mathewhe/aqua_rat huggingface dataset:
Question: Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (p,w). If w = 2, which of the following could be the equation of line m, which is perpendicular to line L?
(A)  2x + y = px + 7
(B)  2x + y = –px
(C)  x + 2y = px + 7
(D)  y – 7 = x ÷ (p – 2)
(E)  2x + y = 7 – px
Rationale: we need m=p-2, so we should get y=mx+bform in answer choices
(A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need
(B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong
(C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong
(E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong
A=answer
Answer: (A)  2x + y = px + 7
Question: A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?
(A) 1/5
(B) 1/6
(C) 1/7
(D) 1/8
(E) 1/9
Rationale: Given that B alone can complete the same work in days = half the time taken by A
= 9days
A’s one day work = 1/18
B’s one day work = 1/9
(A+B)’s one day work = 1/18+1/9 = 1/6
Answer : B.
Answer: (B) 1/6
Question: A, B and C invest Rs. 28000, Rs. 42000 and Rs. 56000 respectively. If C's share at the end of 1 yr is Rs. 4120, find the total profit.
(A) Rs. 8120
(B) Rs. 9270
(C) Rs. 8240
(D) Rs. 9150
(E) None of these
Rationale: Explanation:
Let ratio of capitals of A, B and C
= 28000 : 42000 : 56000
= 2 : 3 : 4
Let the total profit be Rs x.
Then, C's share = Rs. (4x/9)
But 4x/9 = 4120
=> x = (4120 × 9)/4 = 9270
Hence, the total profit = Rs. 9270.
Answer: Option B
Answer: (B) Rs. 9270
Question: P and Q had the same number of candies. P gave Q 28 candies so that now Q has five times as many candies as P has. How many candies does Q have now?
(A) 65
(B) 70
(C) 75
(D) 80
(E) 85
Rationale: Let P and Q be the number of candies they had at the start.
P = Q
5(P-28) = Q+28
5(Q-28) = Q+28
4Q = 168
Q = 42
Now person Q has 42+28 candies which is 70 candies.
The answer is B.
Answer: (B) 70
Question: Which of the following lines has x-intercept and y-intercept that are integers R?
(A) y=3x+1
(B) y=√x+1
(C) y=-2/x
(D) y=x^2-1
(E) xy=1
Rationale: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers R and the correct answer is D.
Answer: (D) y=x^2-1
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first n stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories?
(A) (a – b)( a + b + n)
(B) a – b
(C) a^2 – b^2
(D) n( a – b)
(E) an + bn – an
Rationale: total earned for n+a stories =a + a(a+b)
total earned for n+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
ANSWER:C
Answer: (C) a^2 – b^2
Question: A number is doubled and 6 is added. If resultant is trebled, it becomes 72. What is that number
(A) 8
(B) 10
(C) 9
(D) 14
(E) 16
Rationale: Explanation:
=> 3(2x+6) = 72
=> 2x+6 = 24
=> x = 9
Option C
Answer: (C) 9
Question: A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed Y of the train.
(A) a) 45
(B) b) 33
(C) c) 48
(D) d) 55
(E) e) 61
Rationale: Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=Y
Ans = C
Answer: (C) c) 48
Question: Sushi invested an amount of Rs. 10,000 at the rate of 15% p.a simple interest and another amount at the rate of 16% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
(A) 10900
(B) 10800
(C) 10500
(D) 10600
(E) 10580
Rationale: Let the second amount be Rs. x. Then,
(10000 * 15 * 1)/100 + (x * 16 * 1)/100 = [(12000 + x) * 14 * 1] / 100
15000+ 16x= 16800 + 14x
x = 900
Total investment = 10000 + 900 = Rs. 10,900.Answer: A
Answer: (A) 10900
Question: Insert the missing number
165, 195, 255, 285, 345, ...
(A) 375
(B) 420
(C) 435
(D) 390
(E) 984
Rationale: 165, 195, 255, 285, 345, ...has two different seriers with 90 difference between two numbers
165, 255, 345...
195, 285, ..... 375 is the next number
ANSWER:A
Answer: (A) 375
Question: In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 2882
(B) 8277
(C) 3120
(D) 2777
(E) 9112
Rationale: Number of male employees = 6400 * 65/100 = 4160
Required number of male employees who are less than 50 years old = 4160 * (100 - 25)%
= 4160 * 75/100 = 3120.
Answer: C
Answer: (C) 3120
Question: The length of a rectangle is reduced by 30%. By what % would the width have to be increased to maintain the original area?
(A) 42.8%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: Sol. Required change = (30*100)/(100-30)=42.8%
A
Answer: (A) 42.8%
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 376
(C) 299
(D) 276
(E) 111
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12
= 432
A
Answer: (A) 432
Question: Pipe A can fill a tank in 12 hours. Due to a leak at the bottom it takes 20 hours to fill the tank. In what time the leak alone can empty the full tank?
