mathewhe/aqua_rat huggingface dataset:
Question: The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 5 seconds than it was moving after 3 seconds?
(A) 4
(B) 9
(C) 15
(D) 20
(E) 63
Rationale: Given: z=s^2+2s for 0≤s≤7
z(3) = 3^2 + 2*3 = 15
z(5) = 5^2 + 2*5 = 35
Therefore z(7) - z(3) = 35 - 15 = 20 km/hr
Option D
Answer: (D) 20
Question: A college starts from 10 AM continues till 1:30 PM. In this duration there are five periods. If 5 minutes are provided before each period to leave the room and enter the other, then what is the duration of each period?
(A) 38 min
(B) 41 min
(C) 40 min
(D) 42 min
(E) 52 min
Rationale: before first period no need to leave the room and enter the room.
so,for 5 periods 4 times 5 minutes break will be provided. that is 20 mins.
10 A.M-1:30 P.M=210mins
210-20=190
therefore 190/5=38 mins.
ANSWER:A
Answer: (A) 38 min
Question: John has taken four (4) tests that have an average of 90. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
(A) 81
(B) 90
(C) 82
(D) 94
(E) 97
Rationale: Traditional Method:
Total scored till now 90*4=360
Total score to avg 87 in 6 tests = 87*6=522
Total to be scored on 2 tests = 522-360=162
Avg on 2 tests = 162/2 = 81
Answer: A
Answer: (A) 81
Question: If 2x + y = 7 and x + 2y = 10, then (x + y)/3 =
(A)  1
(B)  4/3
(C)  17/9
(D)  18/5
(E)  4
Rationale: We have two equations:
2x + y = 7
x + 2y = 10
Notice that something nice happens when we ADD them. We get:
3x + 3y = 17
Divide both sides by 3 to get:x + y = 17/3
So, (x + y)/3 =17/9
Answer: C
Answer: (C)  17/9
Question: A man buys an article for $20. and sells it for $25. Find the gain percent?
(A) 25%
(B) 50%
(C) 20%
(D) 15%
(E) 30%
Rationale: C.P. = $20
S.P. = $25
Gain = $5
Gain% = 5/20 *100 =25%
Answer is A
Answer: (A) 25%
Question: The distance between Delhi and Mathura is 185 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 10.50 a.m.
(B) 11.40 a.m.
(C) 10.30 a.m.
(D) 11.50 a.m.
(E) 1.40 a.m.
Rationale: D = 185 â€“ 20 = 165
RS = 20 + 25 = 45
T = 165/45 = 3 2/3 hours
8 a.m. + 3 hrs 40 min = 11.40 a.m.
ANSWER:B
Answer: (B) 11.40 a.m.
Question: A car runs at the speed of 50 km per hour when not serviced and runs at 60 kmph when serviced. After servicing the car covers a certain distance in 6 hours. How much time will the car take to cover the same distance when not serviced?
(A) 8 hours 12 minutes
(B) 6 hours 15 minutes
(C) 8 hours 15 minutes
(D) 7 hours 12 minutes
(E) None
Rationale: Explanation :
Time = 60*6 / 50 = 7 hours 12 mins
Answer – D
Answer: (D) 7 hours 12 minutes
Question: Answer: Option D
Explanation:
(A) 11 3/3
(B) 11 3/8
(C) 11 3/2
(D) 11 3/7
(E) 11 3/1
Rationale: (x – 5)/15 + x/20 = 1
x = 11 3/7 days
Answer: D
Answer: (D) 11 3/7
Question: A train 300 m long, running with a speed of 54 km/hr will pass a tree in?
(A) 17 sec
(B) 16 sec
(C) 20 sec
(D) 14 sec
(E) 12 sec
Rationale: Speed =54 * 5/18
= 15 m/sec
Time taken = 300 * 1/15
= 20 sec
Answer: C
Answer: (C) 20 sec
Question: A fort of 3000 soldiers has provisions for 75 days. After 15 days some of them left and the food was now enough for the same period of 75 days as before. How many of them left?
