divelab/Sys2Bench huggingface dataset:
Question: A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so?
Options:
A)6 Â½ sec
B)6 Â½ sec
C)9 Â½ sec
D)8 sec
E)7 Â½ sec
Rationale: D
8 sec
D = 160
S = 72 * 5/18 = 20 mps
T = 160/20 = 8 sec
Answer: D
Question: Sarah invested $38,700 in an account that paid 6.2% annual interest, compounding monthly. She left the money in this account, collecting interest for three full years. Approximately how much interest did she earn in the last month of this period?
Options:
A)$239.47
B)$714.73
C)$2793.80
D)$7,888.83
E)$15,529.61
Rationale: 1% of 38700 is 387
6% is approximately 2400
At the end of first year, total amount = 38700+2400 = 41000 (approx)
At the end of second year, total amount = 41000+2400 (6% of 41000 works out to approximately the same) = 43400 (approx)
So total earnings for third year cannot be more than 6% of 43400 i.e at max $3000
So monthly earning has to be in the range of 250.
Answer is A
Answer: A
Question: There is a 35 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 35 cm, how many insects were still left after the race was over?
Options:
A)0
B)4
C)6
D)7
E)10
Rationale: Only the prime numbers greater than 10 and less than 35 were left.
That is 11, 13, 17, 19, 23, 29, and 31.
The total is 7.
The answer is D.
Answer: D
Question: If 4 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
Options:
A) 20
B) 24
C) 36
D) 40
E) 60
Rationale: Let the Capacity of the tank=C
(3/4)C + 4= (9/10)C
=>(9/10)C - (3/4)C = 4
=>(3/20)C = 4
=>C = (4*20)/3 = 26.66
Number of gallons of gasoline that the tank currently holds = 3/4*C +4 = 19.99+4 = 23.99=24
Answer B
Answer: B
Question: A man has Rs. 800 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)370
B)380
C)220
D)900
E)150
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 800 16x = 800 x = 50.
Hence, total number of notes = 3x = 150.
Answer:E
Answer: E
Question: Find the area of circle whose radius is 7m?
Options:
A)121 sq m
B)184 sq m
C)174 sq m
D)124 sq m
E)154 sq m
Rationale: the area of circle =pie* r^2
=22/7 * 7 * 7 = 154 sq m
ANSWER:E
Answer: E
Question: A man sold two similar houses each for Rs. 1,00,000 one at a gain of 20% and another at a loss of 20%. What is net gain or loss?
Options:
A)4%
B)6%
C)5%
D)3%
E)2%
Rationale: Explanation :
Solution: Here always net loss of (20/100)^2 % = 4%.
Answer : A
Answer: A
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 65000, then the share of B is?
Options:
A)A)30000
B)B)34000
C)C)34098
D)D)33007
E)E)44098
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 65000
Share of B = 6/13 (65000)
= Rs. 30000
Answer:A
Answer: A
Question: If 9 spiders make 9 webs in 9 days, then how many days are needed for 1 spider to make 1 web?
Options:
A)5 days
B)7 days
C)8 days
D)9 days
E)6 days
Rationale: Let, 1 spider make 1 web in a days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)9:1
}::a:9
(webs)1:9
⇒7×1×7=1×7×a
⇒a=7
ANSWER:B
Answer: B
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)145
B)180
C)181
D)184
E)150
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: Option B
Answer: B
Question: A group of 4 students bought movie tickets in one row next to each other. If Bob and Lia are in this group, what is the probability that Bob and Lia will each sit next to only one of the three other students from the group?
Options:
A)5.67%
B)16.67%
C)15.57%
D)20.25%
E)25.75%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 4!.
Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.
P=(favorable)/(total)=(2*2!)/4!=1/6.
Answer: B.
Answer: B
Question: X and Y start a business with Rs.3000 and Rs.6000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:1
B)2:1
C)1:2
D)1:3
E)1:4
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by X and Y =
3000 : 6000 => 1:2
Answer:C
Answer: C
Question: During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years?
Options:
A)60 percent decrease
B)20 percent decrease
C)20 percent increase
D)60 percent increase
E)140 percent increase
Rationale: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-80/100)=100*0.2=20 and in 2002 its value would be 20*(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%.
Answer: B.
Answer: B
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 6 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 4 kilograms of liquid, what percent of this new solution is liquid X?
Options:
A)33%
B)35 1/2%
C)37%
D)40%
E)42%
Rationale: In 8 kilograms of solution Y there are 0.3*6=1.8 kilograms of solution X;
After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 1.8 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 6 kilograms there are 1.8+0.6=2.4 kilograms of solution X, which is 2.4/6*100=40% of this new solution.
Answer: D.
Answer: D
Question: (51+ 52 + 53 + ... + 100) = ?
