mathewhe/aqua_rat huggingface dataset:
Question: A train covers a distance of 12 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
(A) 100
(B) 110
(C) 200
(D) 130
(E) 140
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 10 = 200 m.
Answer: Option C
Answer: (C) 200
Question: A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area Q covered by the two roads?
(A) 400
(B) 1550
(C) 1575
(D) 1600
(E) 1625
Rationale: Area Covered by Road Along the Length = 5*200 = 1000 Square Meter
Area Covered by Road Along the Width = 5*120 = 600 Square Meter
Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25
Total Area of the Roads Q= 1000+600-25 = 1575
Answer: option C
Answer: (C) 1575
Question: One year ago, Mrs Promila was four times as old as her daughter Swati. Six year hence,Mrs. Promila’s age will exceed her daughter’s age by 9 years. The ratio of the present ages of Promila and her daughter is
(A) 9:2
(B) 11:3
(C) 12:5
(D) 13:4
(E) None of these
Rationale: Let Swati’s age 1 year ago = x
Then Promila’s age 1 year ago = 4x
Then, (4x + 6) - (x + 6) = 9
=> 3x = 9
=>x = 3
Present age of Promila
= (12 + 1) years =13 years
Present age of Swati
=(3 + 1)years
= 4 years
Thus, Ratio of their ages
= 13:4
ANSWER:D
Answer: (D) 13:4
Question: If abc^2 = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1
(A) I
(B) II
(C) none
(D) III
(E) I&II
Rationale: C
Answer: (C) none
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 8 cm. What is the length of the wire?
(A) 16 cm
(B) 24 cm
(C) 28 cm
(D) 36 cm
(E) 39 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(8)^2 * h = (4/3)π (12)^3 => h
= 36 cm
Answer:D
Answer: (D) 36 cm
Question: A man rows his boat 90 km downstream and 70 km upstream, taking 3 hours each time. Find the speed of the stream?
(A) 76 kmph
(B) 6 kmph
(C) 3.5 kmph
(D) 4.5 kmph
(E) 4 kmph
Rationale: Speed downstream = d/t = 90/(3)
= 30 kmph
Speed upstream = d/t = 70/(3)
= 23 kmph
The speed of the stream = (30 - 23)/2
= 3.5 kmph
Answer:C
Answer: (C) 3.5 kmph
Question: Claire has a total of 86 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
(A) 39
(B) 50
(C) 60
(D) 54
(E) 60
Rationale: G+H =86 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =86-H OR 3(86-H) +4H =300 H = 300-258 =42 THEN G= 96-42 =54
D
Answer: (D) 54
Question: When a positive integer A is divided by 11 and 7, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 11 and 7, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
(A) 18
(B) 36
(C) 50
(D) 65
(E) 77
Rationale: A = 11k+1 = 7j+2
B = 11m+1 = 7n+2
A-B = 11(k-m) = 7(j-n)
A-B is a multiple of both 11 and 7, so it is a multiple of 77.
The answer is E.
Answer: (E) 77
Question: How many E ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?
(A) 6C4
(B) 6P4
(C) 4^6
(D) 6^4
(E) 6!
Rationale: Each marble has 4 options, so there are total of E=4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).
Answer: (C) 4^6
Question: Wendy begins sanding a kitchen floor by herself and works for 5 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?
(A) 9/80 hours
(B) 3/20 hours
(C) 20/3 hours
(D) 80/9 hours
(E) 272/35 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 5 hours and is then joined by Bruce to finish the work in 2 more hours,
5/W + 2/W+2/B = 1 (1 denotes the total amount of work)
7/W + 2/B =1 and given B =20 hours.
Thus W = 272/35 hours , E is the correct answer.
Answer: (E) 272/35 hours
Question: The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
(A) 144 m2
(B) 140 m2
(C) 108 m2
(D) 158 m2
(E) None of these
Rationale: Area of the outer rectangle = 23 Ã— 16 = 368 m2
Area of the inner rectangle = 19 Ã— 12 = 228 m2
Required area = (368 â€“ 228) = 140 m2
Answer B
Answer: (B) 140 m2
Question: When a certain number X is divided by 143, the remainder is 21. Which of the following numbers, if added to X, would result in a number divisible by 13?