(A) 500
(B) 550
(C) 600
(D) 650
(E) 700
Rationale: 2000 ---- 50
3000 ---- 60
x ----- 75
x*75 = 3000*60
x=2400
3000
-------
600
Answer: C
Answer: (C) 600
Question: P can do a certain work in 9 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?
(A) 60/9
(B) 45/8
(C) 30/7
(D) 25/6
(E) 18/4
Rationale: Each day, P can do 1/9 of the work.
Each day, Q can do 1.6/9 of the work = 16/90 of the work
The time taken by B alone to complete the total work is 90/16 = 45/8 days.
The answer is B.
Answer: (B) 45/8
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 26,000 is made?
(A) 328897
(B) 122000
(C) 877888
(D) 277768
(E) 188871
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 26,000 is made = 96,000 + 26,000 = Rs. 1,22,000
Answer: B
Answer: (B) 122000
Question: The L.C.M. of two numbers is 60. The numbers are in the ratio 2 : 3. Then sum of the number is:
(A) 28
(B) 32
(C) 40
(D) 53
(E) 50
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 60 or x = 10.
The numbers are 20 and 30.
Hence, required sum = (20 + 30) = 50.
Answer: Option E
Answer: (E) 50
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=13. What is the value of f(6)?
(A) -1
(B) 0
(C) 1
(D) 2
(E) 4
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=13 then f(5)=13-5=8 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=8-6=2.
Answer: D.
Questions on funtions to practice:
Answer: (D) 2
Question: The sum of the present ages of a father and his son is 57 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Let the present ages of son and father be x and (57 - x) years respectively.
Then, (57 - x) - 6 = 4(x - 6)
51 - x = 4x - 24
x = 15
The son's age after 6 years will be 21.
The answer is E.
Answer: (E) 21
Question: Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ?
(A) 6000
(B) 5400
(C) 6200
(D) 7200
(E) 8200
Rationale: Investment Ratio = Profit Sharing Ratio.
Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6.
Giri share =
13200
× 6 / 11 = Rs.7200
Hari share =
13200 × 5 / 11 = Rs.6000
Option A
Answer: (A) 6000
Question: If mno < 0 and no > 0, which of the following must be positive?
(A)  xy
(B)  xz
(C)  (m^2)no
(D)  m(n^2)o
(E)  xy(z^2)
Rationale: Given that no is positive and mno is negative, you can say that m MUST be negative. As for n and o either they are both positive or both negative.
Option (C) has m^2 which is positive and no which is positive. So (C) must be positive.
Answer: (C)  (m^2)no
Question: The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
(A) 58
(B) 70
(C) 63
(D) 65
(E) 72
Rationale: 1/2bh=1/2(2a+1)(2a+6)
Now 4a-2=2a+6
2a=8 . a=4
Therefore,
A(0,0); B(0,14); C(9,14)
1/2*9*14=63
Answer: C
Answer: (C) 63
Question: On increasing the price of T.V. sets by 60%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
(A) 4
(B) 5
(C) 56
(D) 28
(E) 7
Rationale: Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(160 × 80) = Rs.12800
Increase% = 2800/10000 × 100 = 28%
Answer: D
Answer: (D) 28
Question: A box contains SEVEN bulbs out of which 3 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good?
(A) 32/33
(B) 35/36
(C) 37/39
(D) 34/39
(E) 34/35
Rationale: Required probability= 1- 3C3/7C3= 1 - 1/35= 34/35Answer:E
Answer: (E) 34/35
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) 3 1/4
(C) 4 1/3
(D) 6 1/2
(E) 8 1/2
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
ANSWER A
Answer: (A) 2 1/4
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
(A) 5/5
(B) 5/9
(C) 5/3
(D) 5/2
(E) 5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: (B) 5/9
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $312.50, what did the first person pay for it?
