mathewhe/aqua_rat huggingface dataset:
Question: Two positive integers differ by 4, and sum of their reciprocals is 6. Then one of the numbers is
(A) a) 3
(B) b) 1
(C) c) 5
(D) 4
(E) e) 28
Rationale: Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 6
or ((n+4)+n)/n(n+4) =6 or (n^2+4n)*6 =2n+4 or n=2 as n cannot be -negative
Solve for n => n=4. Hence,
D
Answer: (D) 4
Question: A committee is composed of w women and m men. If 4 women and 4 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
(A) w/m
(B) w/(w+m)
(C) (w+4)/(m+4)
(D) (w+4)/(w+m+4)
(E) (w+4)/(w+m+8)
Rationale: The number of women is w+4.
The total number of people is w+m+8.
P(a woman is selected) = (w+4) / (w+m+8)
The answer is E.
Answer: (E) (w+4)/(w+m+8)
Question: A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle T in terms of h?
(A) h/ √2
(B) h/2
(C) h/4
(D) (h)^2
(E) (h)^2/4
Rationale: IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA T= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E
Answer: (E) (h)^2/4
Question: The average of 25 results is 24. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
(A) 740
(B) 228
(C) 690
(D) 780
(E) 458
Rationale: Solution: Sum of 1st 12 results = 12*14
Sum of last 12 results = 12*17
13th result = x (let)
Now,
12*14+12*17+x = 25*24
Or, x = 228.
Answer: Option B
Answer: (B) 228
Question: The ration between the present ages of P and Q is 2:5. If Q is 12 years older than P, what will be the ratio of the ages of P and Q after 12 years?
(A) 2:3
(B) 1:2
(C) 5:7
(D) 4:7
(E) 5:8
Rationale: Let P's and Q's age be 2x and 5x
5x-2x = 12
x = 4
Required ratio = (2x+12):(5x+12) = 20:32 = 5:8
Answer is E
Answer: (E) 5:8
Question: In a consumer survey, 65% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 30
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: pick 100 and x= all set with exactly two items
65=30+50+20 -(X)-10
X=25
so the answer is 25+5/100= 30%
Answer A
Answer: (A) 30
Question: At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 30 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?
(A) 66.67
(B) 66
(C) 67
(D) 65.99
(E) 67.26
Rationale: All birds = 54210
Currently Tagged = 54210 * 30/100 = 16263
So Untagged birds = 54210 - 16263 = 37947
Half of all birds = 27105
The number of birds to be tagged to make half of all birds tagged = 27105 - 16263 = 10842
So now the question remains - 10842 is how much percentage of untagged birds (16263)
= 10842*100/16263
= 66.67
Answer (A)
Answer: (A) 66.67
Question: Renuka got married 8 years ago. Today her age is 4/3 times of marriage. Her daughter age is 1/8 times her age. her daughter age is
(A) 3 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Renuka got married 8 years ago. Today her age is 4/3 times of marriage.
If her age at time of marriage was x, then
x*4/3 = x+8x/3=8
x=24 yrs
Her present age = 24+8=32 yrs
Daughter's age = 32/8= 4 years
ANSWER:B
Answer: (B) 4 years
Question: A cricket player whose bowling average was 24.50 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.50. What will be the number of wickets taken by him till the last match?
(A) 64
(B) 72
(C) 141
(D) 96
(E) 108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 24.50w + 52
Total wickets after last match = w + 5
(24.50w + 52) / (w + 5) = 24.5 - 0.50 = 24
w = 136
so total wickets aftr last match = w+5 = 141
ANSWER:C
Answer: (C) 141
Question: The average of first 18 even numbers is?
(A) 19
(B) 18
(C) 16
(D) 11
(E) 17
Rationale: Sum of 18 even numbers = 18 * 19 = 342
Average = 342/18 = 19
Answer:A
Answer: (A) 19
Question: Mr. RIDDLE invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $200,000. In one year, Fund X paid 43% and Fund Y paid 28%. The interest earned in Fund Y was exactly $200 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X?
(A) 43,870.34
(B) 56,876.45
(C) 77,789.45
(D) 78,450.70
(E) 87,987.34
Rationale: X+Y=200,000
0.28Y=0.43A+300
Take away decimals first: 28Y+43X+20,000
Isolate first equation to solve for X (your goal): Y=200,000-Y
Plug in for B:
28(200,000-X)=43X+30,000
5,600,000-28X=43X+30,000
5,570,000=71X
5,570,000/71=X
5,570,000/71=X
X=78,450.70=Answer Choice D
Answer: (D) 78,450.70
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 22
(B) 88
(C) 25
(D) 99
(E) 01
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer: C
Answer: (C) 25
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is?
