60%
C)50%
D)55%
E)70%
Rationale: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 2:4:8
Initial Total dogs = 14X ( x assumed; 2+4+8= 14), Since the total dogs are less than 30 therefore initial total value has to be 14
L = 2, A = 4 E = 8
L:A= 2:5
This ratio doubles
Hence New Dog count is
L= 4 , A = 4 E= X: Also 4+4+x<30
We need to Find X*100/(4+4+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 4*100/(8+x) %A = 4*100/(8+x); Only Value for X is 2 or 12 ; 9+x<30 and % integer
Therefore, Enormus Dogs % is = 12*100/(20) or 2*100/20 = 60% or 10%
B
Answer: B
Question: A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?
Options:
A)1/9
B)1/6
C)1/2
D)1/1
E)1/4
Rationale: Given that B alone can complete the same work in days = half the time taken by A
= 9days
A’s one day work = 1/18
B’s one day work = 1/9
(A+B)’s one day work = 1/18+1/9 = 1/6
Answer : B.
Answer: B
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 20 nor by 35?
Options:
A)567
B)850
C)560
D)923
E)240
Rationale: In 1000 consecutive numbers, number of multiples of 20 = 1000/20 = 50 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 20*35 i.e. 700 = 1000/700 = 1
Number of integers from 1 to 1000 that are divisible by neither 20 nor by 35 = 1000 - (50 + 28 - 1) {Using the concept of sets here) = 923
Answer is D
Answer: D
Question: 5 kg of adulterated rice has 2% stones in it and the rest is rice. Half of the stone
content was removed. Now the percentage of stone content in it is
Options:
A)0.99%
B)1%
C)1.1%
D)1.01%
E)2.01%
Rationale: 2% of 5=0.1
Half of the stone has been remove so stone becomes 0.1/2=0.05
Total wt. becomes 5-0.05=4.95
% of stone=0.05*100/4.95=1.01%
ANSWER:D
Answer: D
Question: In 2008, a certain factory produced 10% more widgets than it did in 2007, and its production in 2009 was 110% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?
Options:
A)12%
B)17%
C)20%
D)24%
E)30%
Rationale: Let P be the original level of production in 2007.
Let x be the rate of production in 2010 compared to 2009.
x*1.1*1.1*P = P
x = 1/1.21 = 0.826 which is a decrease of about 17%.
The answer is B.
Answer: B
Question: In how many different ways can 3 girls and 3 boys form a circle such that the boys and the girls alternate?
Options:
A)15
B)12
C)17
D)20
E)None of these
Rationale: Explanation :
In a circle, 3 boys can be arranged in 2! ways
Given that the boys and the girls alternate.
Hence there are 3 places for girls which can be arranged in 3! ways
Total number of ways = 2! x 3! = 2 x 6= 12. Answer : Option B
Answer: B
Question: What is the median from the below series 90, 92, 94, 88, 95, 88, 97, 87, and 98
Options:
A)80
B)85
C)93
D)97
E)100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 93, 94, 95, 96, 98
The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.)
C
Answer: C
Question: In what ratio must be a grocer mix two varities of tea worth Rs.60 a kg and Rs.65 a Kg so that by selling the mixture at Rs.68.20 a Kg he may gain 10%?
Options:
A)3 : 4
B)3 : 2
C)3 : 5
D)4 : 5
E)None
Rationale: Solution
S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10 %
C.P. of 1 kg of the mixture = Rs. (100 / 110 x 68.20) = Rs. 62.
Required ratio = 3 : 2.
Answer B
Answer: B
Question: What is the value of 5x^2 − 1.9x − 3.7 for x = − 0.3?
