mathewhe/aqua_rat huggingface dataset:
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 2.9 hrs
(B) 4.5 hrs
(C) 2.9 hrs
(D) 7.2 hrs
(E) 8.6 hrs
Rationale: Net part filled in 1 hour = (1/3 - 1/9)
= 2/9
The cistern will be filled in 9/2 hrs i.e., 4.5 hrs.
Answer:B
Answer: (B) 4.5 hrs
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 13 from the product of their ages a year from today. What is their age today?
(A) 2.
(B) 6.
(C) 5.
(D) 7.
(E) 9.
Rationale: ad = (a+1) (d+1) -13
0= a+d-12
a+d = 12
a=d (as they are twin brothers)
a=d=6
B is the answer
Answer: (B) 6.
Question: P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?
(A) 12 days
(B) 12.5 days
(C) 13 days
(D) 13.5 days
(E) 15.5 days
Rationale: Both together worked for 3 days.
In 3 days , P can do = 3 x
1
18
=
1
6
th work
In 3 days, Q can do = 3 x
1
15
=
1
5
th work
In 3 days , work finished =
1
6
+
1
5
=
11
30
Balance work =
19
30
Balance work finished by Q => Time taken by Q to finish the balance work =
19
30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days
B
Answer: (B) 12.5 days
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -.
(A) 2/10
(B) 4/13
(C) 3/5
(D) 9/7
(E) 1/4
Rationale: Explanation:
P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: B
Answer: (B) 4/13
Question: Mr X mixed 10 kg of variety A rice with 15 kg of variety B rice and sold the mixture at a price 40% more than that of A. He did not get any profit.What is the ratio of the cost price of variety A to that of B per kg?
(A) 2:5
(B) 3:5
(C) 4:5
(D) 5:8
(E) 8:5
Rationale: Let Rs X, Rs Y be the cost price per kg of variety A and variety B of rice
By data 10X + 15Y = 25 (1.4) X.
Since sale price of the mixture is 40% more than the cost price or A.
Therefore 10X + 15Y= 35X
Thus,15Y = 25X.
Hence, X : Y = 15 : 25 = 3 : 5
ANSWER:B
Answer: (B) 3:5
Question: What is the greatest prime factor of (11! × 10!  + 10! × 9!)/111?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: (11!×10! +10!×9!)/111
In numerator take out 10!*9! as common term
10!∗9!(11×10 +1)/111
10!∗9!∗111/111
10!∗9!
10! has 7 as the greatest prime factor, so ans is 7
ANSWER:D
Answer: (D) 7
Question: Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 16 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?
(A) 24 km/hr
(B) 30 km/hr
(C) 36 km/hr
(D) 42 km/hr
(E) 48 km/hr
Rationale: Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/16 = 3x
x = 25/6 m/s
So, the speed of the faster train is 50/6 = 50/6 * 18/5 = 30 km/hr
The answer is B.
Answer: (B) 30 km/hr
Question: Find the 10th term of the arithmetic progression 1, 3.5, 6, 8.5,...?
(A) 20
(B) 23.5
(C) 22.5
(D) 18.25
(E) 19.5
Rationale: common difference = d = 3.5 - 1 = 2.5 ,, n = 10, a = first term = 1----- By using arithmetic progression , t10 = a + (n-1)*d = 1 + (10-1)*2.5 = 1+22.5 = 23.5 Ans - B
Answer: (B) 23.5
Question: A candidate scoring 25% in an examination fails by 30 marks , while another candidate scores 50 % mark, gets 20 marks more than the minimum pass marks . Find the minimum pass marks. Find the minimum pass percentage.
(A) 40%
(B) 45%
(C) 50%
(D) 55%
(E) 60%
Rationale: Let x be the maximum marks,
Then (25% of x)+30 = (50% of x)-20
=>X/4 + 30 =X/2 - 20
=>X=200
Hence maximum marks = 200
Minimum pass marks = 200/4 + 30 =80
Hence, minimum pass marks =80/200 X 100 =40%
ANSWER IS A
Answer: (A) 40%
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 7 games?