(A) 5/19
(B) 5/12
(C) 5/18
(D) 2/12
(E) 5/11
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer: B
Answer: (B) 5/12
Question: On dividing 171 by a number, the quotient is 8 and the remainder is 3. Find the divisor.
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: d = (D-R)/Q
= (171 - 3)/8
= 168/8 = 21
D
Answer: (D) 21
Question: If 0 < a < b and k = (2a + 8b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 10
(D) k > 10
(E) k > 11
Rationale: Here's another approach:
k = (2a + 8b)/b
= 2a/b + 8b/b
= 2(a/b) + 8
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 8
From here, we can see that k must be less than 10
Answer: C
Answer: (C) k < 10
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 278
(B) 279
(C) 999
(D) 287
(E) 287
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
Answer:C
Answer: (C) 999
Question: How many seconds will it take for a car that is traveling at a constant rate of 14 miles per hour to travel a distance of 96 yards?	(1 mile = 1,160 yards)
(A) 11
(B) 12
(C) 13
(D) 14
(E) 17
Rationale: speed = 14 miles/hr = 6.84 yard/s
distance = 96 yards
time = distance/speed
=96/6.84
=14 sec
ans - D
Answer: (D) 14
Question: The present value of a bill due at the end of 2 years is Rs.1250. If the bill were due at the end of 2 years and 11 months, its present worth would be Rs.1200. Find the rate of interest and the sum.
(A) rs.1175
(B) rs.1375
(C) rs.1475
(D) rs.1575
(E) NONE OF THESE
Rationale: Explanation:
PW=100*Amount / 100+(R+T)
ANSWER IS B
Answer: (B) rs.1375
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 11. The larger of the two numbers is:
(A) 276
(B) 253
(C) 322
(D) 345
(E) 395
Rationale: Clearly, the numbers are (23 x 10) and (23 x 11).
Larger number = (23 x 11) = 253.
Answer: Option B
Answer: (B) 253
Question: How many different 6-letter sequences are there that consist of 1A, 4B's and 5C's ?
(A) 6
(B) 60
(C) 100
(D) 360
(E) 720
Rationale: How many different 6-letter sequences are there that consist of 1 A, 4B's, and 5 C's?
(A) 6
(B) 60
(C) 100
(D) 360
(E) 720 (ANS C)
Answer: (C) 100
Question: How many litres of 6% acid solution must be mixed with 120 gallons of 20% acid solution to obtain an acid solution that is 16%?
(A) 48 litres
(B) 98 litres
(C) 28 litres
(D) 49 litres
(E) 41 litres
Rationale: QUESTION : Rs. 2250 is divided among three boys named Rama, Krishna and Kalki in such a way that 1/6th of Rama’s share, 1/4th of Krishna’s share and 2/5th of Kalki’s share are equal. Find Rama’s share.
ANSWER : A
Answer: (A) 48 litres
Question: A woman can row upstream 5 kmph and downstream 10 kmph. Find the woman rate in still water and rate of the stream.
(A) 2.5,2.5
(B) 7.5,2.5
(C) 5.5,2.5
(D) 5,2.5
(E) 1.5,2.5
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(10+5) = 7.5 kmph
=> Rate of current = 1/2(10-5) = 2.5 kmph
Option B
Answer: (B) 7.5,2.5
Question: If 6^r is a factor of (10!)^2, What is the greatest possible value of r ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: r 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: (D) 8
Question: In the following equation what value would come in place of question mark (?)?
5798 – ? = 7385 – 4632
(A) 3225
(B) 2595
(C) 2775
(D) 3045
(E) None of these above
Rationale: ? = 5798 + 4632 – 7385 = 3045
Answer D
Answer: (D) 3045
Question: There are, in a certain league, 14 teams, and each team face another team for a total of 5 times. How many games are played in the season?
(A) 455
(B) 525
(C) 1400
(D) 180
(E) 560
Rationale: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 455
Option A.
Answer: (A) 455
Question: If John invested $ 1 at 4 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^4
(D) 1 + (0.04)^4
(E) 1 + 4(0.05)
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of 4. We'd have....
Answer :C
Answer: (C) (1.05)^4
Question: If the product of 8 integers is negative, at most how many of the integers can be negative?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: The product of 8 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 7
Correct Option : E
Answer: (E) 7
Question: If a and b are odd integers, which of the following is an even integer?
(A) 2a+b
(B) 3a+b
(C) 4a+b
(D) 2a-b
(E) a-8b
Rationale: If a is odd, then 3a is odd.
Then 3a+b is even.
The answer is B.
Answer: (B) 3a+b
Question: A man walks at a speed of 7 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 1 hours
(B) 1 1/2 hours
(C) 2 1/6 hours
(D) 2 1/1 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/7 + (5 1/4)/7
= 1 1/2 hours.
Answer:B
Answer: (B) 1 1/2 hours
Question: In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?
