mathewhe/aqua_rat huggingface dataset:
Question: How many odd three-digit integers greater than 700 are there such that all their digits are different?
(A) 40
(B) 56
(C) 72
(D) 80
(E) 104
Rationale: 2 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 144
Now take numbers in the range 700 - 900.
Total numbers where all digits are different = 144 (as before)
[highlight]Number of odd numbers = 2 * 8 * 5 = 80[/highlight] (now there are 5 possibilities for the unit's digit)
D
Answer: (D) 80
Question: The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
(A) 5
(B) 4
(C) 1/2
(D) 1/5
(E) 1/8
Rationale: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5.
The answer is D.
Answer: (D) 1/5
Question: The months of the calendar have been coded in the following ways:
January = 1071
February = 682
March = 1353
April = 154
May = 1335
June = 1046
July = 1047
August = 168
Using the same coding method, can you find out how to code September
(A) 19|9|9
(B) 19|9|8
(C) 19|9|7
(D) 19|9|6
(E) 19|9|5
Rationale: Solution:
19|9|9
Explanation:
This is simple. All the months have been coded with a distinctive way.
Let's see about January:
January = 1071 = 10|7|1
10 is the position of J, the first letter of January in alphabetical order.
7 is the number of letters used in forming the word January.
1 is the position of January in the calendar.
For February:
February = 682 = 6|8|2
6 is the position of F, the first letter of February in the alphabetical order.
8 are the number of letters used in forming the word.
2 is the position of February in the calendar.
Similarly, September = 19|9|9
19 is the position of S, the first letter of September in the alphabetical order.
9 are the number of letters used in forming the word.
9 is the position of September in the calendar.
Answer A
Answer: (A) 19|9|9
Question: The price of a certain painting increased by 10% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
(A) 102%
(B) 105%
(C) 95%
(D) 93.5%
(E) 90%
Rationale: Easiest thing to do: Assume that price is 100
Price at the end of yr 1: 100+ 10 = 110
Price at the end of year 2 = 110 - 110*0.15 = 110*0.85 = 93.5
Hence required answer = (93.5/100)*100% = 93.5%
Answer is D.
Answer: (D) 93.5%
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
(A) 1877 ways
(B) 1440 ways
(C) 1678 ways
(D) 1976 ways
(E) 1286 ways
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer: B
Answer: (B) 1440 ways
Question: total 52 matches are conducted in Knockout match type. How many players will be participated in that tournament?
(A) 60
(B) 51
(C) 53
(D) 56
(E) 50
Rationale: 51 players
ANSWER:B
Answer: (B) 51
Question: The sum of three numbers is 343. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
(A) 20
(B) 30
(C) 38
(D) 105
(E) None of these
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 343
or 49x = 343 or x = 7
⇒ Second number = 15x = 15 × 7 = 105
Answer D
Answer: (D) 105
Question: Pipes A and B can fill a tank in 8 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
(A) 1 13/17 hours
(B) 2 8/11 hours
(C) 3 9/17 hours
(D) 4 4/5 hours
(E) None
Rationale: Solution
Net part filled in 1 hour	= (1/8 + 1/6 -1/12)
= 5/24.
Therefore, the tank will be full in 24/5 hrs.	â€¹=â€º 4 4/5 hrs.
Answer D
Answer: (D) 4 4/5 hours
Question: WHEN A PERSON SELLS TWO ITEMS $1300 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
(A) no loss no gain
(B) 2% gain
(C) 5% gain
(D) 4% loss
(E) 1% loss
Rationale: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : D
Answer: (D) 4% loss
Question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 30 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
(A) 64%
(B) 66%
(C) 72%
(D) 76%
(E) 80%
Rationale: Let in May Lee family's total income =100
in May Mrs Lee's income =60
in May rest of the family's income = 40
In june Mrs Lees income = 60*130/100 = 78
In june Total income = 78+ 40 = 118
% of Mrs Lee's income = 72/112 =66.10
(B)
Answer: (B) 66%
Question: If you roll 2 dice, what is the probability of rolling a 5?
