mathewhe/aqua_rat huggingface dataset:
Question: The positive difference of the fourth powers of two consecutive positive integers must be divisible by
(A) one less than twice the larger integer
(B) one more than twice the larger integer
(C) one less than four times the larger integer
(D) one more than four times the larger integer
(E) one more than eight times the larger integer
Rationale: Using Picking Numbers for this, Let the two positive integers be 2, 3
3^4−2^4=81−16=65
(A) one less than twice the larger integer = 2(3) - 1 = 5 --> 65 is divisible by 5
(B) one more than twice the larger integer = 2(3) + 1 = 7 --> ruled out
(C) one less than four times the larger integer = 4(3) - 1 = 11 --> ruled out
(D) one more than four times the larger integer = 4(3) + 1 = 13 --> 65 is divisible by 13
(E) one more than eight times the larger integer = 8(3) + 1 = 25 --> ruled out
Another set of numbers, 3,4
4^4−3^4=256−81=175
(A) one less than twice the larger integer = 2(4) - 1 = 7 --> 175 is divisible by 7
(D) one more than four times the larger integer = 4(4) + 1 = 17 --> ruled out
Answer : A
Answer: (A) one less than twice the larger integer
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) Rs.41
(B) Rs.48
(C) Rs.40
(D) Rs.42
(E) Rs.92
Rationale: Explanation:
800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C
Answer: (C) Rs.40
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) 277
(B) 299
(C) 125
(D) 99
(E) 22
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
Answer:C
Answer: (C) 125
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 17 a.m
(B) 10 a.m
(C) 70 a.m
(D) 16 a.m
(E) 18 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: (B) 10 a.m
Question: How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 12km/hr?
(A) 52sec
(B) 45sec
(C) 60sec
(D) 25sec
(E) 39sec
Rationale: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 50*4 = 200m
Time taken = 200*3/10 = 60sec
Answer is C
Answer: (C) 60sec
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 5%
(B) 3 1/2%
(C) 4%
(D) 5 1/2 %
(E) 6%
Rationale: 150 = (750*5*R)/100
R = 4%
Answer :C
Answer: (C) 4%
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 228km apart?
(A) 1 1/4 hours
(B) 2 1/3 hours
(C) 4hours
(D) 3 3/4 hours
(E) 6hours
Rationale: To be (18+20) km apart, they take 1 hour
To be 228 km apart, they take 1/38 * 228 = 6 hrs
Answer is E
Answer: (E) 6hours
Question: Twenty years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
(A) 120
(B) 76
(C) 108
(D) 105
(E) 86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-20)=3 (x-20)
x=40.
Required sum =(2x+x)=3x=120 years.
Answer is A
Answer: (A) 120
Question: The total of company C's assets in 1994 was 300% greater than the total in 1993, which in turn was 200% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
(A) 7N
(B) 8N
(C) 9N
(D) 12
(E) 20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 200% GREATER, which means 1992 PLUS 200% of 1992:
$100 + 2x$100 = $100 + $200 =$300
In 1994, the total assets were 300% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$300 + 3x$300 = $300 + $900 =$1200
This is 12 times the 1992 number, so the correct answer is 12N.
D
Answer: (D) 12
Question: Zada has to distribute 15 choclates among 5 of her children Sana,ada,jaya,amir and farhan. She has to make sure that sana gets at least 3 and ada at most 6 choclates. In how many ways can this be done?
(A) 495
(B) 77
(C) 417
(D) 435
(E) 455
Rationale: (3,1,11)=165
(4,1,10)=120
(5,1,9)=84
(6,1,8)=56
ANSWER:A
Answer: (A) 495
Question: Meg and Bob are among the 6 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
(A) 24
(B) 30
(C) 60
(D) 90
(E) 360
Rationale: Total # of ways the race can be finished is 6!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 6!/2=360.
Answer: E
Answer: (E) 360
Question: A number when divided by 219 gives a remainder 32, what remainder will be obtained by dividing the same number 12?
(A) 7
(B) 11
(C) 9
(D) 2
(E) 3
Rationale: Explanation:
219 + 32 = 251/12 = 9 (Remainder)
Answer: B
Answer: (B) 11
Question: To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of P dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
(A) P/T
(B) P/(T-S)
(C) SP/(T-S)
(D) SP/T(T-S)
(E) P(T-S)/T
Rationale: Since no absolute values are given in the question we can replace the given parameters with assumed numbers,
Let Total colleagues be 100 (T)
Let total contribution be 700 (P) (point to note is that its total cost not per person)
Those who dont pay are S (30)
Per person cost = P/T = 700/100 = 7
So cost for those who failed to pay = (P/T) * S = SP/T = 30*7=210
The equation for people who would bear the total cost after S people fail = (T-S)=70
There fore the solution is (SP/T)/ (T-S) = SP/T(T-S) = 210/70
Answer D
Hope this helps !!!