(A) $148
(B) $152
(C) $156
(D) $160
(E) $164
Rationale: 1.25*1.25*1.25 * original price = 312.5
(5/4)^3 * original price = 312.5
original price = 64*312.5 / 125 = $160
The answer is D.
Answer: (D) $160
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 6 hours?
(A) 675
(B) 750
(C) 1,800
(D) 1,350
(E) 7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(6 hours)= 1350 cans. The answer is D.
Answer: (D) 1,350
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs.500
(B) Rs.1190
(C) Rs.1200
(D) Rs.163
(E) Rs.897
Rationale: Explanation:
S.P. = 85% of Rs. 1400 = Rs(85/100*1400)=Rs.1190
ANSWER:B
Answer: (B) Rs.1190
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 51. What is that number
(A) 4
(B) 10
(C) 12
(D) 14
(E) 15
Rationale: Explanation:
=> 3(2x+9) = 51
=> 2x+9 = 17
=> x = 4
Answer: Option A
Answer: (A) 4
Question: 8 years ago there were 5 members in the Arthur's family and then the average age of the family was 36 years. Mean while Arthur got married and gave birth to a child. Still the average age of his family is same now. What is the age of his wife at the time of his child's birth was.If the difference between the age of her child and herself was 26 years?
(A) 16 years
(B) 26 years
(C) 36 years
(D) 66 years
(E) 86 years
Rationale: Since we know that the difference b/w the age of any two persons remains always constant, while the ratio of their ages gets changed as the time changes.
so, if the age of his child be x (presently)
Then the age of wife be x + 26 (presently)
Thus the total age = x + ( x + 26) = 32 [\inline \because 252-220 =32]
Rightarrow x = 3
age of her child is 3 years and her self is 29 years. Hence her age at the time of the birth of her child was 26 years.
Answer: B
Answer: (B) 26 years
Question: What percent of a day is 8 hours?
(A) 12%
(B) 12.5%
(C) 33.3%
(D) 11.3%
(E) None of these
Rationale: Explanation :
Solution: required percentage = (8/100 * 24) = 33.3%
Answer : C
Answer: (C) 33.3%
Question: A new savings account offers 7 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
(A) $80.00
(B) $84.40
(C) $360.00
(D) $6,360.00
(E) $6,427.35
Rationale: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.07) (1/2) = $210. (Note: the 6 months are “1/2” in the equation since 6% is a yearly rate, not a bi-yearly one).
Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,210. The interest earned during the final 6 months of the year is $6,210(.07)(1/2) = $217.35. Therefore, the total balance is the original amount ($6000) + $210 + $217.35 = $6,427.35.
The correct answer is E.
Answer: (E) $6,427.35
Question: One used-car salesperson receives a commission of $ 600 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
(A) $ 5,000
(B) $ 6,000
(C) $ 8,000
(D) $ 10,000
(E) $ 12,000
Rationale: This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
E
Answer: (E) $ 12,000
Question: In how many ways can the letters C, A, A, R, W, A be arranged so that the three A's are not next to each other?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 128
Rationale: 1 C
3 A
1 R
1 W
Number of ways these letters can be arranged = 6!/3! (3! to account 3 same As) = 120
Consider 3 As as 1 entity and thus the number of arrangements for (AAA)CRW = 4! = 24
Total allowed cases = 120-24 =96
D is the correct answer.
Answer: (D) 96
Question: Which of the following is NOT a prime number?
(A) 21
(B) 31
(C) 41
(D) 11
(E) 51
Rationale: Ans is A
A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number
Answer: (A) 21
Question: If 4 men working 10 hours a day earn Rs. 600 per week, then 9 men working 6 hours a day will earn how much per week?