(A) 7
(B) 21
(C) 5
(D) 47
(E) 55
Rationale: Now X= 143q + 45 = 11*13*q + 21..so we have to make only 21 div by 13..
21 + 5 = 26 divisible by 13 , add 5
ans C
Answer: (C) 5
Question: √(25)^2
(A) 5
(B) 14
(C) 25
(D) 21
(E) None of these
Rationale: explanation
√(25)^2=?
or, ? = 25
Answer C
Answer: (C) 25
Question: In how many ways E can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
(A) 1. 10!/(2! * 3!)
(B) 2. 10!/(8! * 7!)
(C) 3. 5!/(3! * 2!)
(D) 4. (5!)^3/(3! * 2!)
(E) 5. 5!/(8! * 7!)
Rationale: Ans is D.
Going by the assumtion that both the Bow side and Stroke side will have 5 person each.
Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.
and the 5 crew of each side can be arranged in 5! ways.E
Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!.D
Answer: (D) 4. (5!)^3/(3! * 2!)
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
(A) 21093
(B) 26667
(C) 26888
(D) 2668
(E) 91971
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer: A
Answer: (A) 21093
Question: How many odd integers between 100 and 300 are there such that their tens digit is even?
(A) 100
(B) 200
(C) 300
(D) 50
(E) 75
Rationale: I guess the easier way to do this would be.
200 numbers between - 100 and 300
Out of which half would be even, half odd.
Number of odd = 100. Of this.. the one with even tenth digit would be half again. hence 50.
correct option is D
Answer: (D) 50
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 210 games will be played during the tournament. What is the number of participants?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: Let n be the number of participants.
The number of games is nC2 = n*(n-1) / 2 = 210
n*(n-1) = 420 = 21*20 (trial and error)
The answer is D.
Answer: (D) 21
Question: A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?
(A)  24
(B)  30
(C)  36
(D)  90
(E)  96
Rationale: For every household that did not spend at least $100 per month on gasoline or electricity = P ,
4 spent at least $100 per month on electricity but not on gasoline = 4P
Spent = 300 - P
again spent = 60+120+4P
Now,
300 - P = 60+120+4P
or, 5P = 120
or, P = 24 (Answer)
Answer: (A)  24
Question: The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
(A) 276
(B) 300
(C) 299
(D) 322
(E) 345
Rationale: the numbers are (20 x 11) and (20 x 15).
Larger number = (20 x 15) = 300.
ANSWER :B
Answer: (B) 300
Question: A water tank is half full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?
(A) 6.5 min.to empty
(B) 9 min.to empty
(C) 5.5 min.to empty
(D) 4 min.to empty
(E) 7.5 min.to empty
Rationale: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 1/2
part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15
so, the tank will be emptied in 7.5 min
Answer: E
Answer: (E) 7.5 min.to empty
Question: What is the remainder when 1201 × 1202 ×1205 × 1207 is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The remainders when dividing each number by six are: 1, 2, 5, and 1.
The product is 1*2*5*1 = 10
The remainder when dividing 10 by 6 is 4.
The answer is D.
Answer: (D) 4
Question: With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?
(A) 100
(B) 1,000
(C) 10,000
(D) 100,000
(E) None of these
Rationale: Explanation: The decimal must be moved four places to the right. To do this, we must multiply by a number with four zeroes. The correct answer is 10,000.The decimal must be moved four places to the right. To do this, we must multiply by a number with four zeroes. The correct answer is 10,000.
Answer : (C)
Answer: (C) 10,000
Question: The work done by a man, a woman and a child is in the ratio of 3:2:1. There are 20 men, 30 women & 48 children in a factory. Their weekly wages amount to Rs.840, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women & 30 children for 2 weeks?