(A) 1/9
(B) 1/12
(C) 1/3
(D) 5/12
(E) 2/13
Rationale: The answer is 1/9, as there are 4/36 ways to add the sum of 5 with 2 dice. Answer: A
Answer: (A) 1/9
Question: There are 12 red balls, 10 blue balls, 12 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
(A) 10
(B) 23
(C) 43
(D) 40
(E) 16
Rationale: The worst case scenario would be if we pick 11 red balls, 9 blue balls, 11 (?) balls and 8 black balls. In this case we'll have 11+9+11+8=39 balls and still won't have all the balls of one color. The next 40rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: D
Answer: (D) 40
Question: Two poles of height 6 meters and 11 meters stand on a plane ground. If the distance between their feet is 12 meters then find the difference in the distance between their tops:
(A) 12m
(B) 5m
(C) 13m
(D) 11m
(E) 12m
Rationale: distance between their tops = sqrt( 12^2+(11-6)^2) = sqrt 169=13m
ANSWER:C
Answer: (C) 13m
Question: One fourth of a solution that was 10 percent salt by weight was replaced by a second solution resulting in a solution that was 16 percent salt by weight. The second solution was what percent salt by weight ?
(A) 34%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of salt in 2nd sol)=34%=A
Answer: (A) 34%
Question: Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 5x boxes?
(A) 3 minutes
(B) 4 minutes
(C) 5 minutes
(D) 6 minutes
(E) 10 minutes
Rationale: Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 4x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10
Now combine Time = combine work needs to be done / Combine Rate = 5x/5x * 10 = 10 Min
Ans: E
Answer: (E) 10 minutes
Question: A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone?
(A) 6 days
(B) 8 days
(C) 12 days
(D) 10 days
(E) 5 days
Rationale: Explanation:
A and B 1day's work = 1/6
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/6) - (1/12) = 12 Days
Answer: Option C
Answer: (C) 12 days
Question: 28, 26, 21, 19, 14, 12, ?
(A) 3
(B) 2
(C) 8
(D) 7
(E) 5
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : D.
Answer: (D) 7
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 8000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college?
(A) $20000
(B) $15000
(C) $32000
(D) $10000
(E) $9000
Rationale: Since investment doubles in 70/r years then for r=4 it'll double in 70/4=~18 years (we are not asked about the exact amount so such an approximation will do). Thus in 36 years investment will double twice and become ($8,000*2)*2=$32,000 (after 18 years investment will become $8,000*2=$16,000 and in another 18 years it'll become $16,000*2=$32,000).
Answer: C.
Answer: (C) $32000
Question: An article is bought for Rs.400 and sold for Rs.360, find the loss percent?
(A) 18 2/3%
(B) 16 7/3%
(C) 16 2/8%
(D) 10%
(E) 76 2/3%
Rationale: 400 ---- 40
100 ---- ? => 10%
Answer:D
Answer: (D) 10%
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many X such committees are possible?
(A) X=20
(B) X=40
(C) X=50
(D) X=80
(E) 120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: (D) X=80
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
(A) 10
(B) 15
(C) 21
(D) 18
(E) 29
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60	.0 .
for-^—=18 days.
D
Answer: (D) 18
Question: 14, 18, x, 20
The median of the list of positive integers above is 16. Which of the following could be the average (arithmetic mean) of the list?
(A) 3
(B) 5.5
(C) 6.25
(D) 16
(E) 7.5
Rationale: GivenThe median of the list of positive integers above is 16
So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 16
so the sequence will be x 14 18 20
Lets say x = 12, which gives us mean = sum/4 = 16
D is correct
Answer: (D) 16
Question: The price of an article is reduced by 25% in order to
restore the must be increased by ?