(A) 18 hours
(B) 23 hours
(C) 28 hours
(D) 30 hours
(E) 40 hours
Rationale: Let leak can empty the full tank in x hours.
1/12- 1/X = 1/20
=> 1/12 – 1/20 = 1/X
1/X =5-3 /60= 1/30
x= 30 hours
ANSWER:D
Answer: (D) 30 hours
Question: From a pack of 52 cards, one card is drawn. What is the probability that the card is a color of red?
(A) 1/6
(B) 2/2
(C) 1/2
(D) 8/2
(E) 3/6
Rationale: Let S be the sample space. Then,
n(S) = 52C1	= 52.
Let E = event of getting 1 face card.
n(E) = number of ways of choosing 1 face card out of 26
=26C1 = 26
P(E) = n(E) / n(S)	= 26 / 52
= 1/2.
Answer C
Answer: (C) 1/2
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 40 years
Rationale: Explanation:
Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer: A
Answer: (A) 14 years
Question: Which of the following is a prime number ?
(A) 33
(B) 81
(C) 93
(D) 97
(E) 32
Rationale: Explanation:
Clearly, 97 is a prime number. Because it is not divisible by other numbers.
ANSWER IS D
Answer: (D) 97
Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
(A) 50
(B) 65
(C) 70
(D) 75
(E) 80
Rationale: (x+x1+...x14)/15 = 40
50
Option A
Answer: (A) 50
Question: A train is 300 meter long is running at a speed of 54 km/hour. In what time will it pass a tunnel of 1200 meter length?
(A) 90 seconds
(B) 85seconds
(C) 40 seconds
(D) 100 seconds
(E) 120 seconds
Rationale: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec
Total distance = 300+1200 = 1500 meter
Time = Distance/speed
= 1500 * (15) = 100 seconds
Answer: D
Answer: (D) 100 seconds
Question: A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
(A) 182 km/hr
(B) 180 km/hr
(C) 152 km/hr
(D) 169 km/hr
(E) 179 km/hr
Rationale: Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 2 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 2
=> Vt = 180 + 2 = 182 km/hr
Answer: Option A
Answer: (A) 182 km/hr
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel E if the median is 10 gallons?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel E= 2=B
Answer: (B) 2
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150
(B) 88
(C) 2767
(D) 288
(E) 712
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: A
Answer: (A) 150
Question: How many 3x3x3 cubes could fit in a 10x24x16 box?
(A) 150
(B) 145
(C) 138
(D) 142
(E) 175
Rationale: The answer is D) 142. The 10x24x16 box has an area of 3840. If you divide it by 27 (the total of the 3x3x3 smaller cube) you get 142.2. This means you could fit 142 whole cubes in the larger box.
Answer: (D) 142
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 677 km/hr
(B) 720 km/hr
(C) 790 km/hr
(D) 800 km/hr
(E) 820 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Answer: (B) 720 km/hr
Question: A soccer team played 280 games and won 65 percent of them. How many games did it win?
(A) 182
(B) 100
(C) 104
(D) 150
(E) 124
Rationale: 65% of 280 =x
0.65*280 = x
182=x
answer :A
Answer: (A) 182
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 20 overs to reach the target of 282 runs?
(A) 6.25
(B) 5.5
(C) 7.4
(D) 5
(E) 12.5
Rationale: Explanation:
Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 20
Run rate needed = 250/20=12.5
Answer: Option E
Answer: (E) 12.5
Question: In a lottery, there are 9 prizes and 18 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: P(winning a prize) = 9 / (9+18) = 9/27 = 1/3
The answer is B.
Answer: (B) 1/3
Question: The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :
(A) 4/0
(B) 4/1
(C) 4/5
(D) 4/2
(E) 4/3
Rationale: Explanation:
Let the required fraction be x. Then, (1 / x )- x = 9/20
1 - x^(2) / x = 9 / 20 => 20 - 20 * x^(2) = 9 * x.
20 * x^(2) + 9 *x - 20 = 0.
=> (4 * x + 5) (5 * x - 4) = 0.
=> x = 4 / 5.
Answer: C) 4/5
Answer: (C) 4/5
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/8
(B) 11 1/4
(C) 11 2/4
(D) 12 1/4
(E) 17 1/4
Rationale: 3/12 + x/15
= 1
x= 11 1/4
Answer: B
Answer: (B) 11 1/4
Question: A certain bag contains 100 balls â€” 10 white, 30 green, 10 yellow, 47 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.9
(B) 0.75
(C) 0.6
(D) 0.8
(E) 0.5
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (10 + 30 + 10)/100 = 50/100 = 0.5.
Answer is E
Answer: (E) 0.5
Question: If c is 25% of a and 10% of b, what percent of a is b?