(A) 8200
(B) 7500
(C) 7000
(D) 8000
(E) 8400
Rationale: Equal number of candidates appeared in each state.
In state A, 6% candidates got selected.
In state B, 7% candidates got selected.
Given that 80 more candidates got selected in state B than A.
Therefore, 1% of candidates appeared in each state =80
Answer: Option D
= 100% of candidates appeared in each state
=80×100=8000
i.e., number of candidates appeared from each state = 8000
Answer: (D) 8000
Question: If F(x, n) be the number of ways of distributing "x" toys to "n" children so that each child receives at the most 2 toys then F(4, 3) =
(A) 3
(B) 4
(C) 6
(D) 5
(E) 7
Rationale: Explanation :
We have to find the number of ways in which 4 toys can be distributed to 3 children so that each child receives at the most 2 toys.There are two possible cases:Case 1: Two of them receive 2 toys each and one of them doesn’t get any toy.There are 3 possible ways to distribute the toys in this case i.e., the three possible ways of selecting the child who will not get any toy.Case 2: Two of them receive 1 toy each and one of them receives 2 toys.Again there are 3 possible ways to distribute the toys in this case i.e., the three possible ways of selecting the child who will get 2 toys.So there are a total of 6 possible ways.
Answer : C
Answer: (C) 6
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability E that all three secretary are assigned at least one report?
(A) 8/9
(B) 64/81
(C) 4/9
(D) 16/81
(E) 5/9
Rationale: I got the same answer: Here's my reasoning
First Report you have 3 choices
Second Report you have 2 choices
Third Report you have 1 choice
Fourth report 3 choices again
Then total number of ways is: 3*2*1*3=3^2*2
This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.
The number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36
Required probability E= 36/81.C
Answer: (C) 4/9
Question: Of the 200 math majors at a certain university, 30 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 80 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?
(A)  15
(B)  20
(C)  30
(D)  45
(E)  60
Rationale: 30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140
60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 80
Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:
All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.
The remaining 45 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.
Answer is D.
Answer: (D)  45
Question: Frances can complete a job in 8 hours, and Joan can complete the same job in 12 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?
(A) 6 p.m.
(B) 7 p.m.
(C) 8 p.m.
(D) 10 p.m.
(E) 12 p.m.
Rationale: Let the total work be 24 units.
Frances can complete 3 units/hr
Joan can complete 2 units/hr
Work done by Frances in 6 hours is 18 units ; work left for Joan is 6 units ( 24 - 18)
Time required by Jones to complete the remaining work will be 6/2 => 3 hours
Given Jones starts at 4PM , so she would complete the work at 7 PM
Answer will be (B)
Answer: (B) 7 p.m.
Question: Amar takes as much time in running 15 meters as a car takes in covering 40 meters. What will be the distance covered by Amar during the time the car covers 1.9 km?
(A) 700 m
(B) 720 m
(C) 712 m
(D) 600 m
(E) 640 m
Rationale: Distance covered by Amar
= 15/40 (1.9km)
= 3/8(1900) = 712 m
Answer: C
Answer: (C) 712 m
Question: Ms. Mary sold two properties, X and Y, for $25,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) $2100
(B) $2222
(C) $2320
(D) $2083.33
(E) $2183.33
Rationale: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...
Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (20/10)^2 = 4%
which means he recovered only 96% of his investment which amount to a total revenue = 25000 + 25000 = 50000
i.e. 96% of cost = 40000
therefore, 4% of cost (Loss) = $2083.33
Answer: D
Answer: (D) $2083.33
Question: The ratio of the selling prices of three articles is 5:6:9 and the ratio of their cost prices is 4:5:8 respectively. What is the ratio of their respective percentages of profit, if the profit on the first and the last articles is the same?
(A) 4:5:6
(B) 10:8:5
(C) 5:6:9
(D) 7:6:9
(E) Cannot be determined
Rationale: Given that the selling prices of three articles,
S.P1 =5X, S.P2 =6X, S.P3 =9X,
And their cost prices are C.P1 =4Y, C.P 2 =5Y, C.P3 =8Y
Given that , S.P1 –C.P1 =S.P2 –C.P2, 5X-4Y =9X-8Y, X =Y,
Their profit percentages are, p1 =(5-4)/4*100 = 25% ,
p2 = (6-5)/5*100 = 20%, p3 = (9-8)/8*100 = 12 1/2 %
Ratio of the percentages is 25:20:12 1/2 = 10:8:5
ANSWER:B
Answer: (B) 10:8:5
Question: 42 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 16
(C) 13
(D) 14
(E) 19
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 42 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 42 x 5 x 12
x = (42 x 5 x 12)/(30 x 6)
x = 14
ANSWER D
Answer: (D) 14
Question: What is the remainder when 8^1 + 8^2 + 8^3 +...+ 8^9 is divided by 8?