(A) 3/100%
(B) 100/3%
(C) 6/25%
(D) 25/6%
(E) 4/75%
Rationale: [x/(100-x)]*100 =[25/(100-25)]*100
=(25/75)*100=100/3%
ANSWER B 100/3%
Answer: (B) 100/3%
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
(A) 287 km
(B) 480 km
(C) 127 km
(D) 177 km
(E) 2698 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 4
2x/15 - x/8 = 4 => x
= 480 km
Answer: B
Answer: (B) 480 km
Question: The salary of a person was reduced by 15%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
(A) 10%
(B) 17.6%
(C) 13.7%
(D) 15.1%
(E) 12.3%
Rationale: Let the original salary be $100
New salary = $85
Increase on 85=15
Increase on 100 = 15/85* 100 = 17.6%
Answer is B
Answer: (B) 17.6%
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 30% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 14.28%
Rationale: 0.1 M = 0.70 E
=> E/M = 1/7 * 100 = 14.28%
So answer is E.
M - # of Motorists
E - # of Motorists exceeding speed
Answer: (E) 14.28%
Question: Two numbers are such that the ratio between them is 3:5 but if each is increased by 10, the ratio between them becomes 5 : 7, the numbers are
(A) 3, 5
(B) 7, 9
(C) 13, 22
(D) 15, 25
(E) None
Rationale: Explanation:
Let the numbers be 3a and 5a
Then 3a+10/5a+10=5/7
⇒7(3a+10)=5(5a+10)⇒a=5
The numbers are 15 & 25
Correct Option: D
Answer: (D) 15, 25
Question: A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Adjacent sides of parallelogram = 2 cm and 9 cm
Distance between shorter sides = 8 cm
Area of parallelogram = b × h
= 9 × 8 cm²
= 72 cm²
Again, area of parallelogram = b × h
72 = 12 × h
h = 72/12
h = 6 cm
Therefore, the distance between its longer side = 6 cm.
ANSWER-OPTION C
Answer: (C) 6
Question: A person buys an article at Rs.550. At what price should he sell the article so as to make a profit of 30%?
(A) 600
(B) 715
(C) 772
(D) 662
(E) 521
Rationale: Cost price = Rs.550
profit = 30% of 550 = Rs.165
Selling price = Cost price + Profit
= 550 + 165 = 715
Answer: B
Answer: (B) 715
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) 12 years
(B) 14 years
(C) 15 years
(D) 20 years
(E) 11 years
Rationale: 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 B
Answer: (B) 14 years
Question: If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?
(A) 3
(B) 6
(C) 11
(D) 22
(E) 222
Rationale: Maybe there is a faster way to do it but I did it like this:
How many ways can you arrange abc?
abc
acb
bac
bca
cab
cba
which are equivalent to:
100a + 10b + c
100a + 10c + b
100b + 10a + c
100b + 10c + a
100c + 10a + b
100c + 10b + a
if you add them all together you get 222a + 222b + 222c
ANSWER:E
Answer: (E) 222
Question: On Thursday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up C percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of C?
(A) 20%
(B) 30%
(C) 33 1⁄3%
(D) 40%
(E) 50%
Rationale: Let the original price be 100
discounted Price = 80
New Price = 20 +100 =120
C=(40/80)*100
Ans:E
Answer: (E) 50%
Question: In a group of cows and chickens, the number of legs was 18 more than twice the number of heads. The number of cows was:
(A) 5
(B) 7
(C) 9
(D) 12
(E) 14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 18 more than twice the number of heads.
Therefore, 2 × (x + y) + 18 = 4x + 2y.
or, 2x + 2y + 18 = 4x + 2y.
or, 2x + 18 = 4x [subtracting 2y from both sides].
or, 18 = 4x – 2x [subtracting 2x from both sides].
or, 18 = 2x.
or, x = 9 [dividing by 2 on both sides].
Therefore, the number of cows = 9.
Correct Answer:C)9
Answer: (C) 9
Question: If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers.
(A) 50
(B) 30
(C) 125
(D) 25
(E) None of these
Rationale: H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.
ANSWER:D
Answer: (D) 25
Question: 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?
(A) 40
(B) 45
(C) 50
(D) 35
(E) 30
Rationale: Work done by 4 men and 6 women in 1 day = 1/8
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 × (1/400) = 1/40
Ie, 10 women can complete the work in 40 days
Answer is A.