Options:
A)−4.72
B)−3.82
C)−3.58
D)−2.68
E)0.57
Rationale: 5x^2 - 1.9x - 3.7, x =-0.3
Firstly, 5x^2 can be written as 5 * x * x - substituting one of the x with -0.3
We have -1.5x - 1.9x -3.7 ---> -3.4x-3.7 ---> -3.4 (-0.3) -3.7 ---> 1.02 - 3.7 = -2.68
ANSWER:D
Answer: D
Question: A man gains 20% by selling an arƟcle for a certain price. If he sells it at double the price, the
percentage of profit will be
Options:
A)130%
B)140%
C)150%
D)160%
E)None of these
Rationale: Explanation:
Let the C.P. = x,
Then S.P. = (120/100)x = 6x/5
New S.P. = 2(6x/5) = 12x/5
Profit = 12x/5 - x = 7x/5
Profit% = (Profit/C.P.) * 100
=> (7x/5) * (1/x) * 100 = 140 %
Answer: B
Answer: B
Question: the length of the bridge is 200m,which a 100 m long train cross in 60sec. then what is the speed of train?
Options:
A)6
B)5
C)4
D)10
E)8
Rationale: speed = length/time
length=(200+100)=300m
time=60 sec
speed = 300/60=5m/sec
answer B
Answer: B
Question: If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+3 is divided by 41?
Options:
A)3
B)5
C)6
D)16
E)18
Rationale: X can be written as 82K + 5 or X = 5,87,169,etc.
X + 3 = 82K + 5+3= 82K +8 or X + 3 = 8,90,172 etc.
When divided by 41, we will get the remainder 8.
E
Answer: E
Question: In a hostel there were 100 students. To accommodate 40 more students the average is decreased by rupees 10. But total expenditure decreased by Rs.400. Find the total expenditure of the hostel now?
Options:
A)1400
B)2500
C)3000
D)1500
E)2100
Rationale: 100x - 400 = 140(x – 10)
x = 25
100 * 25 - 400 = 2100
Answer:E
Answer: E
Question: 826924 × 9999 = ?
Options:
A)8248402936
B)8268413076
C)8268413071
D)8064329671
E)8244563371
Rationale: B
8268413076
826924 × 9999 = 826924 × (10000 - 1)
= 826924 × 10000 - 826924 × 1
= 8269240000 - 826924
= 8268413076
Answer: B
Question: In N is a positive integer less than 200, and 24N/60 is an integer, then N has how many different positive prime factors?
Options:
A)1
B)3
C)5
D)6
E)8
Rationale: (A).
24n/60 must be an integer. => 2n/5 must be an integer. Hence n must be a multiple of 5.
=> n has 1 different prime integers.
Answer: A
Question: Rosy also matched the London Eye which stands at 443ft and Las
Vegas’ High Roller standing at 550ft. Being the tallest Ferris wheel in
the world, how much taller is High Roller than the London Eye?
Options:
A)99
B)78
C)110
D)150
E)107
Rationale: 550-443=107. Answer is E.
Answer: E
Question: Express a speed of 36 kmph in meters per second?
Options:
A)10 mps
B)18 mps
C)19 mps
D)17 mps
E)12 mps
Rationale: 36 * 5/18
= 10 mps
Answer:A
Answer: A
Question: If I walk at 3 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 10 minutes before the arrival of the bus. How far I walk to reach the bus stand ?
Options:
A)2.19 km
B)2.22 km
C)2.00 km
D)1.19 km
E)1.99 km
Rationale: d = product of speed difference of time /difference of speed
d = 3x6/60[12âˆ’(âˆ’10)/6-3]
[Here, â€“ve sign indicates before the schedule time]
â‡’ d = 2.19 km
Answer A
Answer: A
Question: Eight persons in an organization including A and B were to be divided in two groups of 4 members each. The total number of groups which not containing both A and B is what fraction of the total number of groups which can be formed?
Options:
A)1/4
B)1/70
C)3/14
D)1/10
E)11/14
Rationale: The fraction is nothing but the probability..
Number to choose 4 out of 8= 8C4..
Number to choose A and B and 2 from remaining 6=6C2..
prob of A and B choosen=6C2/8C4= {6!/4!2!}/{8!/4!4!}..
6!4!4!/8!4!2!=3/2*7=3/14
Answer = 1-3/14 = 11/14
Answer : E
Answer: E
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.5000 and B Rs.1000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Options:
A)1978
B)2707
C)7728
D)8160
E)7291
Rationale: 5000:1000 => 5:1
9600*10/100 = 960
9600 - 960 = 8640
8640*5/6 = 7200 + 960
= 8160
Answer: D
Answer: D
Question: A car moves at the speed of 80 km/hr. what is the speed of the car in metres per second?