Answer: (D) SP/T(T-S)
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.78 days
(C) 3.65 days
(D) 3.77 days
(E) 5.75 days
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer:A
Answer: (A) 3.75 days
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 2997
(B) 2776
(C) 2988
(D) 1640
(E) 7612
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer: D
Answer: (D) 1640
Question: If a car went the first third of the distance at 10 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?
(A) 36 kmh
(B) 19 kmh
(C) 42 kmh
(D) 44 kmh
(E) 50 kmh
Rationale: Assume D/3 = 240 (this number is convenient because it is divisible by 10, 24 and 48)
So:
240 = 10*T1 = 24 hrs
240 = 24*T2 = 10 hrs
240 = 48*T3 = 5 hrs
T = T1 + T2 + T3 = 39 hrs
D = RT
(240*3) = R*39
R = 19
ANSWER: B
Answer: (B) 19 kmh
Question: The difference between compound interest and simple interest on an amount of $15,000 for 2 years is $96. What is the rate of interest per annum?
(A) 6%
(B) 7%
(C) 9%
(D) 8%
(E) 5%
Rationale: [15000 x (1 + R/100)^2 - 15000] - [(15000 x R x 2)/100] = 96
==> 15000[(1 + R/100)^2 - 1 - 2R/100] = 96
==> 15000[((100 + R)^2 - 10000 - (200 x R))/10000] = 96
==> R^2 = (96 x 2)/3 = 64
==> R = 8. Rate = 8%
Answer D)8%
Answer: (D) 8%
Question: Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 2 hours and machine B produces k bottles in 3 hours. How many hours does it take machines A and B , working simultaneously , to produce 15k bottles?
(A) 10
(B) 15
(C) 12
(D) 30
(E) 18
Rationale: x rate = k/2
y rate = k/3
k/2 + k/3 = 15k / T
solving T = 18
Answer E
Answer: (E) 18
Question: The perimeter of a semi circle is 126 cm then the radius is?
(A) 22
(B) 28
(C) 98
(D) 24.5
(E) 13
Rationale: 36/7 r = 126
=> r
= 24.5
Answer: D
Answer: (D) 24.5
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 60 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip?
(A) (180-x)/2
(B) (x+60)/4
(C) (300-x)/5
(D) 12,000/(300-x)
(E) 12,000/(x+200)
Rationale: D....
X% traveeled at 60 mph
100-X% traveeled at 40 mph
total timt taken = x/60 +(100-x)/40 = (300-x)/120
Total distance = x+(100-x) = 100
Av speed = Tot Dis/Time Taken which is D
Answer: (D) 12,000/(300-x)
Question: Martha has 5 dogs and 6 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?
(A) 22
(B) 9
(C) 10
(D) 18
(E) 20
Rationale: 5 dogs, 4 cats; park/barber shop
1 dog - 2 options - either park or barber shop, so, 5 dogs - 10 options and 6 dogs - 12 options.
Total = 22 options.
A
Answer: (A) 22
Question: A boy runs 200 metres in 48 seconds. What is his speed ?
(A) 10 km/hr
(B) 15 km/hr
(C) 11 km/hr
(D) 12 km/hr
(E) 14 km/hr
Rationale: 200/48 * 18/5 = 15 km/hr
ANSWER:B
Answer: (B) 15 km/hr
Question: Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?
(A) $27,000
(B) $30,000
(C) $33,000
(D) $36,000
(E) $63,000
Rationale: Plug in numbers...
Say on the lowest side we have $10,000 & the highest, $40,000
$10,000 x .10 = $1,000 --> New low side = $11,000
$40,000 x .10 = $4,000 --> New high side = $44,000
New range --> $44,000-$11,000 = $33,000
Correct answer is C
Answer: (C) $33,000
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/8
(B) 80/7
(C) 80/1
(D) 80/3
(E) 80/4
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
Answer: (B) 80/7
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
(A) 123
(B) 127
(C) 235
(D) 305
(E) 505
Rationale: Explanation:
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127. Answer: B
Answer: (B) 127
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
(A) 285m
(B) 207m
(C) 280m
(D) 270m
(E) 290m
Rationale: Speed =72 x5/18 m/sec= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
x + 250/26=20
x + 250 = 520
x = 270m
Answer D
Answer: (D) 270m
Question: 6^7 is equal to which of the following?