(A) x + 3y/(n + 3)
(B) x + y/(n + 3)
(C) (x + 3y)/(n + 3)
(D) (nx + 3y)/(n + 7)
(E) (3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 7 games = (nx+3y)/(n+7)
Hence, correct answer will be (D)
Answer: (D) (nx + 3y)/(n + 7)
Question: 0.0004?=0.02
(A) 0.02
(B) 0.2
(C) 2
(D) 20
(E) None of these
Rationale: Explanation :
Required Answer = 0.0004/0.02 = 0.04/2 = 0.02. Answer : Option A
Answer: (A) 0.02
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $40,000?
(A) $38,796.
(B) $40,000.
(C) $38,976.
(D) $39,679.
(E) $36,796.
Rationale: 40,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option C fulfills the condition and hence is the answer
Answer: (C) $38,976.
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
(A) 3 1/5min
(B) 3 2/5min
(C) 3 3/5min
(D) 3 4/5min
(E) 3 min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/9+1/6)=(5/18)
So both punctures will make the type flat in
(18/5)mins=3 3/5mins
Option C
Answer: (C) 3 3/5min
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 77 m
(B) 17 m
(C) 82 m
(D) 28 m
(E) 26 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: (B) 17 m
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
(E) None
Rationale: EXPLANATION
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) – 34009 ]
= Rs. (39000 – 34009)
= Rs. 4991.
Answer A
Answer: (A) Rs. 4991
Question: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 30 items in the same time Machine Z produces 24 items. If machine Y takes 36 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?
(A) 60
(B) 90
(C) 9 1/2
(D) 45
(E) 13 1/2
Rationale: rate z/rate y=24/30
time z/time y=30/24
30/24*36=45 minutes
D
Answer: (D) 45
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) Rs.250
(B) Rs.257
(C) Rs.228
(D) Rs.229
(E) Rs.226
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Answer: (A) Rs.250
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 10% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 18%
(C) 15%
(D) 22%
(E) 11.11%
Rationale: 0.1 M = 0.90 E
=> E/M = 1/9 * 100 = 11.11%=E.
M - # of Motorists
E - # of Motorists exceeding speed
Answer: (E) 11.11%
Question: What is the are of an equilateral triangle of side 6 cm?
(A) 8√3
(B) 9√3
(C) 7√3
(D) 4√3
(E) 3√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 6, Area of triangle = √3/4 * 6 * 6
= 9√3 cm2;
Answer:B
Answer: (B) 9√3
Question: John left home and drove at the rate of 50 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?
(A) 235 miles.
(B) 245 miles.
(C) 255 miles.
(D) 265 miles.
(E) 275 miles.
Rationale: The total distance D traveled by John is given by
D = 50 * 2 + 3 * 55 = 265 miles.
Answer D
Answer: (D) 265 miles.
Question: If a large pizza has a radius that is 10% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
(A) 15%
(B) 21%
(C) 25%
(D) 30%
(E) 36%
Rationale: Let the radius of medium pizza be r. Then the radius of large pizza is 1.1r.
The area of the medium pizza is pi*r^2
The area of the large pizza is pi*(1.1*r)^2 = 1.21*pi*r^2, an increase of 21%.
The answer is B.
Answer: (B) 21%
Question: When you multiply a number by 4 and
then subtract 6, the result is the same as
if you first subtracted 6 from the same
number and then multiplied by 10. What
is the number?
(A) A)23
(B) B)9
(C) C)19
(D) D)31
(E) E)10
Rationale: Let x equal the number and then change the words into an equation and solve for x:
4x – 6 = 10(x – 6)
4x – 6 = 10x – 60
54 = 6x
9 = x
correct answer B)9
Answer: (B) B)9
Question: The ages of two persons differ by 16 years. 4 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
(A) 15
(B) 20
(C) 28
(D) 30
(E) 35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 4) = 3 (x-16-4)
=> x � 4 = 3x � 60
=> 2x = 56
=> x = 60/2 = 28
Answer: Option C
Answer: (C) 28
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
(A) 2160
(B) 3120
(C) 3972
(D) 6240
(E) 5240
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
ANSWER:C
Answer: (C) 3972
Question: How many numbers with 3 different digits can be formed using only the even-numbered digit?