(A) Rs 840
(B) Rs 320
(C) Rs 810
(D) Rs 680
(E) None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 600 : x
hence 4 * 10 *x = 9 * 6 * 600
or x = 9*6*600/ 4*10 = 810
Answer : C
Answer: (C) Rs 810
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:18
(C) 18:10
(D) 18:12
(E) 18:14
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A
Answer: (A) 18:11
Question: Two vertical ladders length of 6 m and 11 m are kept vertically at a distance of 12 m. Find the top distance of both ladders?
(A) 22
(B) 27
(C) 13
(D) 19
(E) 17
Rationale: So distance between the top points = AD = 122+52−−−−−−−√=13122+52=13
So in paper B he did well.
Answer:C
Answer: (C) 13
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 7th position from either end of the row.
Can you find out how many girls are practicing together?
(A) 4
(B) 9
(C) 13
(D) 16
(E) 18
Rationale: As judith is 7th from either end of the row, it means that 6 girls are on one of her sides and 6 are present on the other.
6 + 6 + 1(judith herself) = 13.
Hence, 13 girls are practicing the dance together.
correct answer is C)13
Answer: (C) 13
Question: If a shoppkepper has two type of rice. One at Rs 50/- and another at Rs 80/- . He mixed the rice at 2:1 ratio. Find the average price of the mixture.
(A) 75
(B) 65
(C) 60
(D) 50
(E) 55
Rationale: Ratio = 2x:x, Total quantity=50*2x+80*x=180x
Average price=180x/(2x+x)=60
ANSWER:C
Answer: (C) 60
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 480 m, its area is?
(A) 150
(B) 240
(C) 277
(D) 261
(E) 281
Rationale: 5x + 12x + 13x = 480 => x = 16
a = 80, b = 192, c = 208
S = (80 + 192 + 208)/2 = 240
Answer: B
Answer: (B) 240
Question: Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: For these type of questions, use the formula 7x/4 =[sum of ages] where x is the age of elder.
2)7x/3 = [sum of ages] whr x is the age of younger. Here peter is elder is 7x/4=35. Solve you get x= 20
ANSWER:A
Answer: (A) 20
Question: Tom wants to buy items costing $25.35, $80.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.
(A) 8 hours
(B) 48 hours
(C) 38 hours
(D) 18 hours
(E) 33 hours
Rationale: $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $80.69 + $85.96 = $192 total needed
$192 ÷ $5.85 = 32.8... rounds to 33 hours
correct answer E
Answer: (E) 33 hours
Question: If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 1/6 = 0.1666666... (a repeating pattern one digit long)
A
Answer: (A) 1
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(A) 4.5
(B) 4.6
(C) 4.7
(D) 4.8
(E) None of the above
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.4 × 2) + (3.85 × 2)]
= 23.70 – (6.8 + 7.7)
= 23.70 – 14.5 = 9.20
∴ Required average = (9.2⁄2) = 4.6
Answer B
Answer: (B) 4.6
Question: If A got 60 marks and B got 30 marks, then what percent of A's mark is B's mark?
(A) A)60%
(B) B)80%
(C) C)65%
(D) D)50%
(E) of these
Rationale: A's marks = 60 ; B's marks = 30.
Let x% of A = B => x/100 * 60 = 30
=> x = (30 * 100)/60 = 50
B's marks is 50% of A's marks.
ANSWER:D
Answer: (D) D)50%
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
(A) 1677
(B) 1683
(C) 2523
(D) 3363
(E) 6546
Rationale: L.C.M. of 5, 6, 7, 8 = 840. Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683. Answer : B
Answer: (B) 1683
Question: How many 6 letter words ( with or without meaning) can be formed using all the following 5 letters U,P,Q,R,S,and T so that letter P is to the left of letter R?
(A) 160
(B) 400
(C) 300
(D) 360
(E) 320
Rationale: Two positions can be selected out of 5 positions in 6C2 ways = 15 ways.
