mathewhe/aqua_rat huggingface dataset:
Question: If the ratio of the roots of the equation x2 – 2ax + b = 0 is equal to that of the roots x2 – 2cx + d = 0, then:
(A) a2b = c2d
(B) a2c = b2d
(C) a2d = c2b
(D) d2 b = c2 a
(E) none
Rationale: x^2-2ax+b=0 for this eqn..roots r....R1=2a/1,R2=b/1;
x^2-2cx+d=0 for this eqn ..roots r...R3=2c/1,R4=d;
As per question ,2a/b=2c/d
=>2ad=2bc
ANSWER:C
Answer: (C) a2d = c2b
Question: Which of the following CAN be the least common multiple of two positive integers 5 and 25?
(A) 5
(B) 10
(C) 15
(D) 25
(E) 20
Rationale: LCM of 5, 25 is 25
Answer : D
Answer: (D) 25
Question: A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
(A) $200
(B) $250
(C) $100
(D) $350
(E) $875
Rationale: Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 )
$30000 is 30% of total amount.
So total amount = 30000 * 100/60
Remaining amount is 70% of total amount.
70% of total amount = 30000 * (100/60) * (70/100) = 35000
This amount has to be divided by 40 ( remaining people are 40 )
So per head amount is 35000/40 = $875;
ANSWER:E
Answer: (E) $875
Question: Aqua regia is a mixture containing 50 per cent concentrated HCL and 70 per cent concentrated HNo3 in the ratio 1 : 3 respectively. Aqua regia is to be formed with 15 l of HCl of 80 percent concentration and 56 l of HNO3 of 90 per cent concentration by adding water as a diluting agent. Another mixture ’X’ having 40 percent concentrated HCL and 30 percent concentrated H2SO4 in the ratio 5 : 7 respectively is added to the Aqua regia to form a solution of 111 l. Find the ratio of HCL to water in the solution. Only water is used as a diluting agent
(A) 3 : 8
(B) 4 : 7
(C) 1 : 3
(D) 2 : 5
(E) 5 : 2
Rationale: 80 % concentrated HCL is to be diluted to form a 50% concentrated HCL solution.
The quantity of water to be added to the l5 l solution is i.e 5:3
Thus, (3/5) X 15 = 9
9 litres of water is added to HCL solution Similarly 16 l of water is added to 90%
concentrated solution of HNO3 to dilute it to 70% concentration.
The total quantity of HCL and HNO3 solutions are 24 l and 72 l respectively and that of the
aqua regia formed is 96 I and that of water in it is 33.6 l
The quantity of mixture ’X’ is 11 I - 96 = 15.
In the mixture X, the quantity of HCL is [(5/12) X 0.6 + (7/12) X 0.7] X 15=(0.25 + 0.41) X 15 = 9.91.
The required ratio is (12 + 2.5)/(33.6 + 9.9) = 14.5/43.5 = 1/3
ANSWER:C
Answer: (C) 1 : 3
Question: JOHN and ANDREW can finish John work 30 days if they work together. They worked together for 20 days and then ANDREW left. JOHN finished the remaining work in another 20 days. In how many days JOHN alone can finish the work?
(A) 30 days
(B) 60 days
(C) 70 days
(D) 80 days
(E) 90 days
Rationale: Amount of work done by JOHN and ANDREW in 1 day = 1/30
Amount of work done by JOHN and ANDREW in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
JOHN completes 1/3 work in 20 days
Amount of work JOHN can do in 1 day = (1/3)/20 = 1/60
=> JOHN can complete the work in 60 days
B
Answer: (B) 60 days
Question: What is the remainder when 1271 * 1275 * 1279 *1285 is divided by 12?
(A)  0
(B)  1
(C)  11
(D)  3
(E)  7
Rationale: 1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 5)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-5)(1) = 15. Thus the question becomes: what is the remainder upon division of 15 by 12? The answer to this question is 3
Answer: D.
Answer: (D)  3
Question: Under whose chairmanship did RBI constitute a Working Group for making balance of payments manual?
(A) Anand Sinha
(B) Harun Rashid Khan
(C) Kamalesh Chandra Chakrabarty
(D) Deepak Mohanty
(E) Kamalesh Chandra Chakrabarty2
Rationale: Explanation:
Deepak Mohanty is the highest ranked economist in Reserve Bank of India.
ANSWER: D
Answer: (D) Deepak Mohanty
Question: Jim and Cara begin running at the same time and they start at the same place on a straight path. Jim runs at 6 miles per hour, and Cara runs at 5 miles per hour. After 30 minutes, Jim stops to stretch. If it takes Jim 18 minutes to stretch and Cara continues to run during this time, how many minutes will it take Jim to catch up to Cara?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: In 30 minutes, Jim runs 3 miles.
