mathewhe/aqua_rat huggingface dataset:
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
(A) 23 years
(B) 20 years
(C) 24 years
(D) 21 years
(E) 22 years
Rationale: Explanation:
Number of members in the team = 11
Let the average age of of the team = x
=> Sum of ages of all 11 members/11=x
=> Sum of the ages of all 11 members = 11x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper
=11x−26−29=11x−55
Average age of 9 members of the team excluding captain and wicket keeper
=11x−5/59
Given that 11x−55/9=(x−1)
⇒11x−55=9(x−1)
⇒11x−55=9x−9
⇒2x=46
⇒x=46/2 = 23 years
Answer: Option A
Answer: (A) 23 years
Question: A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number of degrees of angle ADB is:
(A) 27
(B) 30
(C) 837
(D) 37
(E) 18
Rationale: Answer: B
Answer: (B) 30
Question: Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 15 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
(A) A)8/100
(B) B)9/100
(C) C)1/8
(D) D)1/13
(E) E)9/10
Rationale: Total letters 15, out of which the first letter is anything of 10 but N or X...
So there are 13 possible letters for first place..
And only one of them is correct..
So 1/13
Answer: D
Answer: (D) D)1/13
Question: ? x 12 = 173 x 240
(A) 3460
(B) 685
(C) 865
(D) 495
(E) 534
Rationale: Let y x 12 = 173 x 240
Then y = (173 x 240) / 12
=3460
ANSWER :A
Answer: (A) 3460
Question: A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen?
(A) Rs.6.40
(B) Rs.10
(C) Rs.9.6
(D) Rs.10.2
(E) None of the above
Rationale: 4 dozens of bananas cost is rs12
then 4*12=48
6 dozens of bananas cost is rs8
then 6*8=48
48+48/4+6=96/10=9.6
ANSWER:C
Answer: (C) Rs.9.6
Question: If 5^21 X 4^11 = 2x10^n. What is the value of n?
(A) 11
(B) 21
(C) 22
(D) 23
(E) 32
Rationale: If 5^21 x 4^11 = 2x10^n what is the value of n
4^11 = (2^2)^11 = 2^22
10^n = (5x2)^n = 5^n x 2^n
5^21 x 2^22 = 2x 2^n x 5^n = 2^n+1 x 5^n = 2^22 x 5^21
n = 21
Option B
Answer: (B) 21
Question: Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 45% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 60%
(B) 50%
(C) 25%
(D) 15%
(E) 5%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 20 + 45 - {both} + 40
{both} = 5%.
The answer is E.
Answer: (E) 5%
Question: In an examination 42% students failed in Hindi and 52% failed in English. If 17% failed in both of these .subjects, what is the percentage of students who passed in both the subjects ?
(A) 52
(B) 25
(C) 72
(D) 35
(E) 23
Rationale: Hindi = 42% - 17% =25%
English = 52% - 17% = 35%
Middle is 17%.
so 35 in English and 25 in Hindi which means that 35+25+17 = 77% 100%-77% = 23%
Therefore 23% passes both
Answer : E
Answer: (E) 23
Question: Find the least number that must be subtracted from 1387 so that the remaining number is divisible by 15.
(A) 1
(B) 5
(C) 7
(D) 9
(E) 13
Rationale: On dividing 1387 by 15 we get the remainder 7, so 7 should be subtracted. The answer is C.
Answer: (C) 7
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230m
(B) 240m
(C) 250m
(D) 260m
(E) 270m
Rationale: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 270 + x
therefore, D= speed*time
thus 270 + x = 500/9 * 9
x= 500-270=230 m
ANSWER:A
Answer: (A) 230m
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 2/3
(B) 3/4
(C) 3/5
(D) 3/7
(E) 4/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/4
Question: A classroom has equal number of boys and girls. TEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
(A) 16
(B) 24
(C) 32
(D) 48
(E) 40
Rationale: after 10 girls left remaining 10 girls
now boys 20 are twice as many as remaining girls.
initially boys=20 and girls=20.
ANSWER:E
Answer: (E) 40
Question: Celine worked for h hours each day for d consecutive days. If she earns $7.50 per hour, what is the total amount she earned?
(A) 7.50/d + h
(B) 7.50 + d + h
(C) 7.50 + dh
(D) 7.50dh
(E) 7.50h + d
Rationale: H hours for d days.
Income each day = 7.5*h
Total income = 7.5*h*d
Correct option: D
Answer: (D) 7.50dh
Question: The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway?
(A) 2 feet per second
(B) 2.5 feet per second
(C) 3 feet per second
(D) 4 feet per second
(E) 5 feet per second
Rationale: I get E.
Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.