Options:
A)2/8
B)2/9
C)2/6
D)2/4
E)2/3
Rationale: Answer: D
Explanation:Formula
For convert km/hr into m/sec multiply the speed with 5/18
For convert m/sec into km/hr multiply the speed with 18/5
80 × 5/18 ⇒ 2/2 × 2/9 m.sec.
Answer:B
Answer: B
Question: If a(a - 7) = 8 and b(b -7) = 8, where a ≠ b, then a + b =
Options:
A)−48
B)−2
C)2
D)7
E)48
Rationale: i.e. if a = -1 then b = 8
or if a = 8 then b = -1
But in each case a+b = -1+8 = 7
Answer: option D
Answer: D
Question: If the simple interest on a sum of a money for 1 years at 4% per annum is rs 70 what is the compound interest on the sum of the same rate and same time
Options:
A)$856.38
B)$752.36
C)$523.98
D)$1822.8
E)$523.65
Rationale: sum= 70*100/1*4=1750
amount=$(1750(1+4/100)^2)
=1700*26/25*26/25
=$1892.8
C.I=Rs.(1892.8-70)=$.1822.8
Answer (D)
Answer: D
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
Options:
A)7500
B)3388
C)2665
D)2888
E)2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer: A
Answer: A
Question: In how many ways the word "CALORIES" can be arranged?
Options:
A)40322
B)40320
C)45340
D)None
E)Cannot be determined
Rationale: Explanation :
The required number of ways = 8!
= 40320
Answer : B
Answer: B
Question: (0.15)(power 3) - (0.1)(power 3)/ (0.15)(power 2) + 0.015 + (0.1)(power 2) is:
Options:
A)0.68
B)0.08
C)0.05
D)0.06
E)None of them
Rationale: Given expression
= (0.15) (power 3) - (0.1)(power 3) / (0.15)(power 2) + (0.15 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.15 - 0.1)
= 0.05
Answer is C.
Answer: C
Question: In a certain pond, 55 fish were caught, tagged, and returned to the pond. A few days later, 55 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)625
C)1250
D)1528
E)10 000
Rationale: The percent of tagged fish in the second catch is 2/55*100 = 3.64%.
We are told that 3.64% approximates the percent of tagged fish in the pond. Since there are 55 tagged fish, then we have 0.036x = 55 --> x = 1,528.
Answer: D.
Answer: D
Question: A businessman earns $27800 in December, thus decreasing his average annual (January to December) earnings by $1200. His average annual earnings would be
Options:
A)$29000
B)$33500
C)$40200
D)$41000
E)$42300
Rationale: (x - 27,800)/11 - x/12 = 1,200
x = 492,000
x/12 = 41,000
Answer: D.
Answer: D
Question: How many kg of pure salt must be added to 30kg of 2% solution of salt and water to increase it to 10% solution ?
Options:
A)3/5
B)4/3
C)5/7
D)2/3
E)8/3
Rationale: Amount of salt in 30kg solution = [(20/100)*30]kg=0.6kg
Let x kg of pure salt be added
Then , (0.6+x)/(30+x)=10/100
60+100x=300+10x
90x=240
x=8/3.
Answer is E.
Answer: E
Question: A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 15 cm by 13 cm. The total number of bricks required is :
Options:
A)16000
B)18078
C)11076
D)11456
E)None of these
Rationale: Explanation:
Number of bricks =Courtyard area /1 brick area
=(1800Ã—1200 /15Ã—13)=11076
Option C
Answer: C
Question: Which one of the following numbers is exactly divisible by 11?
Options:
A)417269
B)315624
C)615624
D)715624
E)415624
Rationale: E
415624 is exactly divisible by 11.
Answer: E
Question: If a person walks at 25 km/hr instead of 10 km/hr, he would have walked 31 km more. The actual distance traveled by him is?