Options:
A)2525
B)2975
C)3225
D)3775
E)2753
Rationale: Explanation:
This is an A.P. in which a = 51, l = 100 and n = 50.
Sum =	n	(a + l)	=	50	x (51 + 100) = (25 x 151) = 3775.
2	2
Answer: D
Answer: D
Question: The cost to park a car in a certain parking garage is $10.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?
Options:
A) $1.09
B) $1.67
C) $2.225
D) $2.47
E) $2.50
Rationale: Total cost of parking for 10 hours = 10$ for the first 2 hours and then 1.75 for (9-2) hours = 10+7*1.75 = 22.25
Thus the AVERAGE parking price = 22.25/9 = 2.47 $
D is the correct answer.
Answer: D
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Options:
A)18
B)20
C)22
D)24
E)26
Rationale: Explanation:
x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer: B
Answer: B
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability u that the World Series will consist of fewer than 7 games?
Options:
A) 12.5%
B) 25%
C) 31.25%
D) 68.75%
E) 75%
Rationale: In order to determine the probability u that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Answer: D
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
Options:
A)1/38
B)1/36
C)1/37
D)1/39
E)1/32
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B
Answer: B
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)80 km/hr
B)66 km/hr
C)60 km/hr
D)67 km/hr
E)22 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/6 = 3x => x = 100/9
So, speed of the faster train = 200/9 = 200/9 * 18/5 = 80 km/hr.
Answer:A
Answer: A
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.83. How much was lent at 5%?
Options:
A)299
B)566
C)678
D)700
E)8277
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83
5x/100 + 90 – 6x/100 = 83
x/100 = 7
=> x =700
Answer:D
Answer: D
Question: The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 30 percent, then the value of T decreases by what percent?
Options:
A)25%
B)33 ¹/₃%
C)50%
D)66 ²/₃%
E)20%
Rationale: We can assign numbers:
lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)
Now increasing S by 30% gives S=5, K remains constant, so T = 2 (6/2=3)
decrease in T= 1, percent decrease in T = (1/5)*100 =20%
Answer E
Answer: E
Question: Arjun and Sajal are friends . each has some money. If Arun gives Rs. 30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives Rs. 10 to Arjun, the Arjun will have thrice as much as is left with Sajal. How much money does Arjun have?
Options:
A)62 Rs
B)63 Rs
C)64 Rs
D)72 Rs
E)68 Rs
Rationale: If arun had x rs , and sejal had y rs, then
2*(x-30) = y+30 or 2x-60= y+30 or y= 2x-90
and
x+10 = 3*(y-10)= 3*(2x-90-10)=6x-300
or
5x=310
x= 310/5 = 62 Rs with Arjun
ANSWER:A
Answer: A
Question: In a camp, there is a meal for 90 men or 180 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal ?
Options:
A)16
B)20
C)13
D)15
E)17
Rationale: Explanation :
There is a meal for 180 children. 150 children have taken the meal.
Remaining meal is to be catered to 30 children.
Now, 180 children = 90 men
So, 30 Children = (90/180) * 30 = 15 men
Answer : D
Answer: D
Question: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I.	x = z
II.	x > y > z
III. x > y
Options:
A)I and II
B)I only
C)II only
D)III only
E)None
Rationale: 3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
III correct.
We can't say much about z though;
x=-5; y=-100; z=-95
II and I incorrect.
Ans:D
Answer: D
Question: An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of
Options:
A)440
B)540
C)640
D)740
E)250
Rationale: Speed of aeroplane = 420 Kmph
Distance travelled in 6 hours
= 420 * 6 = 2520 Km
Speed of aeroplane to acver 2520 Km in 14/3
= 2520*3/14 = 540 Km
Answer B.
Answer: B
Question: A sum of Rs. 1190 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
Options:
A)Rs. 120
B)Rs. 210
C)Rs. 240
D)Rs. 300
E)None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 1190
=> 17x/12 = 1190
=> 1190 x 12/ 17 = Rs.840
Hence, B’s share = Rs. (840/4) = Rs. 210.
Answer B
Answer: B
Question: John bought 9.25m of cloth for $397.75. Find the cost price per metre.
Options:
A)46
B)47
C)58
D)56
E)43
Rationale: Cloth bought by John = 9.25 m
Cost of 9.25 m = $397.75
Cost per metre = 397.75 ÷ 9.25
The cost of the cloth per metre = $ 43
Answers: E
Answer: E
Question: Initially, the boys and girls in a classroom were in the ratio of 2:3. Then, 4 boys entered the room and 3 girls left the room. Then, the number of girls tripled. Now there are 24 boys in the room. How many girls are currently in the room?
