divelab/Sys2Bench huggingface dataset:
Question: Ten coins are tossed simultaneously. In how many of the outcomes will the first coin turn up a head?
Options:
A)2^7
B)2^10
C)3 * 2^8
D)2^9
E)3 * 2^10
Rationale: Fix the third coin as H. The remaining 9 coins have 2^9 outcomes.
Ans:D
Answer: D
Question: Bill and Jane play a simple game involving two fair dice, each of which has six sides numbered from 1 to 6 (with an equal chance of landing on any side). Bill rolls the dice and his score is the total of the two dice. Jane then rolls the dice and her score is the total of her two dice. If Jane’s score is higher than Bill’s, she wins the game. What is the probability the Jane will win the game?
Options:
A)15/36
B)175/432
C)575/1296
D)583/1296
E)1/2
Rationale: There are three possible outcomes in the game:
1. B Wins
2. J Wins
3. Draw
So, 1=P(J)+P(B)+P(Draw)1=P(J)+P(B)+P(Draw)
The probability of B winning or J winning the game is same.
so, 1=2∗P(J)+P(Draw)1=2∗P(J)+P(Draw)
So, we need to calculate the probability of a draw.
A draw can happen when both will have the same sum.
The possible sums are - 2,3,4,5,6,7,8,9,10,11,12
Prob. of each sum is -
2 - 1,1 - 1/36
3 - 1 2, 2 1 - 2/36
4 - 1 3, 2 2, 3 1 - 3/36
5 - 1 4, 2 3, 3 2, 41 - 4/36
6 - 1 5, 2 4, 3 3, 4 2, 5 1 - 5/36
7 - 1 6, 2 5, 3 4, 4 3, 5 2, 61 - 6/36
8 - 2 6, 3 5, 4 4, 5 3, 6 2, - 5/36
9 - 3 6, 4 5, 5 4, 63 - 4/36
10 - 4 6, 5 5, 6 4 - 3/36
11 - 5 6, 6 5 - 2/36
12 - 6 6 - 1/36
Now, since both have to get the same sum, the probability will be same for both and the combined probability will be the square of the probabilities
i.e. 2 - (1/36)^2
3 - (2/36)^2
etc.
Squaring the probabilities and adding them will give 146/1296
So, P(D) = 146/1296
1 = 2*P(J) + P(D)
2*P(J) = 1150/1296
P(J) = 575 / 1296
Ans. C
Answer: C
Question: A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?
Options:
A)5
B)6
C)8
D)None of these
E)Cannot determined
Rationale: 7 + 4 + 0 + 3 + 1 + 5 + 1 + x = 26
21 + x = 26
x = 5 patrons have none of these animals
A)
Answer: A
Question: Two trains of equal are running on parallel lines in the same direction at 18 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)25
B)26
C)27
D)28
E)21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/18 = 25/9 => x = 25.
Answer: A
Answer: A
Question: The tax on a commodity is diminished by 10% and its consumption increased by 25%. The effect on revenue is?
Options:
A)12% decrease
B)18% decrease
C)19% decrease
D)13% decrease
E)12.5% increase
Rationale: 100 * 100 = 10000
90 * 125 = 11250
-----------
10000-----------1250
100-----------? => 12.5% decrease
Answer: E
Answer: E
Question: Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 2 times before stopping?
Options:
A)11/180
B)125/216
C)25/216
D)91/216
E)1/6
Rationale: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:
The probability that Molly will roll the die once: P=1/6 (she gets 1on the first roll)
P = 1/6
Answer: E
Answer: E
Question: Wendy begins sanding a kitchen floor by herself and works for 7 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
Options:
A)9/80 hours
B)3/20 hours
C)20/3 hours
D)80/9 hours
E)10 hours
Rationale: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 7 hours and is then joined by Bruce to finish the work in 2 more hours,
7/W + 2/W+2/B = 1 (1 denotes the total amount of work)
9/W + 2/B =1 and given B =20 hours.
Thus W = 10 hours , E is the correct answer.
Answer: E
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 7 hours. How long would it take Taimour to paint the fence alone?
