mathewhe/aqua_rat huggingface dataset:
Question: P is four times as fast as Q and working together, they can complete a work in 5 days. In how many days can Q alone complete the work?
(A) 5 3/4 days
(B) 6 1/4 days
(C) 16 days
(D) 25 days
(E) 18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 5 days, which means Q can do the work in 25 days.
Hence, P can do the work in 6 1/4 days.
ANSWER:B
Answer: (B) 6 1/4 days
Question: If y exceeds x by 60%, then x is less than y by?
(A) 1/2%
(B) 1/3%
(C) 1/4%
(D) 1/5%
(E) 1/6%
Rationale: X=100	y=160
160------60
100-------? => 37 1/2%
Answer:A
Answer: (A) 1/2%
Question: The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
(A) 1:28
(B) 1:27
(C) 1:29
(D) 1:39
(E) 1:22
Rationale: Explanation:
r1 : r2 = 1:3
r13 : r23 = 1:27
Answer: Option B
Answer: (B) 1:27
Question: A plane travels in the shape of equilateral triangle have sped of 20km/hr, 40km/hr and 60km/hr. Find the average speed of the palne.
(A) 42.73 km/h
(B) 52.73 km/h
(C) 32.73 km/h
(D) 62.73 km/h
(E) 72.73 km/h
Rationale: average speed = total distance/total time taken
=(d+d+d)/[(d/20)+(d/40)+(d/60)] where d= side of eq. triangle
=3d/d[1/20 + 1/40 + 1/60]
=3*20*40*60/[20*40+40*60+20*60]
= 360/11 km/h
= 32.73 km/h
ANSWER:C
Answer: (C) 32.73 km/h
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 8%?
(A) 0—1.5 gal
(B) 1.5—3 gal
(C) 3—4.5 gal
(D) 4.5—6 gal
(E) 6+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 8
=>100 = 80 + 8x
=> x= 20/8 = 2.5
Answer B
Answer: (B) 1.5—3 gal
Question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
(A) 287
(B) 699
(C) 677
(D) 300
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 300 m
Answer: D
Answer: (D) 300
Question: In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race?
(A) 150 seconds
(B) 165 seconds
(C) 135 seconds
(D) 66.67 seconds
(E) 180 seconds
Rationale: Explanatory Answer
In a 1000 metre race A gives B a start of 100 m or 15 seconds.
This essentially means that B takes 15 seconds to run 100 m.
Therefore, B will take 150 seconds to run the stretch of 1000 metres. (1000 m = 10 times 100 m and therefore the time taken will also be 10 times 15 seconds = 150 seconds).
As A gives B a start of 15 seconds, A obviously takes 15 seconds less than B to complete the race.
Hence, A will take 135 seconds to run the 1000 m.
Answer C
Answer: (C) 135 seconds
Question: Find the surface area of a cuboid 16 m long, 14 m broad and 7 m high
(A) 868 sq.cm
(B) 920 sq.cm
(C) 727 sq.cm
(D) 900 sq.cm
(E) None of these
Rationale: Explanation:
Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] cm2 = (2 x 434)cm2 = 868 cm2.
Answer: A
Answer: (A) 868 sq.cm
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 60 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
(A) 79
(B) 89
(C) 95
(D) 81.81
(E) 97.2
Rationale: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 60*5 = 300
Student's average = (600+300)/11 = 81.81
Answer D
Answer: (D) 81.81
Question: The average weight of 40 girls sitting in a bus had some value. A new girl added to them whose weight was 60 kg only. Due to her arrival, the average weight of all the girls decreased by 20 kg. Find the average weight of first 40 boys?
(A) 850
(B) 80
(C) 176
(D) 500
(E) 880
Rationale: 40x + 60 = 41(x â€“ 20)
x = 880
E
Answer: (E) 880
Question: In how many ways 8 different tickets E can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
(A) From 2 to 6 inclusive.