(A) 279,936
(B) 148,752
(C) 149,660
(D) 510,662
(E) 511,608
Rationale: A is the correct answer. We do not really need to calculate it. The last digit for 6^7 will be 6. Hence A is the correct answer
Answer: (A) 279,936
Question: The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is?
(A) 0.35 cm2
(B) 17.5 cm2
(C) 8.75 cm2
(D) 55 cm2
(E) 50 cm2
Rationale: Explanation:
(5 * 3.5)/2 = 8.75
ANSWER IS C
Answer: (C) 8.75 cm2
Question: The perimeter of one square is 48 cm and that of another is 28 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√4
(B) 13√2
(C) 23√2
(D) 13.9√2
(E) 13√9
Rationale: 4a = 48 4a = 28
a = 12 a = 7
a2 = 144 a2 = 49
Combined area = a2 = 193 => a = 13.9
d = 13.9√2
Answer: D
Answer: (D) 13.9√2
Question: A family consists of two grandparents, two parents and 6 grandchildren. The average age of the grandparents is 60 years, that of the parents is 30 years and that of the grandchildren is 5 years. What is the average age of family?
(A) 5/7years
(B) B)21
(C) C)30
(D) D)33
(E) E)35
Rationale: Required average
= (60 x 2 + 30 x 2 + 5 x 6 )/(2 + 2 + 6)
= (120 + 60 + 30)/10
= 210/10
= 21 years.
Answer is B
Answer: (B) B)21
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (2,2), (8,2), (3,5), (9,5) ?
(A) 18.
(B) 28.
(C) 35.
(D) 49.
(E) 52.
Rationale: Delta x will give us the dimension of one side of the parallelogram = 8-2= 6 unit
Delta y will give us the dimension of the other side of parallelogram = 5-2=3 unit
Area of parallelogram = 6*3 = 18
ANSWER IS A
Answer: (A) 18.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 20 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 88
(C) 48
(D) 99
(E) 72
Rationale: Relative speed = 20 + 30 = 50 km/hr.
50 * 5/18 = 125/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9 /125 = 72 sec
Answer: E
Answer: (E) 72
Question: If six machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?
(A) 45
(B) 60
(C) 72
(D) 80
(E) 100
Rationale: using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have
6*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
4=10/3*x
x=6/5 hour
so 72 minutes
ANSWER:C
Answer: (C) 72
Question: Carl is facing very difficult financial times and can only pay the interest on a $8,000 loan he has taken. The bank charges him a quarterly compound rate of 5%. What is the approximate interest he pays annually?
(A) $1200
(B) $2000
(C) $2150
(D) $2500
(E) $1600
Rationale: Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.
The bank charges him a quarterly compounded ANNUAL rate of 20%.
Here you find per quarter rate as (20/4)% = 5%
I have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5% annual rate of interest, it is apparent that the intent was a 5% quarterly rate. So the bank charges 5% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 5% of 8,000 = $1600 as our answer.
But since, the interest is compounded, it will be a bit more than $1600. Option (E) looks correct.
Answer: (E) $1600
Question: A man can row a boat at 24 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 100 km downstream?
(A) 24/8
(B) 25/8
(C) 23/8
(D) 21/8
(E) 20/8
Rationale: Speed downstream = 24 + 8 = 32 kmph.
Time required to cover 60 km downstream = d/s = 100/32
= 25/8 hours.
Answer: B
Answer: (B) 25/8
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 600. What is the manager's monthly salary ?
(A) Rs.16003
(B) Rs.16029
(C) Rs.11288
(D) Rs.14100
(E) Rs.16011
Rationale: Explanation:
Manager's monthly salary Rs. (2100 * 21 - 1500 * 20) = Rs.14100.
Answer: D
Answer: (D) Rs.14100
Question: A box contains 50 balls, numbered from 1 to 50. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Answer: (A) 1/4
Question: In the first week of last month, Company X realized an average wholesale profit of $2856 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?
(A) $3
(B) $4
(C) $7
(D) $13
(E) $51
Rationale: The key operator that everyone seems to have missed is the average. The average profit of $2856 per day is equivalent to a total profit of $19992 for the whole week.