Options:
A)6 hours
B)8 hours
C)14 hours
D)21 hours
E)32 hours
Rationale: I believe the answer is D. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 7 => 1/21
Working alone Taimour can do the job in 1 = 1/21 * hours => 21
Answer D
Answer: D
Question: A bat is bought for Rs.800 and sold at a gain of 20% find its selling price
Options:
A)Rs.920/-
B)Rs.950/-
C)Rs.860/-
D)Rs.960/-
E)None of these
Rationale: Explanation:
100 % ------> 800 (100 * 8 = 800)
120 % ------> 960 (120 * 8 = 960)
Selling price = Rs. 960/-
Answer: Option D
Answer: D
Question: A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
Options:
A)7 km
B)3 km
C)6 km
D)9 km
E)2 km
Rationale: Average speed = (2 * 3 * 2) / (3 + 2)
= 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school
= 12/2
= 6 km.
Answer: C
Answer: C
Question: If the mode of Set F is equal to the median of Set F, Set F could be
Options:
A)[0, 1, 2, 2, 3, 4, 5, 6]
B)[2, 2, 5, 7, 9]
C)[x, x+1, x+2, x+2, x+3, x+3]
D)[10, 102, 105, 105]
E)[4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]
Rationale: Correct Answer: (C)
Set F could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set C is equal to the median of set C.
Answer: C
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 2400. Their H.C.F is?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x = 2400
x = 40
The numbers are 3*40 , 4*40 , 5*40
Hence required H.C.F. = 40
Answer is C
Answer: C
Question: There are a total of 12 students in Mr. Sri's gym class. Over the course of a badminton unit, each of the 12 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
Options:
A)68
B)67
C)69
D)60
E)66
Rationale: there are 19 students , if each play with all other members .
then total games can be calculated as 11+10....+1 = 66.
alternate approach is to choose 2 distinct out of 12 = 12c2 = 66
Answer is E.
Answer: E
Question: Which of the following is the sum of all the even numbers between 1 and 97, inclusive?
Options:
A)2550
B)2450
C)2600
D)2449
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 4, 6, 8.....96.
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:
D
Answer: D
Question: An article is bought for Rs.900 and sold for Rs.1000, find the gain percent?
Options:
A)11 2/5%
B)11 2/9%
C)11 1/9%
D)11 2/3%
E)11 3/3%
Rationale: 900 ---- 100
100 ---- ? => 11 1/9%
Answer: C
Answer: C
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $5,100. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
Options:
A)1. $15,600
B)2. $15,750
C)3. $17,100
D)4. $18,100
E)5. $19,200
Rationale: Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 5,100, thus the highest price in June was 16,500+5,100=21,600.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 21,600, thus the range for May-June is 21,600-4,500=17,100.
Answer: C.
Answer: C
Question: A tour group of 25 people paid a total of $945 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
Options:
A)$22
B)$23.94
C)$36
D)$25.20
E)$30
Rationale: Soln:-
945/25=x+0.05x
945/25=1.05x
x=36
ANSWER:C
Answer: C
Question: A parking garage rents parking spaces for $10 per week or $40 per month. How much does a person save in a year by renting by the month rather than by the week?
Options:
A) $140
B) $160
C) $220
D) $40
E) $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 40 = 480$
520 - 480 = 40
Ans D
Answer: D
Question: Which of the following fractions W has a decimal equivalent that is a terminating decimal?
Options:
A)10/189
B)15/196
C)16/225
D)25/144
E)39/128
Rationale: The fraction W will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference?
Options:
A)9 feet
B)12 feet
C)13 feet
D)15 feet
E)18 feet
Rationale: total circuit=12/4=3
total feet squirrel travels=3*3=9 feet
ANSWER:A
Answer: A
Question: James and David work at a grocery shop with 12 other workers. For an internal review, 2 of the 12 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen?
Options:
A)1/26
B)1/36
C)1/46
D)1/66
E)1/56
Rationale: Probability that James and David will both be chosen out of 12 workers
= (2/12)*(1/11)
= 1/66
Answer D
Answer: D
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)149
C)148
D)17
E)143
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: A
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $7 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Options:
A)8n + 2
B)8n + 4
C)9n + 2
D)9n + 3
E)9n + 6
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [7+ (n-1)]
= $ n+6
total cost
8n+n+6 = 9n+6
E
Answer: E
Question: What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle.
Options:
A)1 : 2
B)2 : 1
C)3 : 1
D)Data inadequate
E)None of these
Rationale: Area of ΔEBC = 1⁄2 × BC × EF
= 1⁄2 × BC × AB[Since, EF = AB]
Area of ΔEBC = 1⁄2 × area of ΔABCD
\ Required ratio = 2 : 1.
Answer B
Answer: B
Question: Winners will be announced the following day at 12 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?
Options:
A)13
B)21
C)23
D)24
E)25
Rationale: The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. Thus wrong
C) is the correct answer because Y>xwill give 5 digit numbermiddle digit is Y
E
Answer: E
Question: The cost price of a radio is Rs.2300 and it was sold for Rs.1800, find the loss %?