(A) 12
(B) 20
(C) 40
(D) 60
(E) 120
Rationale: Odd digits are 2, 4, 6, 8.
We want 2 different digits.
First digit can be chosen in 4 ways.
Second digit can be chosen in 3 ways.
Total ways = 4*3
= 12
Hence option (A).
Answer: (A) 12
Question: An electric motor makes 2,800 revolutions per minutes. How many degrees does it rotate in one second?
(A) 16.800 d/sec
(B) 28.000 d/sec
(C) 38.000 d/sec
(D) 26.000 d/sec
(E) 35.000 d/sec
Rationale: 2800 revolutions / minute
= 2800*360 degrees / 60 seconds
= 16,800 degrees / second
A
Answer: (A) 16.800 d/sec
Question: In how many ways can the letters of the word ARRANGED be arranged?
(A) 20160
(B) 20180
(C) 20120
(D) 21021
(E) 20170
Rationale: ARRANGED has 8 words, but r is repeated two times. Thus ways = 8! / 2! = 20160 ways
A
Answer: (A) 20160
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 49 years. What will be the age of the B ten years hence?
(A) 39
(B) 23
(C) 28
(D) 98
(E) 26
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 49 => b + c = 98 --- (2)
Answer: D
Answer: (D) 98
Question: Find compound interest on $ 4000 at 15% per annum for 2 years 4 months, compounded annually.
(A) 1554.5
(B) 1509.5
(C) 1108.5
(D) 1107.5
(E) 1100.5
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = $ [4000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]
=$ [4000 * (23/20) * (23/20) * (21/20)]
= $ 5554.50	.
:. C.I. = Rs. (5554.50 - 4000) = $ 1554.50
Answer A.
Answer: (A) 1554.5
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
(A) 2 1/4
(B) 2 1/9
(C) 2 1/6
(D) 2 1/5
(E) 2 1/2
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A
Answer: (A) 2 1/4
Question: A train 400 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 30 sec. The speed of the train is?
(A) 39 km/hr
(B) 40 km/hr
(C) 41 km/hr
(D) 42 km/hr
(E) 43 km/hr
Rationale: Speed of the train relative to man = 400/30 = 40/3 m/sec.
= 40/3 * 18/5 = 48 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 7 = 48 => x = 41 km/hr.
Answer: C
Answer: (C) 41 km/hr
Question: A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  9/4
(B)  3/2
(C)  4/3
(D)  2/3
(E)  1/2
Rationale: sq rt(4x/3) = x
=> 4x/3 = x^2
=> x = 4/3
Ans - C
Answer: (C)  4/3
Question: In a family 16 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family?
(A) 28
(B) 26
(C) 22
(D) 31
(E) 21
Rationale: Total people eat veg = only veg + both veg and non veg
Total= 16+12= 28
Answer = A
Answer: (A) 28
Question: A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $150,000 and $250,000, one of them is $350,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?
(A) 782.5
(B) 785
(C) 780
(D) 790
(E) 800
Rationale: taking away '000 thousand sfor easy calculation
(1) 2(150)+350+2(500) = 1650
1600*0.95=1567.5 (Revenue considering the minimum values with the discount)
(2) 2(250)+350+2(750) = 2350 (Revenue considering the maximum values without the discount)
So, the the revenue range could be = 2350 - 1567.5 = 782.5
A
Answer: (A) 782.5
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 15 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
(A) 20
(B) 34
(C) 50
(D) 67
(E) 100
Rationale: Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 15 oz can = 300 oz/15 oz = 20
Answer A, 20 cans
Answer: (A) 20
Question: If 9^y = 3^12, what is y?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: (E) 6
Question: What is the sum of the digits of integer k, if k = (10^30- 54)
(A) 251
(B) 261
(C) 262
(D) 269
(E) 278
Rationale: There are 31 digits in 10^30
When we subtract 54 from it, there will be 30 digits left.
