divelab/Sys2Bench huggingface dataset:
Question: What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?
Options:
A)228
B)630
C)998
D)267
E)212
Rationale: L.C.M of 12, 18, 21, 30
= 2 * 3 * 2 * 3 * 7 * 5 = 1260
Required number = 1260/2 = 630.
Answer:B
Answer: B
Question: a,b,c,d,e sitting in a row what is the probability that a & b sitting adjacent.
Options:
A)1/5
B)2/5
C)3/5
D)4/5
E)6/5
Rationale: total number of arrangement is= 5!= 120
Favorable event i.e a and b can be arranged in 2! and the remaining can be arranged in 4! since ab can be in any of the four positions.
so 4!*2!/5! = 2/5
ANSWER:B
Answer: B
Question: Solve the equation 2 – x = 2b – 2ax, where a and b are real parameters. Find for which values of a the equation has for solution a natural number, if b = 7
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Solution:
We write the given equation like this (2a - 1)x = 2(b - 1)
The following cases are possible:
If 2a - 1 ≠ 0, i.e. a ≠ 1/2, the equation has single solution
x = 2(b - 1)/(2a - 1)
If a = 1/2 and b = 1, the equation gets the kind 0.x = 0 and every x is solution
If a = 1/2 and b ≠ 1, we get 0.x = 2(b - 1), where 2(b - 1) ≠ 0
In this case the equation has no solution.
If b = 7 and a ≠ 1/2 the single solution is
x = 2(7 - 1)/(2a - 1) = 12/(2a - 1)
If a is whole number, then 2a - 1 is also whole number and the solution
x = 12/(2a - 1) is natural number when
2a - 1 is positive divisor of 12.
To have a as whole number, the divisor of 12 mu be odd.But the only whole positive odd numbers divisible by 12 are 1 and 3.
Therefore 2a - 1 = 3 <=> a = 2 or 2a - 1 = 1 <=>
a = 1 a = 2 or 2a - 1 = 1 <=> a = 1
Answer B
Answer: B
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
Options:
A)25/42
B)25/49
C)25/46
D)25/48
E)35/49
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer:A
Answer: A
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
A)18 days
B)12 days
C)24 days
D)10 days
E)15 days
Rationale: Explanation:
8/12 + 6/x = 1
X = 18 days
Answer: A
Answer: A
Question: Which of the following is the sum of all the even numbers between 3 and 99, inclusive?
Options:
A)2550
B)2449
C)2600
D)2499
E)2652
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98.
If you take the next smallest and next biggest numbers, you have...
4+96 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-1 = 2449
Final Answer:
B
Answer: B
Question: If Tim had lunch at $50.20 and he gave 20% tip, how much did he spend?
Options:
A)$30.60
B)$60.60
C)$70.60
D)$40.60
E)$60.24
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 50.20 = (20/100)*50.20 = $10.04
Total spent
50.20 + 10.04 = $60.24
correct answer E
Answer: E
Question: Before 5 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
Options:
A)36
B)42
C)58
D)60
E)64
Rationale: A - 5 = 4(B - 5) --> A - 4B = -15.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 23 --> A =3(27)=81
A - B = 81 - 23 = 58
Answer: C
Answer: C
Question: when x is diveded by 299 remainder is 100. then when x is divided by 23 remainder is ?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 299+100=399=>x
399/23 gives a remainder of 8
ANSWER:E
Answer: E
Question: Edward has $732,391 dollars in his savings account. What is the least amount of money (in whole number of dollars) that he must add from his account if he wants to split this money evenly among his nine children?
Options:
A)$1
B)$2
C)$3
D)$4
E)$5
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 732,391 = 25 and 27 is divisible by 9.
Hence we need to add 2 to this number for it to be divisible by 9
Correct Option: B
Answer: B
Question: In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
Options:
A)7
B)6
C)9
D)4
E)8
Rationale: A
7
Add 7 + 10 + 4 to get 21.
Then subtract 21 from the total students ⇒ 28 – 21 = 7.
Answer: A
Question: What will be the reminder when (43^43+43) is divided by 44?
Options:
A)32
B)42
C)83
D)71
E)92
Rationale: (x^n+1) will be divisible by (x+1) only when n is odd;
(43^43+1) will be divisible by (43+1);
(43^43+1)+42 when divided by 44 will give 42 as remainder.
Correct Option : B
Answer: B
Question: An article is bought for Rs.680 and sold for Rs.900, find the gain percent?
Options:
A)33 1/8%
B)33 8/3%
C)33 1/3%
D)32 6/17%
E)32 1/3%
Rationale: 680---- 220
100 ---- ? => 32 6/17%
Answer: D
Answer: D
Question: A box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good?