(A) Rs.1100
(B) Rs.1120
(C) Rs.1170
(D) Rs.1190
(E) Rs.1200
Rationale: sax Ratio of wages of 20 men, 30 women
and 45 chﬂdren perweek
: (3 x 2o):(2 x 30) (1 x 43) 5
Total wages or 20 men per week
= R5 300
Therefore, wages of a man per week : Rs 15,
sirmlarly, wages of woman per week
: Rs 10 and wages ofchwld perweek Rs 5
Total wages of (15 men, 21 women and 30
chﬂdrenj perweek
= 15x15 + 21x10 + 30x5 = 585
Total wages for 2 weeks = Rs.1170
C
Answer: (C) Rs.1170
Question: Adding 40% of x to x is equivalent to multiplying x by which of the following?
(A) 12.5
(B) 1.05
(C) 1.15
(D) 1.2
(E) 1.4
Rationale: 140x/100= 1.4*x
ANSWER:E
Answer: (E) 1.4
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 6 hours, how many machines of type R were used?
(A) 2
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R =1/36
Rate of machine S =1/18
since same no of machines used for R and S to do the same work in 6 hrs
So collective rate needed to finish the work in 6 hrs= 1/6
Let the no of machine be x
So, x/36 +x/18 =1/6
x3/36=1/6
x=2
So no of machine R is 2
Answer A
Answer: (A) 2
Question: In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 40 people were made to stand in a column, how many columns could be formed?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: 16*30 = 40*n
n = 12
The answer is A.
Answer: (A) 12
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 343, what was his profit?
(A) s. 63
(B) s. 69
(C) s.72
(D) s.75
(E) s.90
Rationale: C.P. = Rs. (100/122.5)x343
= Rs. (1000/1225)x343
= Rs. 280
Profit = Rs. (343 - 280) = Rs. 63.
Answer:A
Answer: (A) s. 63
Question: 3 candidates in an election and received 1136, 7636 and 10628 votes respectively. What % of the total votes did the winning candidate gotin that election?
(A) 40%
(B) 55%
(C) 54.8%
(D) 60%
(E) 62%
Rationale: Total number of votes polled = (1136 + 7636 + 10628) = 19400
So, Required percentage = 10628/19400 * 100 = 54.8%
C
Answer: (C) 54.8%
Question: A sum of Rs. 13500 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 4%
(B) 5%
(C) 6%
(D) 8%
(E) 14%
Rationale: S.I. = (15500 - 13500) = Rs. 2000/-
Rate = (100 * 2000) / (12500 * 4) = 4%
ANSWER:A
Answer: (A) 4%
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1
Question: According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 180 six-ounce servings of orange juice?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: 1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture.
60 ounces of mixture gives (60 / 6 ) = 10 servings.
Thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture.
To make 180 servings of the mixture, we need 180 / 10 = 18 cans of the concentrate.
The answer is B.
Answer: (B) 18
Question: How many kilograms of tea powder costing Rs. 31 per kg be mixed with 36 kilograms of tea powder costing Rs. 43 per kg, such that the mixture when sold at Rs. 44 per kg gives profit of 10%?
(A) 12
(B) 15
(C) 20
(D) 10
(E) 30
Rationale: SP of the mixture = 44, Profit =10%, Then CP = SP*100/110
44*100/110 = Rs. 40 per kg
Using alligation rule, the required ratio =
31 43
\ /
40
/ \
3 9
= 1:3
If 36 kg is 3 part then 1 part is 36*1/3 =12
ANSWER:A
Answer: (A) 12
Question: 10 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?
(A) 10
(B) 5
(C) 7
(D) 14
(E) 8
Rationale: Work done by 1 woman in 1 day=1/70
Work done by 1 children in 1 day=1/140
Work done by 5 women =5*1/70=5/70
Work done by 10 children =10*1/140=10/140
Amount of work 5 women and 10 children take to complete =5/70+10/140=1/7
5 women and 10 children will complete the work in 7 days.
C
Answer: (C) 7
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 4 hours?
(A) 2.4.
(B) 3.6.
(C) 4.2
(D) 5.5
(E) 6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 4 carpenters in 4 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 4 = 6.4 desks
E is the correct answer.
Answer: (E) 6.4
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 4 girls Will take to construct?