10^30 can be written as 9999999....(30 times) + 1
So,
10^30 - 54 = 9999999....(30 times) + 1 - 54 = 9999999....(30 times) - 53
Consider the last 2 digits,
99-53 = 46
The last 2 digits will be 46.
And our number would be 99999......99946 with 2 less 9s after subtraction.
Number of 9s left are 28 and the last two digits are 46
The sum of the digits will be
(28*9) + 4 + 6 =262
Answer:- C
Answer: (C) 262
Question: A person buys an article at Rs.350. At what price should he sell the article so as to make a profit of 30%?
(A) 455
(B) 277
(C) 269
(D) 261
(E) 281
Rationale: Cost price = Rs.350
profit = 30% of 350 = Rs.105
Selling price = Cost price + Profit
= 350 + 105 = 455
Answer: A
Answer: (A) 455
Question: If q and r are both odd numbers Z, which of the following must also be odd?
(A) q – r
(B) (q + r)^2
(C) q(q + r)
(D) (qr)^2
(E) q/r
Rationale: We're told that q and r are both ODD numbers Z. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Answer: (D) (qr)^2
Question: Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?
(A) 9, 6, 16
(B) 9, 6, 11
(C) 9, 6, 17
(D) 9, 6, 12
(E) 9, 6, 19
Rationale: Let the numbers be a, b and c.
Given that a, b and c are in the ratio 3 : 2 : 4.
let, a = 3x, b = 2x and c = 4x
Given, (a+b) + (c - b) = 21
= > a + b + c - b = 21 = > a + c = 21
= > 3x + 4x = 21 = >7x = 21 = > x = 3
a , b , c are 3x, 2x, 4x.
Answer:D
a, b, c are 9 , 6 , 12.
Answer: (D) 9, 6, 12
Question: Given that E and F are events such that P(E) = 25, P(F) = 75 and P(E n F) = 75,
find P (E|F) and P(F|E)
(A) 5
(B) 46
(C) 52
(D) 12
(E) 3
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 75/25= 3
P(F|E) = P(EnF)/P(E) = 75/75 =1.
E)
Answer: (E) 3
Question: In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?
(A) 67 kg
(B) 68 kg
(C) 69 kg
(D) 66.5 kg
(E) None of the above
Rationale: Let Arun’s weight be X kg.
According to Arun, 65 < X < 72.
According to Arun’s brother, 60 < X < 70.
According to Arun’s mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
∴ Required average = (66+67/2)=(133/2)=66.5kg.
Answer D
Answer: (D) 66.5 kg
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 345 cm2
(B) 384 cm2
(C) 156 cm2
(D) 657 cm2
(E) 887 cm2
Rationale: Area of a parallelogram
= base * height = 24 * 16
= 384 cm2
Answer: B
Answer: (B) 384 cm2
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 7.5 km apart, if they walk in the same direction?
(A) 12 hrs
(B) 14 hrs
(C) 15 hrs
(D) 17 hrs
(E) None
Rationale: Sol.
to be 0.5 km apart, they take 1 hour.
To be 7.5 km apart, they take [1/0.5 * 7.5] hrs = 15 hrs.
Answer C
Answer: (C) 15 hrs
Question: A man sells a horse for Rs.420 and loses something, if he had sold it for Rs.620, his gain would have been double the former loss. Find the cost price of the horse?
(A) 27
(B) 66.6
(C) 55.2
(D) 60.6
(E) 71
Rationale: CP = SP + 1CP = SP - g
420 + x = 620 - 2x
3x = 200 => x = 66.6
Answer:B
Answer: (B) 66.6
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
(A) 35 years
(B) 40 years
(C) 50 years
(D) 55 years
(E) none of these
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
ANSWER: B
Answer: (B) 40 years
Question: A and B complete a job in 6 days. A alone can do the job in 8 days. If B works alone, how many days will it take to complete the job?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: The rate of A and B is 1/6
A's rate is 1/8
B's rate is 1/6 - 1/8 = 1/24
B can complete the job in 24 days.