(A) 4
(B) 0
(C) 2
(D) 5
(E) None of the above
Rationale: Notice that in the brackets we have the sum of 9 even multiples of 8, which yields remainder of 0 upon division by 8.
Answer : B
Answer: (B) 0
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased?
(A) 50
(B) 96
(C) 100
(D) 125
(E) 250
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 5.6 , so radius is 2.8
New area = 7.84π
Increase in area is 3.84π
% increase in area = 3.84/4*100
So, % increase is 96%
Answer will be (B)
Answer: (B) 96
Question: In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/6 . If the probability that a number 12 or larger is drawn is 1/3 , what is the probability that a number less than or equal to 20 is drawn?
(A)  1/18
(B)  1/6
(C)  1/3
(D)  1/2
(E)  5/6
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 12 or larger
Set 2: Number 20 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)
1/3 + P(Set 2) - 1/6 = 1
P(Set 2) = 5/6
Answer (E)
Answer: (E)  5/6
Question: Ron begins reading a book at 2: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?
(A) 7: 00 p.m.
(B) 7: 30 p.m.
(C) 10: 45 p.m.
(D) 11: 30 p.m.
(E) 11: 45 p.m.
Rationale: M gains 50-30=20 pages per hour on R
at 6pm R has read 105 pages and M is 105+5=110 pages behind him
time=110/20=5.5 hours
they are on the same page at 11:30pm
D
Answer: (D) 11: 30 p.m.
Question: A boat travels 80 km downstream in 8 hours and 60 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
(A) 7.5 km/hr, 2.5 km/hr
(B) 5 km/hr, 4 km/hr
(C) 1 km/hr, 6 km/hr
(D) 2 km/hr, 1 km/hr
(E) 4 km/hr, 1 km/hr
Rationale: Downstream speed=80km/8hrs
=10kmph
upstream speed=60km/12hrs
=5kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(10+5)/2kmph
=7.5kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(10-5)/2kmph
=2.5kmph
ans is 7.5km/hr, 2.5km/hr
ANSWER:A
Answer: (A) 7.5 km/hr, 2.5 km/hr
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) 287
(B) 132
(C) 156
(D) 158
(E) 267
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2 = Rs.132
Answer: B
Answer: (B) 132
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 37
(B) 42
(C) 49
(D) 52
(E) 53
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
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 meter
(B) 286 meter
(C) 186 meter
(D) 288 meter
(E) 265 meter
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 meter
Question: Which of the following equations is NOT equivalent to 4c^2 = d^2 - 9 ?
(A)  4c^2 + 9 = d^2
(B)  4c^2 - d^2 = -9
(C)  4c^2= (d + 3)(d - 3)
(D)  2c = d - 3
(E) c^2 = (d^2-9)/4
Rationale: 4c^2 = d^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2c = d - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of d^2 - 9 is NOT (d-3).
d^2 - 9 can be factored into (d-3)(d+3), but neither of these parentheses is the square root of d^2 - 9.
You can see the proof when you square either of the two parentheses:
(d-3)^2 = d^2 - 6c+ 9
(d+3)^2 = d^2 + 6c + 9
Thus, D is NOT equivalent to the prompt.
Answer: (D)  2c = d - 3
Question: Virat buys an old car for Rs. 50000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 60000, his gain percent is:
(A) 3 (4/7) %
(B) 11 (1/9) %
(C) 12 (2/3) %
(D) 12%
(E) None of these
Rationale: Explanation:
C.P. = Rs. (50000 + 4000) = Rs. 54000
S.P. = Rs. 60000.
Gain% = ( (6000 / 54000) * 100 ) % = 11 (1/9)%
ANSWER B
Answer: (B) 11 (1/9) %
Question: A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. what is the rate of interest ?
(A) 3 %
(B) 4 %
(C) 5 %
(D) 6 %
(E) 7 %
Rationale: Solution
S.I= Rs.(15500-12500) =Rs.3000
Rate=(100*3000/12500*4)% =6%
Answer D
Answer: (D) 6 %
Question: How much is 85% of 40 is greater than 4/5 of 25?
(A) 22
(B) 14
(C) 88
(D) 12
(E) 66
Rationale: (85/100) * 40 – (4/5) * 25
= 14
Answer: B
Answer: (B) 14
Question: On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 28 inch from the base of the mountain. How many km is he from the base of the mountain?
(A) 14.83
(B) 12.2
(C) 14.8
(D) 14.82
(E) 14.12
Rationale: Explanation:
Since 312 inch = 136 km
So 1 inch = 136/312 km
So 28 inch = (136 Ã— 28)/ 312 = 12.2 km
Answer: B
Answer: (B) 12.2