In 48 minutes, Cara runs 4 miles.
Jim can catch Cara at a rate of 1 mile per hour.
Since Cara is ahead by 1 mile, it will take Jim 1 hour = 60 minutes to catch Cara.
the answer is C.
Answer: (C) 60
Question: John bought a 1-year, $20,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
(A) $2150
(B) $2050
(C) $2250
(D) $2350
(E) $2400
Rationale: 10 percent compounded semiannually --> 5% in 6 moths.
For the first 6 moths interest was 5% of $20,000, so $1000;
For the next 6 moths interest was 5% of $21,000, so $1050
Total interest for 1 year was $1000+$1050=$2050
Answer : B
Answer: (B) $2050
Question: If a survey shows that 30 citizens out of a sample of 300 support a particular Senate bill, what percent of the sample does not support the bill?
(A)  90%
(B)  64%
(C)  72%
(D)  82%
(E)  86%
Rationale: 30 out of 300 supports the bill and we are asked to find the percent who the does not support the bill.
30 out of 300 supports the bill = 10 out of 100 supports the bill ( taking in % terms )
14 out of 100 supports the bill = 10 (100-10) doesn't support the bill
So, answer is (A) 90%
Answer: (A)  90%
Question: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/5 hours. How many hours would it take Albert to paint 3n rooms by himself?
(A) 7
(B) 9
(C) 11
(D) 25
(E) 15
Rationale: rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time
Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
5*5 = 3n
25 = 3n.
Answer is D
Answer: (D) 25
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $39,375, how much profit did the business make?
(A) $54,000
(B) $57,000
(C) $60,000
(D) $63,000
(E) $66,000
Rationale: Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = $39,375
P = $63,000
The answer is D.
Answer: (D) $63,000
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.99 km
(B) 5.88 km
(C) 5.76 km
(D) 5.83 km
(E) 9.44 km
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Answer: (C) 5.76 km
Question: Last year the price per share of Stock Y increased by m percent and the earnings per share of Stock Y increased by n percent, where m is greater than n. By what percent did the ratio of price per share to earnings per share increase, in terms of m and n?
(A) 100 (m-n)%
(B) 100*(m-n)/(100+n) %
(C) m/n%
(D) 100 (m+n)%
(E) 100*(m+n)/(100+m)%
Rationale: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+m/100) and the new earning is: E*(1 + n/100)
The new P/E is: (1+m/100)P/(1+n/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+m/100)/(1+n/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(m-n)/(100+n) %
Answer : B
Answer: (B) 100*(m-n)/(100+n) %
Question: In Net's hair salon 45% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?
(A) 5%
(B) 9%
(C) 12%
(D) 15%
(E) 21%
Rationale: Let a total of 100 people visit the salon.
Total = 100
Dye hair blonde (A) = 45 % = 45
Dye Eyebrows blonde (B) = 36% = 36
Straighten Hair (C) = 35% = 35
Neither = 20% = 20
All Three = 12% =12
Total = A+B+C - (Sum of Exactly Two group overlaps) - 2*(All three) + Neither
100 = 45+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20
(Sum of Exactly Two group overlaps) = 9
%of customers coming for exactly 2 of the 3 procedures = 12%
C
Answer: (C) 12%
Question: If an item that originally sold for t dollars was marked up by r percent and then discounted by s percent, which of the following expressions represents the final price of the item?
(A) (10,000t + 100t(r – s) – rst)/10,000
(B) (10,000t + 100t(s – r) – rst)/10,000
(C) (100t(r – s) – rst)/10000
(D) (100t(s – r) – rst)/10000
(E) 10000 /(r – s)
Rationale: Assume t=100, r=10, s=10. So final price is 99. Now put these value each option. Only option A will give right answer.
Answer: (A) (10,000t + 100t(r – s) – rst)/10,000
Question: The present worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. Then banker’s gain is:
(A) 16
(B) 18
(C) 20
(D) 21
(E) None
Rationale: Sol.
B.G. = (T.D.)² / P.W. = Rs.[160 * 160 / 1600] = Rs. 16.
Answer A
Answer: (A) 16
Question: Look at this series: 53, 53, 46, 46, 39, 39, ... What number should come next?
(A) A)12
(B) B)14
(C) C)27
(D) D)32
(E) E)86
Rationale: In this series, each number is repeated, then 7 is subtracted to arrive at the next number.