(A) 2.5%
(B) 15%
(C) 25%
(D) 35%
(E) 250%
Rationale: c is 25% of a --> c=a/4;
c is 10% of b --> c=b/10;
Thus a/4=b/10 --> b=5/2*a=2.5a. Therefore, b is 250% of a.
Answer: E
Answer: (E) 250%
Question: Evaluate: 460 - 12*3*2 = ?
(A) 878
(B) 545
(C) 434
(D) 442
(E) 452
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
460 - 12*3*2 = 460 - 8 = 452
correct answer E
Answer: (E) 452
Question: A train running at 1/2 of its own speed reached a place in 8 hours. How much time could be saved if the train would have run at its own speed?
(A) 8hrs
(B) 10hrs
(C) 4 hrs
(D) 15hrs
(E) 6hrs
Rationale: time taken if run its own speed = 1/2*8 =4 hrs
Time saved = 8 - 4 = 4 hrs
Answer : C
Answer: (C) 4 hrs
Question: A car covers a distance of 813 km in 3 hours. Find its speed?
(A) 104
(B) 288
(C) 271
(D) 276
(E) 128
Rationale: 813/3 = 271 kmph
Answer: C
Answer: (C) 271
Question: How many 3 letter (not necessarily distinct) words can be formed using the letters from the word TWIST ?
(A) 33
(B) 54
(C) 45
(D) 60
(E) None of the above
Rationale: Two T's are used
In this case we have to select just one letter out of the remaining 33 (W, I, S) which can be arranges in 3 places.
So, the total possibilities are 3∗3=9
Total possibilities 24+9=332
So, the answer is A.
Answer: (A) 33
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 120, 30, 240, 25, ___, 20, 480, 15... Which number is missing?
(A) 120
(B) 360
(C) 340
(D) 960
(E) 280
Rationale: B 360This is an alternating addition and subtraction series. In the first pattern, 120 is added to each number to arrive at the next. In the second, 5 is subtracted from each number to arrive at the next.
Answer: (B) 360
Question: If x+y=250, x-y=200, for integers of x and y, y=?
(A) 200
(B) 225
(C) 50
(D) 115
(E) 150
Rationale: x+y = 250
x-y = 200
2x = 50
x = 25
y = 225
Answer is B
Answer: (B) 225
Question: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is
(A) Rs. 258
(B) Rs. 358
(C) Rs. 458
(D) Rs. 558
(E) None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) × h] + (l × b)
= [2(25 + 12) × 6] + (25 × 12) = 744 sq m
Cost of plastering = 744 × (75/100) = Rs.558 Answer: D
Answer: (D) Rs. 558
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 86
(B) 16
(C) 76
(D) 80
(E) 26
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240
= 80
Answer:D
Answer: (D) 80
Question: A man can ride on cycle at 35 kmph upward road and 70 kmph downward road. He takes 6 hours to cycle uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 6 hours? He must return back to base point A in remaining time
(A) 120
(B) 140
(C) 160
(D) 280
(E) 180
Rationale: Upward distance traveled per hour - 35 km,
distance traveled after 4 hours = 140 km.
He remained with 2 hours travel downward, i.e. distance traveled in remaining 2 hours downward = 140 km
so total distance traveled from A to B and Back to point A = 140 km upward + 140 km downhill = 280 km
(Answer : D)
Answer: (D) 280
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.000168?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 8
Rationale: for the 1st no. there are 2 digits after decimal
for the 2nd no. there are 7 digits after decimal
total no. of decimals = 9
req. no. of digits=(n-1)=(9-1)=8
ANSWER :E
Answer: (E) 8
Question: At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.25 to bowl 2 games. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?
(A)  7
(B)  8
(C)  9
(D)  19
(E)  21
Rationale: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/1.25=9.84(2)=19.68<21. ~ 19 games
Answer: D.
Answer: (D)  19
Question: Ram has $100 in her piggy bank. How much will she have in her bank 25 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
(A) 400
(B) 415
(C) 425
(D) 435
(E) 445
Rationale: The dollar deposits are in an A.P.
1,2,3,4...25 with common difference 1
Sum of the terms is n(n+1) / 2
i.e 25* (25+1) /2
= 25* 26/2 = 325
Total deposit therefore with Chiu-Lihas is 100 + 325= 425$
Answer: (C) 425
Question: Ada and Paul received their scores on three tests. On the first test, Ada's score was 12 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
(A) 9
(B) 14
(C) 17
(D) 23
(E) 25
Rationale: My take is Option D (23)
I followed a simple approach (explained below):
Test 1: Ada's score = Paul's score + 10
Test 2: Ada's score = Paul's score + 4
Avg. of Paul's score = 3 points higher than Avg. of Ada's score
This implies that : Sum of Paul's score [3 Tests] = 9 points higher than Sum of Ada's score [3 Tests] (9 points higher since 3 points were given in terms of average of 3 scores)
So, Paul needs to score 25 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 25= 12 + 4 + 9)
E
Answer: (E) 25
Question: If the price of petrol increases by 20, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
(A) 16.7%
(B) 20%
(C) 24.67%
(D) 33.33%
(E) None of these
Rationale: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+20) i.e 120.