Options:
A)12
B)40
C)15
D)34
E)81
Rationale: Working backwards: 24 boys - 4 boys = 20 boys in the room initially.
From ratio boys:girls = 2:3 = 1:3/2 we have:
girls in the room initially = (3/2)(20) = 30.
From this we work forward: (3)(30 girls - 3 girls) = 81 girls in the room.
Answer: E
Answer: E
Question: If six persons sit in a row, then the probability that three particular persons are always together is
Options:
A)1/20
B)3/10
C)1/5
D)4/5
E)2/5
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
ANSWER:C
Answer: C
Question: The average weight of 10 boys increases by 3.5 kg when a new boy comes in place of one of them weighing 50 kg. What might be the weight of the new boy?
Options:
A)85 kg
B)80 kg
C)75 kg
D)72 kg
E)65 kg
Rationale: Total weight increased = 10 x 3.5 kg = 35 kg.
Weight of new person = 50 + 35 kg =85 kg
Answer : A
Answer: A
Question: Ashly and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashly and Vinnie will be chosen?
Options:
A)1/10
B)3/28
C)2/9
D)1/4
E)1/2
Rationale: I did slightly different and hence obviously ended up with the answer 2/9.
I assumed that because Ashly and Winni have to be chosen, the remaining selection is 3 people from 8.
8C3/10C5= 2/9. Option C.
Answer: C
Question: If f(x) = 2*(x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?
Options:
A)f(x)
B)-2f(x)
C)1/f(x)
D)-1/f(x)
E)2*f(x)
Rationale: f(1/x) = ((1/x)^4 - 1) / ((1/x)^2)
= ((1/x^4) - 1) / (1/x^2)
= ((1-x^4)/(x^4)) / (1/x^2)
= (1-x^4)/(x^2)
= - 2( (x^4) -1) / (x^2)
= -2*f(x)
Answer is B.
Answer: B
Question: If x > 0, x/10 + x/25 is what percent of x?
Options:
A)6%
B)14%
C)37 1/2%
D)60%
E)75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/10 + 100/25= 10+4 =14
14 is 14% of 100=B
Answer: B
Question: I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 2 senior and 1 junior staff officers, how many possible committees are there?
Options:
A)12
B)44
C)56
D)60
E)200
Rationale: 6C2*4C1
=60 = D
Answer: D
Question: The present worth of Rs. 2310 due 2 years hence, the rate of interest being 15% per annum, is:
Options:
A)1689
B)1680
C)1682
D)1681
E)1686
Rationale: P.W. = Rs. 100 x 2310 = Rs. 1680.
100 + 15 x	5
2
Answer: B
Answer: B
Question: What is the minimum value of z for which z^2 + z - 3/10 > 0 is not true?
Options:
A) -5/2
B) -3/5
C) -1/5
D) 1/4
E) 1/5
Rationale: I think B -3/5 is the best ans...
Answer: B
Question: If k is an integer and 0.0010101 x 10^k is greater than 100, what is the least possible value of k?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 0.0010101 * 10^k > 100
We need to move the decimal point to the right 5 places to get 101.01
This is equivalent to multiplying by 10^5.
The answer is D.
Answer: D
Question: A fraction becomes 4 when 1 is added to both the numerator and denominator, and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is :
Options:
A)2
B)3
C)7
D)15
E)17
Rationale: Explanation:
Let the required fraction be a/b
Then a+1/b+1=4⇒a−4b=3
and a−1/b−1=7⇒a−7b=−6
Solving these equations we get,
a=15
b=3
Correct Option: D
Answer: D
Question: IF 2+3=31 ; 3+5=134 ; 5+7=368 Then 7+11=?
Options:
A)1250
B)1360
C)1270
D)1380
E)1290
Rationale: 2^2 + 3^3= 4 + 27 = 31
3^2 + 5^3= 9 + 125 = 134
5^2 + 7^3= 25 + 343 = 368
and
7^2 + 11^3= 49 + 1331 = 1380
ANSWER:D
Answer: D
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 700 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
A)511
B)546
C)552
D)562
E)570
Rationale: Number of newborns that can die in first month = 1/10 * 700 = 70
Survived = 630
Number of newborns that can die in second month = 1/10 * 630 = 63
Survived = 567
Number of newborns that can die in third month = 1/10 * 567 = 56
Survived = 511
Answer:A
Answer: A
Question: If 250!/10^n is an integer, what is the largest possible value of n?
Options:
A)65
B)66
C)62
D)69
E)97
Rationale: The question actually asks the highest power of 10 which divides 250! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
250 factorial will have 62 as -
250/5 = 50
50/5 = 10
10/5 =2
So answer will be (C) 62
Answer: C
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Options:
A)28 sec
B)36 sec
C)48 sec
D)52 sec
E)56 sec
Rationale: Relative speed = (60+ 90) km/hr
= 150x5/18
= 120/3 m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = 2000 x 3/125 = 48 sec.