Answer: D
Answer: (D) D)32
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 4 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour?
(A) 38
(B) 47
(C) 50
(D) 53
(E) 54
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 4 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 450/9 = 50, so the median is also 50, and that is the amount eaten in the 5th hour. We need to add 4 to find the total eaten in the next hour, so the answer is 54
option E.
Answer: (E) 54
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 47 years. What will be the age of the B ten years hence?
(A) 94
(B) 23
(C) 28
(D) 96
(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 = 47 => b + c = 94 --- (2)
Answer: A
Answer: (A) 94
Question: In a certain sequence, the first term is 7, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
(A) 13/8
(B) 39/24
(C) 8/5
(D) 5/8
(E) 8/13
Rationale: let five terms in the sequence be a,b,c,d,e
a=7
b= 1+1/7=8/7
c=1+7/8= 15/8
d= 1+8/15 = 24/15
e= 1+15/24 = 39/24
hence answer should be B.
Answer: (B) 39/24
Question: An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period?
(A) (2d)/3
(B) (3d)/4
(C) (4d)/3
(D) (3d)/2
(E) (8d)/3
Rationale: 600 dollars in 2 years means 300 dollars in 1 year.
To get 2400 dollars' it will take 8 years.
To get 2400 in 3 years, we need 8/3 times money.
Answer is E.
Answer: (E) (8d)/3
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 78
(B) 77
(C) 76
(D) 79.2
(E) 75
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: Option D
Answer: (D) 79.2
Question: A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $67500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 15
Rationale: Since the starting point is given as the $4000 scholarship,
Assume $4000 scholarships to be x
By the given information, $2500 scholarships = 2x
and $1250 scholarships = 6x
Gievn: Total $1250 scholarships = $67500
6x*1250 = 67500
Solve for x = 9
Option C
Answer: (C) 9
Question: A person want to give his money of $2700 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?
(A) $200
(B) $900
(C) $700
(D) $600
(E) $400
Rationale: B's share = 2700*3/9 = $900
Answer is B
Answer: (B) $900
Question: An officers identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
(A) 211
(B) 216
(C) 1075
(D) 1080
(E) 2160
Rationale: An officers identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18
now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299
here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)
thus total possible cases are 18 + 8 =26
case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)
if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)
hence total number of ways = 7(18+9) = 189
thus different number of codes = 5(189+26) = 1075
hence C
Answer: (C) 1075
Question: In a bag there are 10 black balls and 25 blue balls and 15 white balls. A ball is drawn at random. What is the probability of getting a white or a black ball?
(A) 3/2
(B) 1
(C) 1/2
(D) 5/2
(E) 3
Rationale: total draws =10+25+15=50
probability of getting a white ball = 15/50 . probability of getting a black ball=10/50. probability of getting a white or black ball=15/50+10/50=25/50=1/2. Correct Answer : C
Answer: (C) 1/2
Question: Find: S.l. on Rs 6250 at 14% per annum for 146 days.
(A) Rs.350
(B) Rs.450
(C) Rs.550
(D) Rs.650
(E) Rs.600
Rationale: Explanation:
P = Rs. 6250, R = 14 % & T = (146/365) years = 2/5 years .
S.I=(6250 *14 * 2/5)/100=Rs.350
ANSWER IS A
Answer: (A) Rs.350
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents B watch all of the shows?
(A)  150
(B)  108
(C)  42
(D)  21
(E)  -21
Rationale: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is 3.5% of 600,B is 21. D is the correct answer
Answer: (D)  21
Question: What is the are of an equilateral triangle of side 20 cm?
(A) 64√5
(B) 64√9
(C) 64√4
(D) 64√3
(E) 100√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 20, Area of triangle = √3/4 * 20 * 20 = 100√3 cm2;
Answer: E
Answer: (E) 100√3
Question: The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half yearly is
(A) 2
(B) 7
(C) 3
(D) 0
(E) 8
Rationale: Explanation:
S.I
= Rs.(1200x10x1/100)
= Rs.120.
C.I
= Rs[(1200x1+5/100)² -1200]
= Rs.123.
Difference
= Rs.[123-120]
= Rs. 3.
Answer: B
Answer: (B) 7
Question: Find the value of 2.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
(A) 2000
(B) 500
(C) 900
(D) 1600
(E) None
Rationale: Answer
2.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 2.5 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 2.5 x 4 x 4 x 50 = 2000
Correct Option: A
Answer: (A) 2000
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.145. Find the unknown rate of two towels?