(A) 7 days
(B) 14 days
(C) 6 days
(D) 8 days
(E) 9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys + 4 girls = 8 Ã— 6/4 + 12 = 12 + 4 = 16 girls
9 days to complete the work
Answer: Option E
Answer: (E) 9 days
Question: Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 60 and the turban. Find the price of the turban.
(A) 27
(B) 30
(C) 29
(D) 10
(E) 11
Rationale: Let the price of turban be x.
Thus, for one year the salary = (90 + x)
For 9 months he should earn 3434 (90 + x).
Now he gets one turban and Rs. 60.
Thus, 3434 (90 + x) = 60 + x or 270 + 3x = 240 + 4x or x = 30
Answer:B
Answer: (B) 30
Question: Pipe A can fill a tank in 6 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 18
(B) 27
(C) 96
(D) 27
(E) 21
Rationale: Let the pipe B be closed after x minutes.
30/6 - x/24 = 1 => x/24 = 30/6 - 1 = 4
=> x = 4 * 24
= 96.
Answer:C
Answer: (C) 96
Question: A radio station surveyed 190 students to determine the types of music they liked. The survey revealed that 114 liked rock music, 50 liked folk music, and 41 liked classical music, 14 liked rock music and folk music, 15 liked rock music and classical music, 11 liked classical music and folk music. 5 liked all the three types of music.how many liked rock music, folk music but not classical only?
(A) 14
(B) 5
(C) 114
(D) 9
(E) 15
Rationale: Let R, F and C represent the sets of students who liked rock music, folk music and classical music respectively.
R=114
F=50, C=41
R and F but not C= 14-5=9
ANSWER D
Answer: (D) 9
Question: 30 % of 2 is equal to
(A) 0.2
(B) 0.4
(C) 0.6
(D) 0.7
(E) 0.9
Rationale: 30 % of 2 = (30 / 100) * 2 = 0.6
Answer: Option C
Answer: (C) 0.6
Question: 5 is added to a certain number, the sum is multiplied by 2, the product is divided by 5 and 5 is subtracted from the quotient. The remainder left is half of 44. What is the number?
(A) 21
(B) 20
(C) 63
(D) 30
(E) 45
Rationale: Let number is X.
When 5 added to it,
= (X+5)
2 multiplied to sum,
= 2 *(X +5)
Now,
= [{2 *(X +5)} /5]
And,
= [{2 *(X +5)} /5] - 5
According to question,
[{2 *(X +5)} /5] - 5 = half of 44
[(2X + 10) /5) = 22 +5
2X + 10 = 27 *5
2X-135-10
X = 125/2=62.5=63
So, required number is: 63.
ANSWER : C
Answer: (C) 63
Question: A batsman in his 12th innings makes a score of 48 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 26
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 2) + 48
∴ x = 26
Answer A
Answer: (A) 26
Question: An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 18%. How much will an air-conditioning unit cost in November?
(A) $466
(B) $470
(C) $472
(D) $484
(E) $491
Rationale: if its prevoius november (before discount) then price is $470.
but if its November of next year then
16% discount on $470=470(1-16/100)=$394.8
again a corrected raised price of 18% over $394.8=394.8(1+18/100)=465.86~$466
Ans A
Answer: (A) $466
Question: 200 pupil total,out of 125 like pizza,115 like burger, then how many like both?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: n(A U B)=n(A) + n(B) - n(A INTERSECTION B)
200 = 125 + 115 - BOTH
BOTH = 240 - 200 = 40.
ANSWER:A
Answer: (A) 40
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 144 grams of water?
(A)  16
(B)  72
(C)  112
(D)  128
(E)  142
Rationale: Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water.
Therefore there are 144*8/9=128 grams of oxygen in 144 grams of water.
Answer: D.
Answer: (D)  128
Question: 105,102,96,?,75,60,42
(A) 80
(B) 75
(C) 60
(D) 82
(E) 87
Rationale: The Pattern is - 3, - 6, -9, -12, ...
96-9=87
Answer :E
Answer: (E) 87
Question: In a two digit number, the digit in the units place is four times the digit in ten's place and sum of the digits is equal to 10. What is the number?