(B) From 98 to 102 inclusive.
(C) From 122 to 126 inclusive.
(D) From 128 to 132 inclusive.
(E) From 196 to 200 inclusive.
Rationale: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
E=1+28+70+28+1 = 128 Answer is D.
Answer: (D) From 128 to 132 inclusive.
Question: he ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 2:6
(B) 2:9
(C) 2:4
(D) 2:1
(E) 2:5
Rationale: Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5.
Answer:E
Answer: (E) 2:5
Question: How many such letter-pairs are there in the word FRONTIER having same no. of letters left between them as they have in the series?
(A) 2
(B) 4
(C) 1
(D) 3
(E) 5
Rationale: We have to find whether for any letter-pair in this word, the same no. of letters exist between them in the alphabet series as that in this word.
So, consider ON - They are consecutive letters in the alphabet series as well as in this word.
Also consider NR - There exists 3 letter between them in the alphabets as O, P, Q. In this word also, there exists 3 letter between them (T, I, E).
So ans is 2
ANSWER:A
Answer: (A) 2
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs.12:29
(B) Rs.18:90
(C) Rs.16.28
(D) Rs.16.50
(E) Rs.82.09
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D
Answer: (D) Rs.16.50
Question: A survey was sent to 80 customers, 9 of whom responded. Then the survey was redesigned and sent to another 63 customers, 12 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 5%
(C) 14%
(D) 28%
(E) 69%
Rationale: Rate of first survey = 9/80
Rate of second survey = 12/63
% Response rate increase (12/63-9/80)/(9/80) = 69%
Answer is E = 69%
Answer: (E) 69%
Question: 50% of a number is more than 40% of 120 by 180. Find the number?
(A) 456
(B) 480
(C) 420
(D) 445
(E) 320
Rationale: (50/100) * X – (40/100) * 120 = 180
1/2 X = 228
X = 456
Answer:A
Answer: (A) 456
Question: 14 times a number gives 210. The number is
(A) 11
(B) 12
(C) 15
(D) None
(E) Cannot be determined
Rationale: Explanation:
Let the number be 'N'
14×N=210⇒N=15
Correct Option: C
Answer: (C) 15
Question: One drier dries certain quantity of material in 24 minutes. Another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?
(A) 1.00 minutes
(B) 1.20 minutes
(C) 1.50 min
(D) 1.85 min
(E) 2.00 minutes
Rationale: By guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes Therefore, answer 1.85 minutes will be correct. Answer-D
Answer: (D) 1.85 min
Question: If a car had traveled 25 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 75 km, at what speed did it travel?
(A) 30 kmh
(B) 40 kmh
(C) 45 kmh
(D) 50 kmh
(E) 55 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
75/x - 75/(x + 25) = 1/2
Substitute the value of x from the options. --> x = 50 --> 75/50 - 75/75 = 3/2 - 1 = 1/2
Answer: D
Answer: (D) 50 kmh
Question: In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and
17 students play all the sports. How many students play only cricket ?
(A) 35
(B) 38
(C) 39
(D) 47
(E) 37
Rationale: PERSONS PLAY CRICKET ONLY=N(C)-N(B∩C)+N(C∩T)-2(N(B∩T∩C))
=75-30+24-(2*17)
=35
ANSWER:A
Answer: (A) 35
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.12350. Find the share of A?
(A) 3002
(B) 3000
(C) 3018
(D) 4000
(E) 5000
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 12350 = 5000
Answer: E
Answer: (E) 5000
Question: After 95 liters of petrol were poured into the tank, it was still 5% empty. How much petrol must be poured into the tank in order to fill it?
(A) 7 liters
(B) 4 liters
(C) 3 liters
(D) 5 liters
(E) 6 liters
Rationale: 95% ----------- 95
5% ------------ ?
=> 5 liters
Answer: D
Answer: (D) 5 liters
Question: In a school 10% of the boys are same in number as 1/2th of the girls. what is the ratio of boys to the girls in the school?