And the remaining 4 letters can be placed in 4 posions in 4! Ways = 24 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 4 letters can be arranged
Final Answer = 24 x 15 = 360 ways
D
Answer: (D) 360
Question: A train after traveling 50 kms from A meets with an accident and proceeds at 4/5th of the former speed and reaches B, 45 min late. Had the accident happened 20 kms further on, it would have arrived 12 mins sooner. Find the original speed and the distance.
(A) 5 hrs 30 mins
(B) 5 hrs 33 mins
(C) 5 hrs 36 mins
(D) 4 hrs 33 mins
(E) 6 hrs 33 mins
Rationale: speed = 25 kmph and distance = 125 kms.
scheduled time = 5 hrs.
Time taken in first case = 50/25 + 75/20 = 2+3.75 hrs = 5.75 hrs = 5 hrs 45 min
in second case, time taken = 70/25 + 55/20 = 111/20 hrs = 5 hrs 33 mins
ANSWER:B
Answer: (B) 5 hrs 33 mins
Question: How long does a train 110 m long traveling at 36 kmph takes to cross a bridge of 170 m in length?
(A) 28
(B) 16.0
(C) 16.4
(D) 16.8
(E) 16.1
Rationale: D = 110 + 170 = 280 m
S = 36 * 5/18 = 10
T = 280 * 1/10 = 28 sec
Answer: A
Answer: (A) 28
Question: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person reaches into the bag and picks out only purple jellybeans, how many jellybeans would the person have to pick out in order to double the probability that a jellybean picked out of the bag at random would be a green jellybean?
(A) 5
(B) 15
(C) 19
(D) 24
(E) 25
Rationale: Chances of picking a green at present = 15 / (26 + 15 + 9) = 15/50 = 3/10
So required is double that chance = 2 * 3/10 = 3/5
since only purple are removed, the new count be x, 3/5 = 15 (x + 15 + 9)
solving for x gives x = 1.
So 26 -1 = 25 purple jellybeans needs to be removed.
Answer is E
Answer: (E) 25
Question: Carmelo and LeBron participate in a nine-person footrace on the basketball court during All-Star Weekend. If all nine contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
(A) 504020
(B) 181440
(C) 720
(D) 120
(E) 42
Rationale: 9! = 362880
362880/2=181440 half the time carmelo is in front, vice versa
Answer:
(B) 181440
Answer: (B) 181440
Question: A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time E it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
(A)  0.8(80 – y)
(B)  0.8 + 0.0025y
(C)  80/y – 1.25
(D)  80/1.25y
(E)  80 – 0.25y
Rationale: This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.
Which means finishing all houses at normal rate E=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.
7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9.
Answer: (B)  0.8 + 0.0025y
Question: A rectangular block 12cm by 36cm by 60cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
(A) 6
(B) 10
(C) 15
(D) 40
(E) 22
Rationale: Volume of the block = 12*36*60 = 25920 cm^3
Side of the largest cube = H.C.F of 12,36,60 = 12cm
Volume of the cube = 12*12*12= 1728 cm^3
Number of cubes = 25920/1728 = 15
Answer is C
Answer: (C) 15
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many R cents does a liter of kerosene cost? [One dollar has 100 cents.]
(A)  0.33
(B)  0.44
(C)  0.55
(D)  44
(E)  55
Rationale: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $
Just multiply by 100, Answer R= 44.D
Answer: (D)  44
Question: In year Y imported machine tools accounted for 70 percent of total machine-tools sales in the United States, and Japanese imports accounted for 50 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 3.86x
(B) 4.86x
(C) 5.86x
(D) 2.86x
(E) 6.86x
Rationale: Sales of imported tools = 70% of the total sales = 0.70*{total} = 7{total}/10;
Sales of Japanese tools = 50% of the sales of imported tools = 5/10*7{total}/10 = 35{total}/100
Since the sales of of Japanese tools was x, then 35{total}/100 = x -->35 {total} = 100x
{total} = 100/35 *x = 2.86 x
Answer: D
Answer: (D) 2.86x