Options:
A)3/7
B)17/35
C)19/35
D)16/35
E)18/35
Rationale: Required probability = (4C2 . 4C2)/8C4 = (6 * 6)/70
= 18/35
Answer:E
Answer: E
Question: Skier Lindsey Vonn completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. She then rides a chairlift back up the mountain the same distance at an average speed of (x - 8) meters per second. If the ride up the mountain took 135 seconds longer than her run down the mountain, what was her average speed, in meters per second, during her downhill run?
Options:
A) 10
B) 15
C) 20
D) 25
E) 30
Rationale: Backsolving is the preferred approach for this one
300/(x-8) - 300/(x+10) = 135
We are asked for the value of x+10
So we can start with C = X+10 = 20
So x = 10
300/2 - 300 / 20 = 135
Hence answer is C
Answer: C
Question: At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
Options:
A)$5,280
B)$11,200
C)$12,000
D)$12,800
E)$13,200
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000)
= 60720
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 60720 = 5280
Hence, A.
Answer: A
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction.
Options:
A)1/12
B)1/8
C)1/6
D)1/4
E)1/5
Rationale: Explanation:
X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
ANSWER IS A
Answer: A
Question: Fred and Frank are partners in a business. Frank runs the business and for this he gets 7% of the profit , and the rest is divided in proportion to their capitals. If Frank invested 15000 and Fred invested 35000, find the share of Frank in a profit of 10000.
Options:
A)1166.7
B)2266.7
C)2766.7
D)2466.7
E)6766.7
Rationale: The amount Frank gets for managing
= 7% of Rs. 10000 = 700
Remaining profit = 10000 â€“ 700 = 9300
This is to be divided in the ratio 10000:35000=10: 35=2:7
Share of Frank = 2/9 of 9300 = 2066.7
â‡’ Total share of Frank = 700 + 2066.7 = 2766.7.
Answer C
Answer: C
Question: Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ?
Options:
A)47.6
B)48.6
C)49.6
D)50.6
E)51.6
Rationale: Given ratio is 7:6;
let weight before and after reduction be 7x and 6x respectively.
A/Q
7x=56.7
=> x=56.7/7
=> x= 8.1
Reduced weight= 6x= 6*8.1= 48.6;
hence reduced weight= 48.6
ANSWER:B
Answer: B
Question: Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 13 years older than Larry, how old is Annie?
Options:
A)6
B)8
C)19
D)26
E)34
Rationale: J = L+13
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+18
Let's subtract equation (1) from equation (2)
A+9 = 15
A = 6
The answer is A.
Answer: A
Question: The sum of all two digit numbers divisible by 8 is
Options:
A)910
B)510
C)611
D)616
E)810
Rationale: Required numbers are 16,24 . . . . . 96
This is an A.P. in which a=16,d=8 and l=96.
Let the number of terms in it be n.Then t=96
So a+(n-1)d=96.
16+(n-1)*8=96
16+8n-8=96
8+8n=96
8n=96-8
n = 88/8
then n=11.
Required sum
=n/2(a+l)
=11/2(16+96)
=616
Answer is D
Answer: D
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $240 million, which represented 12 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
Options:
A)2,010
B)2,000
C)2,890
D)2,701
E)2,100
Rationale: 12% ---- 240 millions
for 100% => ( 240 * 100% )/12% = 2000.
Option B.
Answer: B
Question: I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?
Options:
A)800
B)700
C)900
D)1000
E)750
Rationale: Let x be the number I chose, then
x5−154=6
x5=160
x=800.
So answer is A.
Answer: A
Question: For positive integer x, if the sum of all the digit of x is 170 where x and y are positive integers and x=1020-y, which of the following can be the value of y?
Options:
A)41
B)47
C)50
D)55
E)60
Rationale: ->10^20-y=99999….9( )[ ] is derived.
In this case, the number of the first digits of 9 is 18, which is 9*18=162.
Also, the sum of all digits is 170.
That is, it should be ( )+[ ]=170-162=8.
Then, one should be selected amongst y=29,38,47,56,6,5,74,83,92.
Since 47 is in the option, the answer is B.
Answer: B
Question: Today Mary’s father is four times as old as Mary. Eight years ago, he was 12 times as old. How old is Mary today?
Options:
A)6
B)7
C)10
D)11
E)15
Rationale: Dad's age = 4M
12*(M-8) = 4M-8
8M = 88
M = 11
The answer is D.
Answer: D
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
Options:
A)81000
B)29899
C)26798
D)27799
E)27781
Rationale: 64000* 9/8 * 9/8 = 81000.Answer: A
Answer: A
Question: 4,64,256,1024,...?