(A) 5:1
(B) 2:3
(C) 1:4
(D) 3:7
(E) 2:5
Rationale: 10% of B = 1/2 G
10B/100 = G/2
B = 5G/1
B/G = 5/1
B:G = 5:1
Answer is A
Answer: (A) 5:1
Question: In case P there are 2 red pens and 3 blue pens, in case Q there is 1 red pen and 4 blue pens. A case is randomly picked, what is the probability of picking up a red pen from case Q?
(A) 1/10.
(B) 4/5.
(C) 3/10.
(D) 3/5.
(E) 2/3.
Rationale: Probability of picking up one case out of two= 1/2
probability of picking 1 red pen from case Q= 1/5
Hence the desired probability= 1/2*1/5= 1/10
A is the answer
Answer: (A) 1/10.
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 665
(B) 700
(C) 720
(D) 730
(E) 750
Rationale: Explanation:
8 * 84 = 672 – 7 = 665
A)
Answer: (A) 665
Question: The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance?
(A) 45%
(B) 56%
(C) 64%
(D) 75%
(E) 80%
Rationale: Last year attendance = 100 (assume);
Projected Attendance = 125;
Actual Attendance = 80.
The actual attendance therefore was (Actual)/(Project) = 80/125 *100 = 64$ of the projected attendance.
Answer: C.
Answer: (C) 64%
Question: A train 110 m long is running with a speed of 30 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 11 sec
(E) 2 sec
Rationale: Speed of train relative to man = 30 + 6
= 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Time taken to pass the men = 110 /10
=11 sec.
Answer:D
Answer: (D) 11 sec
Question: A and B can do a piece of work in 8 days. With the help of C they finish the work in 4 days. C alone can do that piece of work in?
(A) 40 days
(B) 20 days
(C) 8 days
(D) 60 days
(E) 40 days
Rationale: C
8 days
C = 1/4 – 1/8 = 1/8 => 8 days
Answer: (C) 8 days
Question: When a certain number X is divided by 143, the remainder is 42. Which of the following numbers, if added to X, would result in a number divisible by 13?
(A) 10
(B) 21
(C) 34
(D) 47
(E) 55
Rationale: Now X= 143q + 42 = 11*13*q + 42..so we have to make only 42 div by 13..
42 +10 = 52 YES
minimum 10 to be added
A
Answer: (A) 10
Question: (√27+√243)/√48=?
(A) 2√2
(B) 2√3
(C) 3√2
(D) 3√3
(E) 3
Rationale: (√27+√243)/√48
=(3√3+9√3)/4√3
=12√3/4√3
=3.
Hence, the correct answer is E.
Answer: (E) 3
Question: Solution A is 20% chlorine and Solution B is 80% chlorine. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% chlorine solution?
(A) 6:4
(B) 6:14
(C) 4:4
(D) 4:6
(E) 3:7
Rationale: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4=C
Answer: (C) 4:4
Question: Find the number, the second digit of which is smaller than its first digit by 4, and if the number was divided by the digit’s sum, the quotient would be 7.
(A) 64
(B) 74
(C) 84
(D) 87
(E) 89
Rationale: 84 is the desired number.
84/12 =7
ANSWER:C
Answer: (C) 84
Question: There is a 40% chance that Betty will visit Denmark this year, while there is a 30% chance that she will visit Peru this year. What is the probability that Betty will visit either Denmark or Peru this year, but NOT both?
(A) 44%
(B) 46%
(C) 48%
(D) 50%
(E) 52%
Rationale: P(Denmark but not Peru)=0.4*0.7=0.28
P(Peru but not Denmark)=0.3*0.6=0.18
P(Denmark or Peru but not both)=0.28+0.18=0.46
The answer is B.
Answer: (B) 46%
Question: The ratio of the arithmetic mean of two numbers to one of the numbers is 5:7. What is the ratio of the smaller number to the larger number?