(A) A)400
(B) B)450
(C) C)500
(D) D)550
(E) E)600
Rationale: 10 * 145 = 1450
3 * 100 + 5 * 150 = 1050
1450 – 1050 = 400
A
Answer: (A) A)400
Question: Calculate 85184 ÷ ? = 352
(A) 241
(B) 242
(C) 244
(D) 247
(E) 240
Rationale: Answer
Let 85184 ÷ X = 242
Then X = 85184/242 = 352.
Option: B
Answer: (B) 242
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 115 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
(A) 8%
(B) 9%
(C) 11%
(D) 12.5%
(E) 13.03%
Rationale: Typical dosage is Dose : weight :: 2: 15.
Now if weight is 115 :(115/15)) then typical dosage would be 2 *7.67 = 15.33 cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 15.33)*100 = 13.03 %
E is the answer.
Answer: (E) 13.03%
Question: There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
(A) 41
(B) 36
(C) 25
(D) 54
(E) 12
Rationale: Number of ways in which one can travel from P to R
=3×4=12=3×4=12
Ans: E
Answer: (E) 12
Question: A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 200 m
(B) 379 m
(C) 400 m
(D) 589 m
(E) 600 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.
Answer: C
Answer: (C) 400 m
Question: The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 27 years
(B) 28 years
(C) 29 years
(D) 20 years
(E) 17 years
Rationale: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
6x = 84 => x = 14
Son's age after 6 years = (x + 6)
= 20 years.
Answer:D
Answer: (D) 20 years
Question: Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 80% more than Bert had in savings, and separately, the same price was also 20% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
(A) 1:4
(B) 4:1
(C) 2:3
(D) 3:2
(E) 3:4
Rationale: Suppose bert had 100 so price becomes 180 , this 180 = 1.2 times R's saving .. so R's saving becomes 150
So required ratio is 100:150=2:3
ANSWER:C
Answer: (C) 2:3
Question: Of 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 54
(B) 59
(C) 61
(D) 71
(E) 92
Rationale: Total = 70
Thrower = 43
Rest = 70 - 43 = 27
Left Handed = 27/3 = 9
Right handed = 18
If all Thrower are right handed then total right handed is 43 + 18 = 61
so C. 61 is the right answer
Answer: (C) 61
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 7 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
(A) 1/60
(B) 1/45
(C) 2/45
(D) 3/22
(E) 5/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 5/22.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/22)*(5), which indeed is 5/22.
E
Answer: (E) 5/22
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $90 to incur a loss 10%?
(A) 45
(B) 41.2
(C) 40
(D) 50
(E) 48
Rationale: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $90*(100% + 10%) = $99
Number of articles to be sold for $108 to incur a 20% loss: $99 / $2.40 = 41.2
Thus, solution B is correct.
Answer: (B) 41.2
Question: Vijay bought 160 shirts at the rate of Rs. 215 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) s.225
(B) s.288
(C) s.485
(D) s.273
(E) s.282
Rationale: Total CP per shirt = 215 + 1400/160 + 1.75 + 320/160 = Rs. 227.5
SP = CP[(100 + profit%)/100]
= 227.5 * [(100 + 20)/100] = Rs.273.
Answer:D
Answer: (D) s.273
Question: A car drove from Town A to Town B without stopping. The car traveled the first 60 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 100 miles if the car’s average speed for the entire trip was 40 miles per hour?
(A) 28.5
(B) 48.5
(C) 50.4
(D) 55.5
(E) 62.5
Rationale: KAPLAN OFFICIAL SOLUTION:
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.
For the first 60 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 60/25, because distance divided by rate equals time.
For the last 100 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 100 miles is 100/R.
If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(60/25 + 100/R) = 40. We can now solve for R and reach our answer.
160/(60/25 + 100/R) = 40
R = 62.5
50 is choice (E) and that’s our correct answer.
Answer: (E) 62.5
Question: 1, 13, 35, 67, 109, ____
(A) 161
(B) 154
(C) 216
(D) 158
(E) none
Rationale: 1, 13, 35, 67, 109, .....
13=1+12
35=13+22
67=35+32
109=67+42
So 109+52=161
ANSWER:A
Answer: (A) 161
Question: For any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 9.2 – 9.2*?
(A) 0.2
(B) 1.2
(C) 1.8
(D) 2.2
(E) 4.0
Rationale: Since y* is defined as the greatest positive even integer less than or equal to y, then 9.2* = 8 (the greatest positive even integer less than or equal to 9.2 is 4).
Hence, 9.2 – 9.2* = 9.2 - 8 = 1.2
Answer: B.
Answer: (B) 1.2