So we get two equations:
3t=d-120
6t=d
Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.
So, Bill's average rate of movement Q is:
He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.
(240+60)/(20+40)= 5 ft/sec=E
Answer: (E) 5 feet per second
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
(A) 6
(B) 9
(C) 24
(D) 20
(E) 29
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage =14	x 100	% = 20%
Answer:C
Answer: (C) 24
Question: A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $38,000 commission, how many machines did she sell?
(A)  90
(B)  103
(C)  105
(D)  115
(E)  120
Rationale: First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 38000 - 30000 = 8000
So 20 more machines..
Total = 120 machines
IMO E...
Answer: (E)  120
Question: The cost of an article is decreased by 10%. If the original cost is $100, find the decrease cost.
(A) 33
(B) 11
(C) 68
(D) 36
(E) 90
Rationale: Original cost = $100
Decrease in it = 10% of $100
= 10/100 Ã—100
= 1000/100
= $10
Therefore, decrease cost = $100 - $10 = $90
Answer:E
Answer: (E) 90
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.95?
(A) 980
(B) 1170
(C) 1530
(D) 1720
(E) 1960
Rationale: The charge is 65 cents for the first 250 grams.
This leaves a charge of $1.95 - $0.65 = $1.30
The charge for the next 1200 grams is $1.20 which leaves a charge of $0.10
The weight is somewhere between 1450 and 1550.
The answer is C.
Answer: (C) 1530
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 487
(C) 720
(D) 729
(E) 268
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 6 = 720
Answer:C
Answer: (C) 720
Question: A person spent Rs. 6,040 from his salary on food and 8,000 on house rent. After that he was left with 70% of his monthly salary. What is his monthly salary ?
(A) 46,800
(B) 66,800
(C) 56,800
(D) 26,800
(E) 76,800
Rationale: Total money spent on food and house rent = 6,040+8,000 = 14,040
Which is 100 - 70 = 30% of his monthly salary
∴ His salary = 14040x100/30 = 46800
Answer : A
Answer: (A) 46,800
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
(A) 1/2
(B) 2
(C) 1
(D) 4
(E) 5
Rationale: d = rt
M: r = 40 mph, t = t + 1/4hr
d = 40 (t + 1/4)
P: r = 60, t = t
d = 60t
since they went the same distance:
40t + 40/4 = 60t
20t = 40/4
t = 1/2 or 1/2 hr
A
Answer: (A) 1/2
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
(A) 7 km
(B) 6 km
(C) 4 3/8 km
(D) 9 km
(E) 5 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Answer: (C) 4 3/8 km
Question: In a particular gumball machine, there are 4 identical blue gumballs, 3 identical red gumballs, 2 identical green gumballs, and 1 yellow gumball. In how many different ways can the gumballs be dispensed, 1 at a time, if the 3 red gumballs are dispensed last?
(A) 105
(B) 210
(C) 315
(D) 420
(E) 630
Rationale: Since the red gumballs are being dispensed last they will not impact the number of permutations of the other gumballs, so we can effectively ignore them. (There is only one way for the three red gumballs to be dispensed last (RRR), so we will multiply the number of permutations of the other colours by 1).
The remaining gumballs are: 4 blue, 2 green, 1 yellow. 7 gumballs in total, so they can be arranged in 7! ways. But since the gumballs of each colour are identical, we must divide by the arrangements of each colour.
Total arrangements of the 7 gumballs = 7!/4!∗2!∗1!=7∗6∗5/2=105
So total arrangements of the 10 gumballs, with all 3 reds chosen last is 105 *1 = 105
Answer: A
Answer: (A) 105
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 35 km/hr
(B) 50 km/hr
(C) 45 km/hr
(D) 65 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: (B) 50 km/hr
Question: What least number must be subtracted from 427398 so that remaining number is divisible by 15
(A) 3
(B) 5
(C) 7
(D) 9
(E) None of these
Rationale: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Answer: Option A
Answer: (A) 3
Question: A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:
(A) 130
(B) 220
(C) 140
(D) 120
(E) 145
Rationale: C
140%
Let C.P. = $x.
Then, S.P. = $(12% of x) = $6x/5
New S.P. = 2 * 6x/5 = $12x/5
Profit = 12x/5 - x = $7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Answer: (C) 140
Question: The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ?
(A) 18
(B) 12
(C) 25
(D) 13
(E) 7
Rationale: Teacher's age= 10x+y so student's age= 10y+x..
after 5 years , 10x+y+5=2*(10y+x+5)....
so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18
Answer: (A) 18
Question: What is the ratio of 3/7 to the product 3*(7/3)?