Therefore, the difference between sale price and cost per unit is equal to $19992, which is divisible by all of the answer choices, except for 13.
So, D is the answer.
Answer: (D) $13
Question: In what time will a train 100 m long cross an electric pole, it its speed be 126 km/hr?
(A) 2.5
(B) 2.9
(C) 2.4
(D) 2.85
(E) 2.1
Rationale: Speed = 126 * 5/18 = 35 m/sec
Time taken = 100/35
= 2.85 sec.
Answer:D
Answer: (D) 2.85
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 78 2/11%
(B) 18 2/11%
(C) 58 2/11%
(D) 18 2/11%
(E) 68 2/11%
Rationale: Explanation:
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer:B
Answer: (B) 18 2/11%
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 2
(II) y = 4
(III) x + y = 0
(A) I
(B) II
(C) III
(D) I and II
(E) II&III
Rationale: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
B
Answer: (B) II
Question: A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually?
(A) 4.5
(B) 3.5
(C) 3
(D) 2
(E) 1
Rationale: We can form equations as following:
Initial amount = P, Total amount after interest = T, Interest per year = I
T = P+I
Given T1 = P+2I = 1400
T2 = P+ 5I = 2000
From this we get, P = 1000I = 200 $
Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)
consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$.
To get a 440 $ compound interest the duration have to be > 1 year and < 3 years.
Only option fitting : Option D.
Answer: (D) 2
Question: A sells a radio to B at a gain of 10% and B sells to c at a gain of 5%.If C pays Rs.462 for it,what did it cost to A?
(A) 200
(B) 300
(C) 100
(D) 400
(E) 500
Rationale: Solution
C.P of radio to C=C.P of radio to A * (1+10/100)(1+5/100)
=> 462=C.P of radio to A * 110/100 *105/100
=>C.P of radio to A=(462*100*100)/(105*110)
=400
Answer D
Answer: (D) 400
Question: The average weight of man, women and children is 45 kg. If the average weight of man and women be 40 kg and that of women and children be 43 kg, thenthe weight of women?
(A) 29
(B) 30
(C) 31
(D) 35
(E) 36
Rationale: Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
C
Answer: (C) 31
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 11
(B) 18
(C) 16
(D) 88
(E) 12
Rationale: 10 * 15 + 36 – 26 = 160/10 = 16.Answer: C
Answer: (C) 16
Question: A pharmaceutical company received $7 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 76%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales = 7/20
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (7/20) x 60 = 21
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 9 and 5 into our percent change formula:
(new – old)/old x 100
[(5 – 21)/21] x 100
-1600/21 x 100
At this point we can stop and consider the answer choices. Since we know that 1600/21 is just a bit less than ½, we know that -1600/21 x 100 is about a 76% decrease.
Answer E.
Answer: (E) 76%
Question: A man can row downstream at the rate of 30 Kmph and upstream at 10 Kmph. Find the man’s rate in still water and rate of current?
(A) 10
(B) 8.0
(C) 9.5
(D) 9.0
(E) 8.25
Rationale: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (30 + 10) = 20 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (30 - 10)
= 1/2 (20)
= 10 kmph
Answer is A.
Answer: (A) 10
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
Rationale: 21-12 < no of hrs < 21-6
9< no of hrs < 17.
D
Answer: (D) 12
Question: If w and u are two positive integers and w/u = 2.20, then w can equal which one of the following?
(A)  15
(B)  28
(C)  33
(D)  30
(E)  23
Rationale: w/u = 2.20 = 220/100 = 11/5
So, p COULD equal 33
Answer: C
Answer: (C)  33
Question: Out of eight consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
(A) 3150
(B) 3360
(C) 3580
(D) 3720
(E) 3940
Rationale: 8C2 x 3C3 x 5! = 3360
The answer is B.
Answer: (B) 3360
Question: A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction W of the selected films are in color?
(A) 1/130
(B) 1/5
(C) 3/13
(D) 10/13
(E) 30/31
Rationale: It's y/xpercentnot y/x.
If x=20 and y=10. Then:
20x=400 black-and-white films;
6y=60 color films.
y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose W 60/62=30/31 of the selected films.
Answer: E.
Answer: (E) 30/31
Question: he average of 25 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 24
(D) 19
(E) 8
Rationale: Average of 25 numbers = 0.
Sum of 25 numbers (0 x 25) = 0.
It is quite possible that 24 of these numbers may be positive and if their sum is a the 25th number is (-a).
Answer: Option C
Answer: (C) 24