Options:
A)18
B)99
C)27
D)26
E)21
Rationale: 2300 ---- 500
100 ---- ? => 21%
Answer: E
Answer: E
Question: The mean of 20 observations was 36. It was found later that an observation 25 was wrongly taken as 40. The corrected new mean is
Options:
A)30
B)25.4
C)40
D)35.25
E)26.55
Rationale: Explanation:
Correct Sum = (36 * 20 + 25 - 40) = 705
Correct mean = = 705/20 = 35.25
Answer: D
Answer: D
Question: For integers x and y, if (x+2)(y+3) is even then 4xy must be divisible by:
Options:
A)4
B)8
C)9
D)10
E)12
Rationale: Just looking at the question, (x+2)(y+3) could be even*even, odd*even, or even*odd in order for the whole expression to be even.
However, just looking at 4xy, since x*y will always be an integer, it will always be divisible by 4. 4 divided by 4 is 1, hence preserving x*y.
Answer: A. 4
Answer: A
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)12 sec
B)30 sec
C)36 sec
D)16 sec
E)18 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50
= 36 sec.
Answer: C
Answer: C
Question: It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
Options:
A)142
B)144
C)3680
D)3280
E)3680
Rationale: Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th .
Now, number of even places = 3.
Number of girls to occupy the even places = 3.
Even places can be filled = P (3, 3) ways.
Number of boys = 4.
The remaining 4 places can be filled by 4 boys = P (4, 4) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144
ANSWER:B
Answer: B
Question: Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores 1/4, what is the value of Y/X ?
Options:
A)3.
B)2.
C)1/5
D)1/3.
E)There isn't enough data to answer the question.
Rationale: Answer is C : 1/5
X - Y = (X + Y)/4
Solving for Y/X = 1/5
Answer: C
Question: A bowl was filled with 10 ounces of water, and 0.010 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
Options:
A)0.004%
B)0.04%
C)0.40%
D)5%
E)40%
Rationale: Total amount of water evaporated each day during a 50-day period = .008 * 50
=.010 * 100/2
= 1.0/2
= .5
percent of the original amount of water evaporated during this period = (.5/10) * 100%
= 5 %
Answer D
Answer: D
Question: The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: Sol.
Let the numbers be x, x + 2 and x + 4.
Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
Answer C
Answer: C
Question: If cyclist is covering a circular distance of diameter 15 inches at the speed of x inches/min, and another cyclist is covering a circular distance of diameter 25 inches at the speed of y inches/min then what is the value of y in terms of x if both the cyclists cover the distance at the same time?
Options:
A)2x/4
B)6x/2
C)7x/3
D)5x/3
E)4x/3
Rationale: t=S1/V1=S2/V2
or 15/x=25/y
or y=25x/15=5x/3
Answer is D
Answer: D
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Options:
A)6:6
B)6:9
C)6:5
D)6:2
E)6:1
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer:C
Answer: C
Question: Zeeshan having a certain number of one rupee,fifty paise and twenty
five paise coins are in the ratio of 3:2:4, add up to
Rs 75. Then how many 1 rupee coins he have?
Options:
A)10
B)20
C)45
D)128
E)49
Rationale: Explanation :
Given ratio = 3:2:4.
Let us assume that there are 3 one rupee coins,2
fifty paise coins and 4 twenty-five paise coins in all.
Their value=(3*1)+(2*.50)+(4*.25)=3+1+1=Rs 5
If the total is Rs 5, number of 1 rupee coins are 3.
If the total is Rs 75, number of 1 rupee coins would be 75*3/5=45.
Answer : C
Answer: C
Question: Yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2.
Also both the needles lie on top of each other.
What time i and talking about ?
Options:
A)10:00
B)11:00
C)09:00
D)12:00
E)07:00
Rationale: D
12:00
both minute and hour clock lie exactly between the number one and two in the number.
Answer: D
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent is 5time of years , then the Time is:
Options:
A)6 1/2 years.
B)5 1/2 years.
C)4 1/2 years.
D)2 1/2 years.
E)3 1/2 years.
Rationale: Explanation :
Let sum = x. Then, S.I. = x/4
Let Time =N and R = 4 N.
[x * N * 4N / 100] = x / 4? N^2 = 25/4
N = 5/2 = 2 1/2 years.
Hence,n = 2 1/2 years.