(A) 3:7
(B) 1:3
(C) 3:21
(D) 1:7
(E) 3:49
Rationale: 3*(7/3) = 7
So, We need to find the ratio of 3/7 : 7 => 3 : 49
Hence , answer will be (E) 3 : 49
Answer: (E) 3:49
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 80. When the number of legs was counted, the number totaled up to 218. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let x be the number of chickens.
Then 80-x is the number of pigs.
2x+4(80-x)=218
2x=102
x=51 (chickens)
70-x=29 (pigs)
There are 51-29=22 more chickens on the farm.
The answer is D.
Answer: (D) 22
Question: In what time will a train 400 meters long cross an electric pole, if its speed is 144 km/hr
(A) 5 seconds
(B) 4.5 seconds
(C) 10 seconds
(D) 2.5 seconds
(E) None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 144*(5/18) = 40 m/sec
Time = Distance/speed
= 400/40 = 10 seconds
Answer: C
Answer: (C) 10 seconds
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be 10 and other will be Queen?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
(A) 8/2652
(B) 1/2652
(C) 12/2652
(D) 18/2652
(E) 16/2652
Rationale: 2 possible cases:
10 - Queen or Queen -10 (4 kings and 4 queens).
Either way,
the total probability = 2( 10 -Queen) = 2 (4/52 * 4/51) = 18/2652. D is the correct answer.
Answer: (D) 18/2652
Question: Simplify 64568 * 9999
(A) 645615432
(B) 236547892
(C) 289546354
(D) 558666666
(E) 236669855
Rationale: Explanation:
Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
64568 * (10000 - 1) = 645680000 - 64568 = 645615432
Answer: Option A
Answer: (A) 645615432
Question: If a positive odd integer N has p positive factors, how many positive factors will 4N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: I have added some extra text to make this question more GMAT-like:
Let's TEST some values of N
Try N = 3
The factors of 3 are {1, 3}. Here, p =2
So, 2N = (2)(3) = 6
The factors of 6 are {1, 2, 3, 6}. So, we have a total of4
Now check the answer choices:
A) p =2No good. We want an output of4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST another value of N
Try N = 7
The factors of 7 are {1, 7}. Here, p =2
So, 2N = (2)(7) = 14
The factors of 14 are {1, 2, 7, 14}. So, we have a total of4
Now check the REMAINING answer choices:
B) 2p = (2)(2) =4. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST one more (non-prime) value of N
Try N = 9
The factors of 9 are {1, 3, 9}. Here, p =3
So, 2N = (2)(9) = 18
The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6
Now check the REMAINING answer choices:
B) 2p = (2)(3) =6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
At this point, it SEEMS LIKELY that the correct answer is E
Answer: (E) Cannot be determined
Question: A man rows his boat 84 km downstream and 60 km upstream, taking 4 hours each time. Find the speed of the stream?
(A) 76 kmph
(B) 6 kmph
(C) 14 kmph
(D) 8 kmph
(E) 3 kmph
Rationale: Speed downstream = d/t = 84/(4)
= 21 kmph
Speed upstream = d/t = 60/(4)
= 15 kmph
The speed of the stream = (21 - 15)/2
= 3 kmph
Answer:E
Answer: (E) 3 kmph
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 65,536,000,000 and x + y + z = 17, what is the value of xy/z?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 7
Rationale: The number 65,536,000,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A.
Answer: (A) 0
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: rx*(t+2) = w
ry*(t) = w.
Also, w/(t+2) + w/t = (5w/4)*(1/3)
or 1/t + 1/(t+2) = 5/12 --> (3+2)/12 = 1/4+1/6
Thus, t = 4. Replacing, rx = w/6,
w/6*T = 2w
or T = 12 days.
ANSWER:E
Answer: (E) 12
Question: A teacher gave the same test to three history classes: M, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: Ans : B (75)
lets say class M indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class M is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = M+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Answer: (B) 75
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/9%
(B) 16 2/4%
(C) 16 2/3%
(D) 16 2/1%
(E) 16 2/6%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: A seamstress sells 200 metres of ribbon for Rs. 10000 at a loss of Rs. 7 per metre. Find her cost price for one metre of ribbon?
(A) 20
(B) 43
(C) 26
(D) 34
(E) 57
Rationale: SP per metre = 10000/200 = Rs. 50 Loss per metre = Rs. 5 CP per metre = 50 + 7= Rs. 57Answer:E
Answer: (E) 57
Question: X and Y are both integers. If X/Y = 57.40, then what is the sum of all the possible two digit remainders of X/Y?
(A) 560
(B) 616
(C) 450
(D) 900
(E) 1024
Rationale: Remainder = 0.40 --> 40/100 --> Can be written as (40/4) / (100/4) = 10/25
So remainders can be 10, 20, 30, 40, ..... 90.