Answer : C.
Answer: C
Question: Nobel played a cricket series. His 7 innings score as {50, 75, 90, 115 120, 135, 150 }, find the mean and median of cricket scores of Nobel respectively ?
Options:
A)105,115
B)100,120
C)143,90
D)115,105
E)100,130
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (50+ 75+ 90+ 115+ 120+ 135+ 150 )/7 = 105
Median = 115
Option A
Answer: A
Question: In how many different ways can the letters of the word 'BANANA' be arranged?
Options:
A)10 ways
B)120 ways
C)30 ways
D)60 ways
E)40 ways
Rationale: Totally there are 6 letters on the word BANANA. it contains 1B,3A,2N.
The no of ways is 6!/3!2!=120 ways.
ANSWER:B
Answer: B
Question: The average age of a group of people were 60 person aged 40 exits the group and average increases to 65. How many people were in the group initally?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Let n be the number of people in the group
the new average;
65=60n-40/(n-1) => 65n-65=60n-40 => 5n=25 => n=5
Answer: C
Answer: C
Question: What is the dividend. divisor 18, the quotient is 9 and the remainder is 5?
Options:
A)A)130
B)B)134
C)C)148
D)D)158
E)E)167
Rationale: D = d * Q + R
D = 18 * 9 + 5
D = 162 + 5
D = 167
Answer E
Answer: E
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A)2:9
B)2:7
C)1:6
D)1:4
E)1:3
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (4 - 3)/(10 - 4) = 1/6
So they should be mixed in the ratio 1:6
Answer - C
Answer: C
Question: At a circular table for eleven will sit nine adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the eleven people be arranged around the table.
Options:
A)12,720
B)16,120
C)20,160
D)24,240
E)28,080
Rationale: Consider the two parents and two children as one unit.
Then there are seven adults and one family unit.
The number of ways 8 can form a line is 8!
Around a circular table, there would be 8 rotations so we divide this number by 8.
There are 7! ways for 8 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 7!*2*2= 20,160
The answer is C.
Answer: C
Question: In a set of integers, one-half of the numbers are multiples of 7 and one-third of the numbers are multiples of 3. If one-fifth of the numbers are multiples of both 3 and 7, then what percentage of the number are multiples of 7 but not multiples of 21?
Options:
A)9
B)15
C)30
D)33.3
E)60
Rationale: Say there are 210 number in the set (LCM of 2, 3, 5, and 7).
Multiples of 7 = 1/2*210 = 105;
Multiples of both 3 and 7, so multiples of 21 = 1/5*210 = 42.
Multiples of 7 but not 21 = 105 - 42 = 63.
The percentage = 63/210 = 3/10.
Answer: C.
Answer: C
Question: If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)18
B)11.2
C)14
D)12
E)91
Rationale: 2 * 22/7 * 15 * x = 1056 => x
= 11.2
Answer: B
Answer: B
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
Options:
A)1/13
B)2/13
C)1/26
D)1/52
E)1/23
Rationale: Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26
ANSWER IS C
Answer: C
Question: if (64)^2 - (36)^2 = 10x, then x = ?
Options:
A)280
B)210
C)330
D)220
E)200
Rationale: a^2−b^2=(a−b)(a+b)
(64)^2 - (36)^2 = (64 - 36)(64 + 36) = 28 × 100
Given that (64)^2 - (36)^2 = 10x
=> 28 × 100 = 10x
=> x = 280
Answer is A
Answer: A
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 30 percent butterfat to obtain milk that is 20 percent butterfat?
Options:
A)6
B)8
C)14
D)16
E)28
Rationale: Equate the fat:
0.1x + 0.30*8 = 0.2(x + 8) --> x = 8.
Answer: B.
Answer: B
Question: If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
A)198
B)288
C)363
D)360
E)484
Rationale: I will go with D (pending elements to match is 2^2*3^2*10^1 = 360
Answer: D
Question: In how many different ways can 4 physics, 4 math, and 4 chemistry books be arranged in a row so that all books of the same subject are together?
Options:
A)76,366
B)78,488
C)80,122
D)82,944
E)84,500
Rationale: Let's think of each subject as a group so there are 3 groups.
The number of ways to arrange these 3 groups is 3!
Within each subject the books can be re-arranged.
So we need to multiply 3! by 4!*4!*4! which is 3!*4!*4!*4! = 82,944
The answer is D.
Answer: D
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:
Options:
A)A)3
B)B)98
C)C)34
D)D)35
E)E)62
Rationale: (3x-9):(5x-9) = 3:2
x = 1 => 3x = 3
Answer:A
Answer: A