Options:
A)1096
B)2096
C)3096
D)4096
E)5096
Rationale: 4
4*16=64
4*64=256
4*256=1024
4*1024=4096
ANSWER:D
Answer: D
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%?
Options:
A)600
B)2998
C)277
D)500
E)271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 84
5x/100 + 90 – 6x/100 = 84
x/100 = 6
=> x = 600.Answer: A
Answer: A
Question: A computer manufacturer produces a certain electronic component at a cost of $150 per component. Shipping costs for delivering the components are $1 per unit. Further, the manufacturer has costs of $19,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)199
B)249
C)233
D)215
E)229
Rationale: $19500 is a fixed cost
Each component is $151 ($150 to produce, $1 to ship)
Manufacturer will be producing and selling 250 components
so therefore the equation to find price would be
250*p = 19500+(250*150)+(250*1)
p = (19500+37500+250)/250
p = 229
Answer: E
Answer: E
Question: Given a two-digit number, the unit's digit exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 90, which of the options is the number?
Options:
A)26
B)15
C)37
D)62
E)73
Rationale: Using the elimination method the option that fits this description is 15
5-1 = 4 (unit's digit that exceeds its ten's digit by 4)
15*6 = 90 (the product of the given number and the sum of its digits is equal to 175)
answer :B
Answer: B
Question: 18 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)8 days
B)6 days
C)7 days
D)9 days
E)1 days
Rationale: 1 women's 1 day work = 1/126
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/126+ 10/140) = 1/9
5 women and 10 children will complete the work in 9 days.
Answer: D
Answer: D
Question: The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?
I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as GCF.
Options:
A)only
B)option II only
C)and III only
D)and II only
E)I and III only
Rationale: Consider the following set: {2, 4, 8}.
GCF = 2.
LCM = 8 = 4*2.
The set discards options I and II. Only B fits.
Answer: B.
Answer: B
Question: In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the the maximum and minimum possible average weight overall?
Options:
A)2.8 kgs
B)3.2 kgs
C)3 kgs
D)4 kgs
E)2 kgs
Rationale: DETAILED SOLUTION
If there are an odd number of terms, say, 2n + 1, then the median is the middle term. And if average is lesser than the middle term, there will at least be n + 1 terms greater than the average. So, there will be more terms above the average than below it.
However, this need not be the case when there are an even number of terms. When there are 2n distinct terms, n of them will be greater than the median and n will be lesser than the median. The average of these two terms can be such that there are n terms above the average and n below it.
For instance, if the numbers are 0, 1, 7, 7.5. The median is 4, average is 3.875. Average is less than the median. And there are more 2 numbers above the average and 2 below the average.
Correct Answer: Median is 4, average is 3.875.
Correct Answer: D
Answer: D
Question: A library has an average of 1000 visitors on Sundays and 700 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
Options:
A)740
B)750
C)760
D)770
E)775
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (1000 * 5 + 700 * 25) / 30 = 22500/30 = 750
Answer: B) 750
Answer: B
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after 3 months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options:
A)4 : 9 : 8
B)5 : 7 : 4
C)6 : 10 : 7.5
D)7 : 9: 4
E)5 : 4 : 8
Rationale: Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 9) = 36 : 60 : 45
= 6 : 10 : 7.5.
ANSWER :C
Answer: C
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are?
Options:
A)450
B)300
C)500
D)610
E)175
Rationale: Let the maximum marks be x
Then, 33% of x = 125+40
33x/100 = 165
x = 500
Answer is C
Answer: C
Question: A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 10 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
Options:
A)1/4
B)7/12
C)2/3
D)7/27
E)8/7
Rationale: Let' take the Number of geese to be 100.
Male = 30. Female = 70.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 10% are male i.e 10/100 *20 = 2 Geese (Males)
And now we know out of the total 20 geese , 2 are male , then 18 have to be female.
Now the ratio part , Male Geese Ratios = 2/30 = 1/15. - A
Female Geese Ratios =18/70=9/35 - B
Cross Multiply Equations A and B and you get = 7/27.
Ans D
Answer: D
Question: If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?
Options:
A)45
B)67
C)75
D)83
E)150
Rationale: We are told that 15 percent discount from the original price is more than $10:
0.15*{price} > 10;
{price} > 1,000/15;
{price} > 66 2/3.
Answer: B.
Answer: B
Question: If the average marks of three batches of 45, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
Options:
A)53.33
B)54.68
C)55
D)57
E)None
Rationale: Sol.