(A) 25
(B) 28
(C) 32
(D) 36
(E) 38
Rationale: Solution
Let the ten digits be x. Then,units digit=4x
Therefore x + 4x = 10
‹=›5x = 10
‹=›x= 2.
So, ten's digit = 2, unit's digit = 8.
Hence, the required number is 28.
Answer B
Answer: (B) 28
Question: Of the 20 members of a kitchen crew in traditional Japanese, 17 can prepare sushi, 18 can prepare noodle, and 15 can prepare both. If one member is chosen at random, what is the probability that the member chosen will be someone who can not prepare either dish?
(A) a) 1/7
(B) b) 1/5
(C) c) 1/4
(D) d) 0
(E) e) 1/2
Rationale: You know how to solve for Total number of people who can use at least one machine:
Total = n(A) + n(B) - n(A and B)
Total people who can prepare at least one dish = 17 + 18 - 15 = 20
So all 20 people know how to prepare at least one dish. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to prepare any dish
Answer (D)
Answer: (D) d) 0
Question: When w is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when w + y is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: In my view the answer should be C
w/5 has Remainder=3 -> w = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Answer: (C) 2
Question: List R contains five numbers that have an average value of 65. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
(A) 25
(B) 31
(C) 35
(D) 39
(E) 43
Rationale: The middle number is 65.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 65, 65, 2x+20, 2x+20.
x + 65 + 65 + 2x + 20 + 2x + 20 = 5*65 = 325
5x = 155
x = 31
The answer is B.
Answer: (B) 31
Question: In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
(A) 5760
(B) 14400
(C) 480
(D) 56
(E) 40320
Rationale: Consider the following arrangement:
*B*B*B*B*B*
Now, if girls occupy the places of 6 stars no girls will be together.
# of ways 3 girls can occupy the places of these 6 stars is C36=20;
# of ways 3 girls can be arranged on these places is 3!=6
# of ways 5 boys can be arranged is 5!=120
So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20∗6∗120=14,400
ANS:B
Answer: (B) 14400
Question: Bradley owns b video game cartridges. If Bradleyâ€™s total is quarter the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 16/3)b
(B) 17/4)b
(C) 13/4)b
(D) 21/4)b
(E) 7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlieâ€™s values in relation to Bradleyâ€™s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradleyâ€™s total
4b = Andrewâ€™s total
(1/4)b = Charlieâ€™s total
Add each total
b + 4b+ (1/4)b = 5b + (1/4)b = (20/4)b + (1/4)b = (21/4)b
Therefore,choose D.
Answer: (D) 21/4)b
Question: If x is an even integer and y is an odd integer, which of the following must be an even integer?
(A) y/x
(B) x+y
(C) 3x + 2y
(D) 3(x + y)
(E) 2y/x
Rationale: x is even and y is odd
Check the options
Option A. y/x - Nothing can be said about whether this will be an integer or not INCORRECT
Option B. x+y - Even + odd = Odd INCORRECT
C. 3x + 2y - 3*even + 2*odd = even + even = even - CORRECT
D. 3(x + y) 3*(even + odd) = 3*odd = odd - INCORRECT
E. 2y/x - Nothing can be said about whether this will be an integer or not INCORRECT
ANSWER:C
Answer: (C) 3x + 2y
Question: When 24 is divided by the positive integer b, the remainder is 4. Which of the following statements about b must be true?
I. b is even
II. b is a multiple of 5
III. b is a factor of 20
(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: 24= m*b + 4
m*b=20
put values of m
m=1 b=20
m=2 b=10
m=4 b=5
I. not true
II. true
III. true
D. correct
Answer: (D) II and III only
Question: In a country named "gpuzzles" 1/2 of 5 = 3.
If the same proportion holds, what is the value of 1/3 of 10 ?
(A) 2
(B) 5
(C) 6
(D) 9
(E) 4
Rationale: E
4
5/2 = 3 and 10/3 = x
(10/3)/(5/2) = 20/15 = 4/3
So x/3 = 4/3
x=4
Answer: (E) 4