We need the sum of only 2 digit remainders --> 10 + 20 + 30 + 40 + 50 + 60 + 70+ 80 + 90 =450
Answer: C
Answer: (C) 450
Question: In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
(A) -4/3
(B) 1/4
(C) -4
(D) 3/4
(E) 4/3
Rationale: The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Answer: (A) -4/3
Question: If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
(A) 2888
(B) 1000
(C) 2878
(D) 27878
(E) 2112
Rationale: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x
1 = 1/10 * 1/10 * 1/10 * x => x = 1000
Answer:B
Answer: (B) 1000
Question: By selling a book for 300, 20% profit was earned. What is the cost price of the book?
(A) A)215
(B) B)250
(C) C)230
(D) D)235
(E) E)240
Rationale: SP = 120% of CP; :. CP = 300 × 100/120 = 250
Option 'B'
Answer: (B) B)250
Question: How many of the following numbers are divisible by 21 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 3
(B) 4
(C) 5
(D) 1
(E) 7
Rationale: By using your calculator you can calculate that the following numbers are divisible by 21 : 462
Required number of number = 1.
D
Answer: (D) 1
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ?
(A) 1287
(B) 2887
(C) 2100
(D) 1129
(E) 1192
Rationale: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 6069
= x= 6069/2.89 = 2100
Therefore, amount invested by Raghu is Rs. 2100.
Answer: C
Answer: (C) 2100
Question: If xy=4, x/y=16, for positive numbers x and y, y=?
(A) 1/2
(B) 2
(C) 1/3
(D) 3
(E) 1/6
Rationale: Very easy question. 2 variables and 2 easy equations.
xy=4 ---> x=4/y - (i)
x/y=16 ---> replacing (i) here ---> 4/(y^2)=16 ---> y^2=4/16=1/4 ---> y=1/2 or -1/2
The question states that x and y are positive integers. Therefore, y=1/2 is the answer.
Answer A.
Answer: (A) 1/2
Question: A theater box office sold an average (arithmetic mean) of 63 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 78, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
(A) 2:3
(B) 1:4
(C) 1:5
(D) 6:11
(E) 4:7
Rationale: Deviation from the mean for the daytime staff = 78 - 63 = 15.
Deviation from the mean for the evening staff = 63 - 60 = 3.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 3:15 = 1:5.
The answer is C.
Answer: (C) 1:5
Question: A boy has 9 trousers and 9 shirts. In how many different ways can he select a trouser and a shirt?
(A) 100
(B) 81
(C) 104
(D) 94
(E) 110
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 9 = 81 ways.
B
Answer: (B) 81
Question: When a jogger moves at an average speed of 6 kmph, they reach their destination on time. When their average speed becomes 4 kmph, they reach their destination 15 minutes late. Find the length of journey.
(A) 3 km
(B) 5 km
(C) 7 km
(D) 6 km
(E) None
Rationale: Sol.
Difference between timings = 15 min = 1/4 hr.
Let the length of journey be x km.
Then, x/4 - x/6 = 1/4
â‡” 3x - 2x = 3
â‡” x = 3 km.
Answer A
Answer: (A) 3 km
Question: The average of 100,200,300 and x is 250 and the average of 300,150,100,x and y is 200. What is the value of y?
(A) 100
(B) 150
(C) 50
(D) 200
(E) 250
Rationale: We have : (100+200+300+x) /4 = 250
600+x = 1000
x = 400
(300+150+100+x+y)/5 = 200
550+400+y = 1000
y = 50
Answer is C
Answer: (C) 50
Question: An express traveled at an average speed of 200 km/hr, stopping for 3 min after every 125 kn. How long did it take to reach its destination 800 km from the starting point?
(A) 5 hrs 21 min
(B) 4 hrs 18 min
(C) 6 hrs 41 min
(D) 6 hrs 21 min
(E) 4 hrs 34 min
Rationale: B
4 hrs 18 min
Time taken to cover 800 km = 800/200 = 4 hrs.
Number of stoppages = 800/125 - 1 = 6
Total time of stoppages = 3 * 6 = 18 min
Hence, total time taken = 4 hrs 18 min.
Answer: (B) 4 hrs 18 min
Question: A rower whose speed is 6 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km/hr. What is the rower's average speed (in km/hr) for the total journey?
(A) 3.9
(B) 4.2
(C) 4.5
(D) 4.8
(E) 5.1
Rationale: time upstream = d / 3
time downstream = d / 9
total time = d/3 + d/9 = 4d/9
average speed = 2d / (4d/9) = 4.5 km/hr
The answer is C.
Answer: (C) 4.5