Answer : D
Answer: D
Question: If m is a positive integer, and m/15 = 8.2, what is the remainder Y when m is divided by 15?
Options:
A)A.1
B)B.2
C)C.3
D)D.4
E)E.8
Rationale: If m were a multiple of 15, the quotient m/15 would be an integer. The fact that it's a decimal tells us that 15 goes into m eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let Y be the remainder.
Y/15 = 0.2 = 1/5
Y = (15)*(1/5) = 3
Answer =(C)
Answer: C
Question: The sum of two number is 25 and their difference is 13. Find their product.
Options:
A)114
B)104
C)315
D)350
E)400
Rationale: Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x + y)2 - (x- y)2=(25)2 - (13)2
= (625 - 169) = = 456 =>114
ANSWER A
Answer: A
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 6 questions. If each question has 5 answer choices, and Kim answers every question, in how many different ways can she complete the test?
Options:
A)a 40
B)b 400
C)c 5^8
D)d 5^6
E)e 40^40
Rationale: different ways to solve each question is 5.
So, 5*5*5*5.. 6 times ----> 5^6
Answer will be D.
Answer: D
Question: In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
Options:
A)33
B)28
C)76
D)54
E)912
Rationale: Explanation:
Let R, G and B represent the number of balls in red, green and blue boxes respectively.
Then,
R + G + B = 108 ...(i),
G + R = 2B ...(ii)
B = 2R ...(iii)
From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.
Putting G = 3R and B = 2R in (i), we get:
R + 3R + 2R = 108 {\color{Blue} \Rightarrow } 6R = 108 {\color{Blue} \Rightarrow } R = 18.
Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.
Answer: D
Answer: D
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
Options:
A)3/7
B)4/7
C)5/7
D)5/9
E)5/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
B)
Answer: B
Question: a man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream.
Options:
A)2 km/hr
B)3 km/hr
C)7 km/hr
D)9 km/hr
E)5 km/hr
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=18 or x=9.
Rate upstream=9 km/hr,rate downstream=27 km/hr.
Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.
ANSWER D
Answer: D
Question: A 60 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)35
B)20
C)17
D)36
E)30
Rationale: 1: 2/5 = 5: 2
2/7 * 60 =17
Answer:C
Answer: C
Question: Twelve contestants at the county fair have entered their cakes to be judged in the cake decorating competition. A purple ribbon, blue ribbon, red ribbon, and white ribbon will be given to the first, second, third, and fourth place competitors, respectively. How many different ways are there to award the four ribbons to the contestants?
Options:
A)8!/(4!*4!)
B)12!/(8!*4!)
C)8!/4!
D)12!/8!
E)12!/4!
Rationale: Number of ways you can select 4 people out of 12 = 12C4
Once you select the 4 people, you have the following arrangement, PBRW (PBRW being the 4 prizes) but the same group of people can also be chosen against BRWP etc. Thus you get 4! ways of arranging 4 prizes.
Thus total possible ways = 12C4*4! = 12!/8!. D is the correct answer.
Answer: D
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 30% of the previous term. What is the value range of the five numbers?
Options:
A)9,375
B)9,750
C)9,919
D)9,984
E)10,736
Rationale: 1st number= 10,000
2nd number =30% of 10,000= 3000
3rd number= 30% of 3000= 900
4th number = 30% of 900= 270
5th number= 30% of 270= 81
Range = 10,000-81= 9919
C is the answer
Answer: C
Question: If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT
Options:
A)30x.
B)15y.
C)15(x + y).
D)15(x - y).
E)15,000.
Rationale: If x=1 and y=1, then 30 x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.
ANSWER:C
Answer: C
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Options:
A)13.8 sec
B)13.2 sec
C)18.9 sec
D)16.8 sec
E)12.9 sec
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer: D
Answer: D
Question: There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 28 possible combinations in which Jim and Ellen are not selected, what is the value of k?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: There are k-2 members in the band, and k-4 members without Jim and Ellen.
(k-4)C2 = 28
(k-4)(k-5)/2 = 28
(k-4)(k-5) = 56 = 8*7
k = 12
The answer is E.
Answer: E
Question: If 2x + y = 4 and x + 2y = 5, then (x + y)/3 =
Options:
A) 1
B) 4/3
C) 17/5
D) 18/5
E) 4
Rationale: We have two equations:
2x + y = 4
x + 2y = 5
Notice that something nice happens when we ADD them. We get:
3x + 3y = 9
Divide both sides by 3 to get:x + y = 3
So, (x + y)/3 =3/3=1
Answer: A
Answer: A