Answer: (A) 40
Question: The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate Y of movement for his trip along the moving walkway?
(A) 2 feet per second
(B) 2.5 feet per second
(C) 3 feet per second
(D) 4 feet per second
(E) 5 feet per second
Rationale: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average Y MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.
Answer: (E) 5 feet per second
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 180 m
(B) 240 m
(C) 260 m
(D) 280 m
(E) 380 m
Rationale: Speed = 54 x 5/18 = 15 m/s
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15
--> x + 300 = 540
x = 240m.
Answer : B.
Answer: (B) 240 m
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/ 27
(D) 5/ 18
(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: 21 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) 625
(B) 600
(C) 576
(D) 676
(E) 420
Rationale: we can go in any bus out of the 21 buses.
Hence He can go in 21 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 24 ways.
Total number of ways = 21 x 20 = 420
ANSWER:E
Answer: (E) 420
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability W that private Benjamin will be chosen for latrine duty?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability W= 1- 3/5 = 2/5. Thus C is the correct answer.
Answer: (C) 2/5
Question: Donovan took a math test and got 35 correct and 10 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
(A) 57.78%
(B) 67.78%
(C) 77.78%
(D) 47.78%
(E) 97.78%
Rationale: 35 correct answers+10 incorrect answers=45 total answers
Multiple the opposites
100 x 35 = 3500
77.777/3500
77.78% (rounded to hundredth)
correct answer C
Answer: (C) 77.78%
Question: If a choir consists of 2 boys and 4 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
(A) 120
(B) 30
(C) 24
(D) 11
(E) 5
Rationale: There are 5 possibilities:
bbgggg
gbbggg
ggbbgg
gggbbg
ggggbb
Think of all 2 boys as a single unit. Together with 4 girls it makes a total of 5 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 5 available positions. If the number of available unique positions is 5, then the number of unique patterns equals 5 as well.
Answer: E.
Answer: (E) 5
Question: If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?
I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9
(A) I only
(B) II and III only
(C) I and II only
(D) I and III only
(E) I, II and III
Rationale: We need to keep two things in mind here:
1. Product of two numbers = LCM*HCF
2. LCM should be a multiple of HCF
Only Statement I follows these two rules.
Correct Option A
Answer: (A) I only
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
(A) 23 minutes
(B) 30 minutes
(C) 87 minutes
(D) 16 minutes
(E) 19 minutes
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: B
Answer: (B) 30 minutes
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 52 years now, the son's age five years back was?
(A) 16 years
(B) 14 years
(C) 18 years
(D) 21 years
(E) 15 years
Rationale: Let the son's present age be x years.
Then, (52 - x) = x
2x = 52 => x = 26
Son's age 5 years back = (26 - 5)
= 21 years.
Answer: D
Answer: (D) 21 years
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 65 Kmph
(D) 70 Kmph
(E) None
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B)
Answer: (B) 60 Kmph
Question: Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?
(A) 31.25
(B) 37.5
(C) 50.0
(D) 52.5
(E) 56.25
Rationale: Soln:-
X*1.25*1.25 = 1.5625 X
so there is a net increase of 56.25% .
Answer E.
Answer: (E) 56.25
Question: A train 300m long takes 9 sec to cross a man walking at 3kmph in a direction opposite to that of the train. Find the speed of the train?
(A) 100kmph
(B) 90kmph
(C) 120kmph
(D) 117kmph
(E) 125kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+3 = (x+3)*5/18 m/sec
300/[(x+3)*5/18] = 9
9(x+3) = 1080
x = 117kmph
Answer is D
Answer: (D) 117kmph
Question: If a^x = b^y, then
(A) log a/b= x/y
(B) log a/ log b = x/y
(C) log a/ log b = y/x
(D) log b/a = x/y
(E) log b/a = y/x
Rationale: a^x = b^y => log a^x = log b^y => x log a = y log b
=> log a/ log b = y/x
ANSWER:C
Answer: (C) log a/ log b = y/x