Now, his consumption should be reduced to :-
=(120−100)/120 ∗ 100.
Hence, the consumption should be reduced to 16.7%.
Answer : A
Answer: (A) 16.7%
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C
Answer: (C) 16
Question: probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits?
(A) 9/27
(B) 10/27
(C) 11/27
(D) 12/27
(E) 11/26
Rationale: (1/3*1/3)[guy1]*(1/3*1/3)[guy2]
for 1 hit each: (4 ways)
(2/3*1/3)*(2/3*1/3), (2/3*1/3)*(1/3*2/3), (1/3*2/3)*(2/3*1/3), (1/3*2/3)*(1/3*2/3)
for 2 hits each:(1 way)
(2/3*2/3)*(2/3*2/3)
Add all these cases, you will get answer as 11/27.
ANSWER:C
Answer: (C) 11/27
Question: It takes Tammy 15 minutes to do one oil change, and it takes Jill 10 minutes. At 2:30 pm, they both finish an oil change simultaneously. If Tammy and Jill both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?
(A) 2:00 pm
(B) 2:05 pm
(C) 2:10 pm
(D) 2:15 pm
(E) 2:20 pm
Rationale: Since Tammy finishes s oil changes after s × 15 minutes and Jill finishes c oil changes after c × 10 minutes, they both finished doing an oil change at the same time when s × 15 = c × 10. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 15 and 10. The question asks for the first time they began a car simultaneously, so you must find the least common multiple and subtract. The least common multiple of 15 and 10 is 30, so in the context of the question, this would be 30 minutes. Therefore, they began changing the oil of a car at the same time at 2:30 - 30 minutes, or 2:00 p.m. The answer is (A).
Answer: (A) 2:00 pm
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 838
(C) 372
(D) 737
(E) 273
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3
= 360.
Answer:A
Answer: (A) 360
Question: If TRAIN is coded as 12 and PANDA is coded as 18, then CURED is coded as
(A) 5
(B) 10
(C) 13
(D) 20
(E) None
Rationale: TRAIN= 20+18+1+9+14=62 i.e 6*2=12
PANDA= 16+1+14+4+1=36 i.e 3*6=18
CURED= 3+21+18+5+4=51 5*1=5
ANSWER:A
Answer: (A) 5
Question: 24 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
(A) 19
(B) 20
(C) 21
(D) 22
(E) 24
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 24
ANSWER:E
Answer: (E) 24
Question: A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 280, how much must C pay as his share of rent?
(A) 45
(B) 50
(C) 55
(D) 65
(E) none
Rationale: Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
âˆ´ Câ€™s rent = Rs. [280 * 9/35] = Rs. 72.
Answer E
Answer: (E) none
Question: Eight years back, a father was 52 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 18 years
Rationale: Using linear equations to convert the word problem:
** F = fathers current ageS = sons current age
#1 Eight years back, a father was 52 years older than his son: F-8 = 52 + (S - 8)
#2 At present the father is 5 times as old as the son: F = 5*S
How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:
(S*5) - 8 = 52 +S -8
4S=52
S = 13
S + 3 = 13+ 3 = 16
Answer: D
Answer: (D) 16 years
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 2 min. to empty
(B) 3 min. to empty
(C) 6 min. to empty
(D) 7 min. to empty
(E) 5 min. to empty
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min.
ANSWER:C
Answer: (C) 6 min. to empty
Question: A Shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed. The ratio of the cost price and the printed price of the book is:
(A) 12:24
(B) 29:23
(C) 32:41
(D) 45:56
(E) 40:42
Rationale: Explanation:
Printed price of the book is Rs. 100
After a discount of 10% S.P = Rs. 90
Profit earned = 12%
C.P of the book = Rs. (100/112 × 90) = Rs. 1125/14
(C.P) : (Printed price) = 1125/14 : 100 or 45 : 56
Answer: Option D
Answer: (D) 45:56
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
(A) 1:3
(B) 2:4
(C) 9:3
(D) 7:8
(E) 3:4
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then,	120/x + 480/y= 8 1/x	+	4/y	=	1/15	....(i)
And,	200/x + 400/y = 25/3 1/x	+	2/y	=	1/24	....(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
answer :E
Answer: (E) 3:4
Question: A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 87 days
(B) 12 days
(C) 16 days
(D) 19 days
(E) 36 days
Rationale: C = 1/2 - 1/4 - 1/6 = 1/12
=> 12 days
Answer:B
Answer: (B) 12 days