Options:
A)30
B)25
C)20.67
D)12.33
E)19.48
Rationale: Let the actual distance traveled is 'x' km
Then by given conditions, we have
x/10 = (x+31)/25
25x = 10x + 310
x = 20.67 km
Ans- C
Answer: C
Question: X, Y and Z invested Rs.3600, Rs.4800 and Rs.5400 respectively, in a partnership business. Find the share of X in profit of Rs.23000 after a year?
Options:
A)6300
B)6200
C)6100
D)6400
E)6000
Rationale: Explanation:
3600:4800:5400
6:8:9
6/23 * 23000 = 6000
E)
Answer: E
Question: A buffet consists of 5 main dishes and 4 side dishes. If a plate is created with 2 main dishes and 2 side dishes, in how many ways can the plates be formed?
Options:
A)36
B)60
C)66
D)180
E)575
Rationale: Choose 2 main dishes from 5 main dishes and 2 side dishes from 3 side dishes:
2C5 * 2C4 = 10*6 = 60
Ans: B
Answer: B
Question: 46080, 3840, 384, 48, 8, 2, ?
Options:
A)0.5
B)1
C)1.5
D)2
E)2.5
Rationale: 46080 ÷ 12 = 3840
3840 ÷ 10 = 384
384 ÷ 8 = 48
48 ÷ 6 = 8
8 ÷ 4 = 2
2 ÷ 2 = 1
Answer is B.
Answer: B
Question: A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.00. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?
Options:
A)$960
B)$1,350
C)$1,725
D)$2,100
E)$2,250
Rationale: Total Volume is 288000
Given LBH = 8*10*12.
the number of hats inside it = 288000/10 * 8 * 12 = 300.
price of each hat is 7.5 $ then total value is 300 * 7.0 = 2100.
IMO option D is correct answer..
Answer: D
Question: The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 12348 pi cubic centimeters, what is hte surface area of the balloon in square centimeters?
Options:
A)a. 40
B)b. 100
C)c. 400
D)d. 1,000
E)e. 5,000
Rationale: The surface area is 4.pi.r^2 (its area remember not volume)
as 4/3.pi.r^3=12348pi
r=21
so area = 4.pi.r^2= 1764.pi= 1764 x 3.14 = 5000 (approx)
E
Answer: E
Question: What is the range of all the roots of |x^2 - 6| = x ?
Options:
A)4
B)3
C)2
D)1
E)5
Rationale: we get 2 quadratic equations here ..
1) x^2-x-2=0 ....... roots 2 , -1
2) x^2+x-2=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=6 or x=1
I guess range is 6-1 =5
E
Answer: E
Question: Kailash loses 20% of his pocket money. After spending 25% of the remainder he has Rs 480 left. What was his pocket money?
Options:
A)Rs 600
B)Rs 800
C)Rs 900
D)Rs 1000
E)none of these
Rationale: Let A be the pocket money,
A ( 1 + x/100) ( 1 + y/100) = 480 (Given)
Here x = - 20, y = - 25
Therefore,
A( 1 - 20/100) ( 1 - 25/100) = 480
A = (480 x 100 x 100) / (80 x 75) = Rs 800
ANSWER:B
Answer: B
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
Options:
A)17 hrs
B)22 hrs
C)25 hrs
D)12 hrs
E)14 hrs
Rationale: The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer : A.
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)120 metres
B)180 metres
C)324 metres
D)228 metres
E)150 metres
Rationale: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 9	m = 150 m.
Option E
Answer: E
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 8th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
Options:
A)45
B)40
C)35
D)30
E)25
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
7th year : 6-7 (age), we take age = 6
8th year : 7-8 (age), we take age = 7
Thus for the 3rd year = 50,
4th year = 50 -3 = 47
5th year = 47-4 = 43
6th year = 43-5 = 38.
7th year =38-6 = 32
8th year =32-7 = 25
The correct answer is E.
Answer: E
Question: In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
Options:
A)1/5
B)1/25
C)2/5
D)3/5
E)Data inadequate
Rationale: Explanation:
A = 2B => B = 1/2 A, so, AB = 2/25
1/2 A2 = 2/25
A2 = 4/25
A = 2/5
ANSWER IS C
Answer: C