(A) 2:3
(B) 2:5
(C) 3:7
(D) 4:9
(E) 5:6
Rationale: For two numbers, the arithmetic mean is the middle of the two numbers.
The ratio of the mean to the larger number is 5:7, thus the smaller number must have a ratio of 3.
The ratio of the smaller number to the larger number is 3:7.
The answer is C.
Answer: (C) 3:7
Question: At a tanning salon, customers are charged $10 for their first visit in a calendar month and $5 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?
(A) $1220
(B) $1200
(C) $1300
(D) $1340
(E) $1880
Rationale: I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(5) = $200
Total revenue: 1000+ 200 = $1200
The answer is B.
Answer: (B) $1200
Question: Light glows for every 16 seconds . How many times did it between 1:57:58 and 3:20:47 am
(A) 311
(B) 322
(C) 313
(D) 314
(E) 385
Rationale: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/16 = 310.
so total 311 times light ll glow
ANSWER:A
Answer: (A) 311
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/95
(B) 33/91
(C) 33/94
(D) 33/16
(E) 33/17
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer:B
Answer: (B) 33/91
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 35/145
(B) 36/145
(C) 36/140
(D) 36/141
(E) 31/142
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: What is the area of square field whose side of length 15 m?
(A) 225
(B) 777
(C) 266
(D) 288
(E) 261
Rationale: 15 * 15 = 225 sq m
Answer: A
Answer: (A) 225
Question: If seven numbers are randomly selected without replacement from set {1, 2, 3, 4, 5, 6, 7}, what is the probability that the numbers are selected in ascending order?
(A) 1/2560
(B) 1/6400
(C) 1/4820
(D) 1/5040
(E) 1/1280
Rationale: The total number of ways to arrange 7 numbers is 7! = 5040.
There is only one way to arrange the numbers in ascending order.
P(ascending order) = 1/5040
The answer is D.
Answer: (D) 1/5040
Question: Solution x contains 75% water and 25% oil; how many more liters of water than liters of oil are in 200 liters of solution x?
(A) 50
(B) 100
(C) 125
(D) 150
(E) 175
Rationale: water = .75 * 200=3/4 of 200=150
oil = .25*200=1/4 of 200=50
difference= 150 - 50=100
ANSWER:B
Answer: (B) 100
Question: What is the greatest prime factor of (14!13!) + (14!15!)?
(A) 31
(B) 71
(C) 151
(D) 191
(E) 211
Rationale: 14!13! + 14!15!
= 14!13! (1+15*14)
= 14!13!(211)
The answer is E.
Answer: (E) 211
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/5.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
(A) 5.
(B) 4.
(C) 3.
(D) 2.
(E) 7.
Rationale: We need to get some number which is less than 50 and exactly divisible by 5,5 and 10
Lets take LCM of three balls 5,5 and 10 = 10.
The probability of drawing a blue ball is 1/5...For every 8 balls we get 1 BLUE ball then out of 10 balls we get 2 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 10 balls we get 2 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 10 balls we get 1 GREEN BALLS.
Then out of 10 - ( 2 + 2 + 1 ) = 5 YELLOW balls.
IMO option A is correct.
Answer: (A) 5.
Question: How many numbers from 45 to 110 are exactly divisible by 12?
(A) 5
(B) 7
(C) 6
(D) 11
(E) 12
Rationale: Option 'C'
45/12 = 3 and 110/12 = 9 ==> 9 - 3 = 6 Numbers
Answer: (C) 6
Question: A train passes a station platform in 36 sec and a man standing on the platform in 24 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 767 m
(B) 240 m
(C) 180 m
(D) 176 m
(E) 186 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 24 = 360 m.
Let the length of the platform be x m . Then,
(x + 360)/36 = 15 => x = 180 m.