Required average = [55x50 + 60x55 + 45x60 / 45 + 60 + 45]
= [2250 + 3300 + 2700 / 150]
= 8250 / 150 = 55
Answer C
Answer: C
Question: Raj has bought the product and sold it for a profit of Rs.30. His cost of buying and selling is in the ratio of 8:9 respectively. How much did Raj spent for buying A?
Options:
A)200
B)240
C)250
D)270
E)300
Rationale: Let cost of buying of product A be x, (x+30/x)=9/8
Up on cross multiplication and solving for x, we get x=240
Answer: B
Answer: B
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
Options:
A)1/14
B)1/7
C)2/7
D)3/7
E)1/2
Rationale: P=Favorable outcomes / Total # of outcomes
Favorable outcomes: 2 women and 2 men = C^2/5∗C^2/3=30
Total # of outcomes: 4 people out of 5+3=8 = C^4/8=70
P=30/70=3/7
Answer: D.
Answer: D
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 100 worth of diesel fuel?
Options:
A)20 seconds
B)2 minute 5 seconds
C)1 minute 20 seconds
D)20 minutes
E)1 hour 20 minutes
Rationale: 2 gal / 5 sec
$2 / gal
$100/$2 = 502 gal
2 gal / 5 sec with 50 gal = 125 sec
B. 2 minute 5 seconds
Answer: B
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.36 per ounce, what is the share of Arabica in this blend?
Options:
A)20%
B)24%
C)30%
D)33%
E)60%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.4a + .3(1-a) = .36
.4a + .3 - .3a = .36
a= .6
therefore: .6/1 ounce = 60%. Therefore, the answer should be E
Answer: E
Question: Which one of the fractions has the highest value?
Options:
A)A)23/77
B)B)23/78
C)C)23/84
D)D)23/87
E)E)23/25
Rationale: 23/25
Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.
Answer (E).
Answer: E
Question: If a is an odd integer and b is an odd integer which of the following must not be an odd integer :
Options:
A)a/b
B)ab
C)2a+b
D)2(a+b)
E)3a/b
Rationale: only when two odd number added then we get even number.
Therefore answer is D
Answer: D
Question: Jane started baby-sitting when she was 16 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Check two extreme cases:
Jane = 16, child = 8, years ago = 32-16 = 16 --> child's age now = 8+16 = 24;
Jane = 22, child = 11, years ago = 32-22 = 10 --> child's age now = 11+10 = 21.
Answer: E.
Answer: E
Question: A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction.In how much time will the train pass the jogger?
Options:
A)3.6 sec
B)18 sec
C)36 sec
D)72 sec
E)none
Rationale: speed of the train relative to jogger = (45-9)km/hr=36km/hr.
(36*5/8)m/sec.
10m/sec.
Distance to be covered = (240 + 120) m = 360 m.
time taken =(360/10)sec=36sec.
Answer: C
Answer: C
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
Options:
A)1/3.
B)1/2.
C)2.
D)3.
E)6.
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 21 and L be 7, 21- 7= (21 + 7 )/2
D
Answer: D
Question: Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 60 films, and broke even on none of them, how many of their films were profitable?
Options:
A)18
B)19
C)20
D)21
E)59
Rationale: After fiddling some more, this is how I got to answer choice E...but did I get here using voodoo math or is it sound?
(.60*.75) + (.40*.25) = .44 + .10 = .55
55/100 = 11/20
Then subtract from 60:
60 - 11/20 = 59 (answer E)
Answer: E
Question: 10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
Options:
A)144
B)131
C)115
D)90
E)45
Rationale: there are 10 business exec and in each handshake 2 business execs are involved.
hence 10C2=45
Also, each of 10 exec will shake hand with every 7 other chairmen for total of 70 handshake.
total=45+70=115
ANS: C
Answer: C
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 97 Θ (33 Θ 17)) ?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: (( 90 Θ 33 ) Θ 17 )
The remainder of 90 divided by 33 is 24;
The remainder of 24 divided by 17 is 7;
( 97 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 97 divided by 16 is 1.
7 - 1 = 6.
Answer: D.
Answer: D
Question: Two trains A and B are 150 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Options:
A)10 s
B)6 s
C)4 s
D)8 s
E)12 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 150 + 150 = 300 m. Time taken = 300/25 = 12 s.
CORRECT ANSWER E.
Answer: E
Question: At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
Options:
A)16 4/19
B)16 4/18
C)16 4/10
D)16 4/11
E)16 4/14
Rationale: Formula : θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|
Here angle is 0. So
11/2 m – 30 h = 0
11/2 m – 30 × 3 = 0
m = 180/11
= 16 4/11
Ans:: D
Answer: D