The answer is D.
Answer: (D) 24
Question: Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 1/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
(A) a) 7/10
(B) b) 2/3
(C) c) 11/15
(D) d) 23/30
(E) e) 4/5
Rationale: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:
• 3/5 of these, or 18 students, board the first bus
• there are 12 students left. 1/3 of these, or 6 students, board the second bus
• this bus breaks down, and 1/2 of the 6 students, or 3 students, board the first bus
• the first bus now contains 21 out of the original 30 students, so the answer is 21/30 = 7/10
Answer A
Answer: (A) a) 7/10
Question: n how many different ways can a group of 8 people be divided into 4 teams of 2 people each?
(A) 90
(B) 105
(C) 168
(D) 420
(E) 2520
Rationale: How many ways can you arrange the following:
T1 T1 T2 T2 T3 T3 T4 T4
That would be: 8!/(2!*2!*2!*2!)
Then also recall that we don't care about the differences between the teams, therefore
8!/(2!*2!*2!*2!*4!) = 105 ANS:B
Answer: (B) 105
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $55. What is the cost of the carpet, in dollars per square yard? (1 square yard = 3 square feet)
(A) xy/297
(B) 11xy/3
(C) 3xy/11
(D) 165/(xy)
(E) 297xy
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 3.
The price per square yard is 55 / (xy/3) = 165/(xy).
The answer is D.
Answer: (D) 165/(xy)
Question: A certain roller coaster has 6 cars, and a passenger is equally likely to ride in any 1 of the 6 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 6 times, what is the probability that the passenger will ride in each of the 6 cars?
(A) 3/1944
(B) 1/96
(C) 2/96
(D) 1/1944
(E) 1
Rationale: If he is to ride 6 times and since he can choose any of the 6 cars each time, total number of ways is
= 6 * 6 * 6 * 6 * 6 * 6
= 46656
Now the number of ways if he is to choose a different car each time is
= 6 * 5 * 4 * 3 * 2 * 1
= 720
So the probability is
= 720/46656 = 3/1944
Answer : A
Answer: (A) 3/1944
Question: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)?
(A) 98
(B) 100
(C) 0
(D) 99
(E) 97
Rationale: g(99) = 1*3*5*7*9*...*99
g(97) = 1*3*5*7*9*...*97
g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98
hence:A.
Answer: (A) 98
Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to q% of stall’s revenue and accounted for r% of sales of juice tetra packs. Which of the following expresses q in terms of r?
(A) 100r/(150 – r)
(B) 200r/(250-r)
(C) 200r/(300-r)
(D) 250r/(400-r)
(E) 300r/(500-r)
Rationale: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.
Total revenue= Revenue due to A + Revenue due to B
= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)
= r *1 + (100-r) *1.5
= r + (150-1.5r) --- (1)
2. But we know, revenue due to A = q %. of the total revenue --- (2)
3. To express q in terms of r we need to relate (1) and (2)
4. q % = r / ( r + (150-1.5r))
or q = 100r / 150-0.5r = 200r/(300-r)
C
Answer: (C) 200r/(300-r)
Question: The product of all the prime numbers less than 16 is closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: Product of Prime numbers less than 16 is 2*3*5*7*11*13
2*5=10 .
10*11*3*7*13 = 10*10*3*10*10 (approximately) ~ Product will be >10^4 <10^6 i.e. 10^5
E is the answer
Answer: (E) 10^5
Question: Can V and can В are both right circular cylinders. The radius of can V is twice the radius of can B, while the height of can V is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can V with the same brand of gasoline?
(A)  $1
(B)  $2
(C)  $4
(D)  $8
(E)  $16
Rationale: Let x be the radius of b and 2h be the height of B. Therefore, radius of V = 2x and height = h
Vol of b = 3.14*x^2*2h
Vol of a = 3.14*4x^2*h
cost to fill half of B = $4 --> cost to fill full B = $8
--> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16
Ans E
Answer: (E)  $16