Answer:C
Answer: (C) 180 m
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 150 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
(A) 1200
(B) 800
(C) 480
(D) 192
(E) 400
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 150hrs. hence, possible scenarios, if
(1)2x =150 => 16x = 1200 (2) 3x =150 => 16x = 800 (3) 5x =150 => 16x = 480 (4) 6x =150 => 16x = 400
Hence Answer is D 192 which can not be any of these.
Answer: (D) 192
Question: There are 2 sections A and B in a class, consisting of 24 and 16 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, Find the average of the whole class?
(A) 35.29kg
(B) 37.25kg
(C) 42kg
(D) 38kg
(E) 29.78kg
Rationale: Total weight of 36+44 students = 24*40 + 16*35 = 1520
Average weight of the class is = 1520/40 = 38 kg
Answer is D
Answer: (D) 38kg
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 56 with him, what was the average amount with the group before his joining the group?
(A) s.13
(B) s.12
(C) s.15
(D) s.22
(E) s.14
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 56. So, the amount with remaining 6 people = 140 - 56 = Rs. 84
The average amount with them = 84/6 = Rs.14.
Answer:E
Answer: (E) s.14
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 40% nuts, what percent of the combined mixture is dried fruit?
(A) 16.7%
(B) 23.33%
(C) 25%
(D) 33.3%
(E) 46.7%
Rationale: 40% is 10%-points above 30% and 20%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 2:1.
2/3*70% = 140%/3 = 46.7%
The answer is E.
Answer: (E) 46.7%
Question: If it is assumed that 65 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?
(A) 400
(B) 420
(C) 461.5
(D) 500
(E) 600
Rationale: Minimum no of mail to be sent for getting 300 responses at 65%
= 300/0.65 = 461.5
Option C
Answer: (C) 461.5
Question: The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 40 per kg. The inflation rate for the years 1994 and 1995 are expected to be 18% each. The expected price of sugar on January 1, 1996 would be
(A) 57.6
(B) 58.4
(C) 54.4
(D) 24.6
(E) None of these
Rationale: Explanation :
Increase in the price of sugar = (18+2)= 20%
Hence, price of the sugar on Jan 1, 1996
=> (40 * 120 * 120)/( 100 * 100 ) = Rs 57.60.
Answer : A
Answer: (A) 57.6
Question: Susan weighs 10 pounds more than Anna does, and together they weigh a total of 110 pounds. Which of the following represents Anna’s weight in pounds?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 85
Rationale: Total weight = 110
Anna's weight = 110-10 /2 = 50
Answer : A
Answer: (A) 50
Question: If the pice of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumpion of sugar by
(A) 22
(B) 20
(C) 98
(D) 77
(E) 32
Rationale: Explanation:
Let original consumption = 100 kg and new consumption = x kg,
So,
Reduction in consumption = 20%.
Answer: B) 20
Answer: (B) 20
Question: Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?
(A) 1/3
(B) 1/30
(C) 1/42
(D) 2
(E) 30
Rationale: Pete covered 3.5*60=210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42.
Answer: C.
Answer: (C) 1/42
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1 : 4
(B) 3 : 4
(C) 2 : 7
(D) 3 : 7
(E) 1 : 3
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
B
Answer: (B) 3 : 4
Question: A seller of used cars has 16 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 24
Rationale: IfNo caris selected more than once then the number of clients = 16/2 = 8
But since every car is being selected three times so No. of Clients must be thrice as well = 8*3 = 24
Answer: option E
Answer: (E) 24
Question: If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.
(A) 40 cm
(B) 45 cm
(C) 50 cm
(D) 52 cm
(E) 57 cm
Rationale: Explanation:
Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(1)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(2)
Solving 1 & 2 , we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
Answer: Option C
Answer: (C) 50 cm
Question: How much is it cost $0.50 each tire for 8 tires?
(A) $3.00
(B) $9.00
(C) $2.00
(D) $4.00
(E) $7.00
Rationale: D. $4.00
Answer: (D) $4.00