mathewhe/aqua_rat huggingface dataset:
Question: Frances can complete a job in 6 hours, and Joan can complete the same job in 12 hours. Frances starts the job at 9 a.m., and stops working at 1 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) 12 p.m.
(D) 10 p.m.
(E) 8 p.m.
Rationale: Let the total work be 24 units.
Frances can complete 4 units/hr
Joan can complete 2 units/hr
Work done by Frances in 4 hours is 16 units ; work left for Joan is 8 units ( 24 - 16)
Time required by Jones to complete the remaining work will be 8/2 => 4 hours
Given Jones starts at 4 PM , so she would complete the work at 8 PM
Answer will be (E)
Answer: (E) 8 p.m.
Question: The population of a bacteria colony doubles every day. If it was started 7 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 128
(B) 256
(C) 512
(D) 1024
(E) 2048
Rationale: 2^7(2) = 2^8 = 256
The answer is B.
Answer: (B) 256
Question: What is the place value of 5 in the numeral 2534?
(A) 450
(B) 500
(C) 700
(D) 800
(E) 840
Rationale: Option 'B'
5 * 100 = 500
Answer: (B) 500
Question: A, B and C invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. A left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of B?
(A) Rs 690
(B) Rs 790
(C) Rs 890
(D) Rs 990
(E) None of these
Rationale: Explanation:
A:B:C = (8000*6):(4000*8):(8000*8)
= 48:32:64
= 3:2:4
So B share = (2/9)*4005 = Rs 890
Option C
Answer: (C) Rs 890
Question: At what rate percent on simple interest will Rs.415 amount to Rs.514 in 4 years ?
(A) 4.58 %
(B) 5.96 %
(C) 6.52 %
(D) 4.98 %
(E) None of these
Rationale: Explanation:
Difference in amount = 514 - 415 = 99
99 = (415 x 4 x R)/100
R = 5.96%
ANSWER IS B
Answer: (B) 5.96 %
Question: A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 126 in his diary to remember his PIN. He also wrote out the way to calculate 126 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 126".
Once, Prafull saw his diary in which Pinaki wrote this number 126. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
(A) 871
(B) 873
(C) 875
(D) 877
(E) 879
Rationale: Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =126.
Thus, (996 × x)/997=126.
=>x= 871.
Answer : A
Answer: (A) 871
Question: In a certain series, each term is m greater than the previous term. If the 22nd term is 560 and the 19th term is 500, what is the first term?
(A) 220
(B) 240
(C) 260
(D) 290
(E) 305
Rationale: a + 21m = 560 (22th term)
a + 18m = 500 (19th term)
You get a = 140 and m = 20
Answer :C
Answer: (C) 260
Question: In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German.
Can you find out the percentage of students who hate all 4 subjects ?
(A) 8%
(B) 5%
(C) 7%
(D) 12%
(E) 19%
Rationale: A
8% of student hate all four subjects.
Answer: (A) 8%
Question: 7x + y = 19 , and x + 3y = 1. Find the value of 2x + y
(A) 20
(B) 18
(C) 11
(D) 5
(E) 50
Rationale: Add these two equations
8x + 4y = 20
Divide by 2 ( to Get 2x + y)
Answer will be D. 10
Answer: (D) 5
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 4
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
Answer: D
Answer: (D) 6
Question: Q. How many 5-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5?
(A) 180
(B) 120
(C) 210
(D) 270
(E) 300
Rationale: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2
i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _
case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6
when the units digit is 2 i.e 1 _ _ _ _ _ 2
number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60
when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30
case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)
number of ways this can be done would be 5! / (2!) for 2 =60
and 5! / 2! for 6 ... = 60
adding all of these ... gives the answer 120 ...
the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat
B
Answer: (B) 120
Question: 4 male farmers and 6 female farmers can cultivate a field in 8 days, while 3 male farmers and 7 female farmers can cultivate the field in 10 days. In how many days 10 female farmers can cultivate the same field?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: WORK DONE IN 1 DAY
4M+6F=1/8
3M+7F=1/10
SOLVING THIS WE GET F=1/400
SO IN 10 DAYS,WORK DONE IS 10/400,hence female farmers take 40 days to complete the work.
ANSWER:D
Answer: (D) 40
Question: Three persons A, B and C divide a certain amount of money such that A's share is Rs. 4 less than half of the total amount, B's share is Rs. 8 more than half of what is left and finally C takes the rest which is Rs. 14. Find the total amount they initially had with them?
(A) 27
(B) 92
(C) 80
(D) 82
(E) 83
Rationale: Let the total amount be Rs. p.
Let shares of A and B be Rs. x and Rs. y respectively.
C's share was Rs. 14
we have, x + y + 14 = p ----- (1)
From the given data, x = (p/2) - 4 ----- (2)
Remaining amount = p - (p/2 - 4) => p/2 + 4.
y = 1/2(p/2 + 4) + 8 => p/4 + 10 ----- (3)
From (1), (2) and (3)
p/2 - 4 + p/4 + 10 + 14 = p
3p/4 + 20 = p
p/4 = 20 => p = Rs. 80.
Answer: C
Answer: (C) 80
Question: A man's speed with the current is 15 km/hr and the speed of the current is 3.2 km/hr. The man's speed against the current is?
(A) 10
(B) 20
(C) 50
(D) 8.6
(E) 40
Rationale: Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 3.2 km/hr
Hence, speed of the man = 15 - 3.2 = 11.8 km/hr
man's speed against the current = speed of the man - speed of the current
= 11.8 - 3.2 = 8.6 km/hr
Answer is D.
Answer: (D) 8.6
Question: 3/4 of 1/2 of 2/5 of 5080 = ?
(A) 392
(B) 229
(C) 753
(D) 493
(E) 762
Rationale: E
762
? = 5080 * (2/5) * (1/2) * (3/4) = 762
Answer: (E) 762
Question: A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student B answers each of the 100 questions on her test and receives a score of 73, how many questions did Student B answer correctly?
(A) 55
(B) 60
(C) 73
(D) 82
(E) 91
Rationale: A score of 73 brings to mind that it is an odd number even though you are subtracting an even number (twice the incorrect responses) out of the correct responses score. So the correct responses score must be an odd number too (Odd - Even = Odd).
Since the overall score is 73, the number of correct responses must be more than 73 since the student answered all questions.
Only 91 satisfies both these conditions.
Answer (E)
Answer: (E) 91
Question: A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 288 m
(B) 256 m
(C) 400 m
(D) 278 m
(E) 287 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60
= 65/3
x = 400 m.
Answer:C
Answer: (C) 400 m
Question: How many times in a day, the hands of a clock are straight?
(A) 22
(B) 24
(C) 44
(D) 48
(E) 52
Rationale: In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer: Option C
Answer: (C) 44
Question: How many odd numbers are possible between 1 to 1000000? find out the number of odd number of digits?
(A) 2999
(B) 3500
(C) 4000
(D) 4599
(E) 499999
Rationale: There are always one odd and one even no. And the question is odd no. Between 1 to 1000000
So we have to find no. Between 1 to 1000000 so we should not includes 1
1000000/2 -1=499999
ANSWER:E
Answer: (E) 499999
Question: Two trains 120 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 11.6 sec
(C) 10.6 sec
(D) 10.8 sec
(E) 20.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 120 + 190 = 310 m.
Required time = 310 * 9/250 = 11.6
= 11.6 sec.
Answer: B
Answer: (B) 11.6 sec
Question: Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
(A) 7 hours 15 minutes
(B) 8 hours 15 minutes
(C) 7 hours 30 minutes
(D) 8 hours 30 minutes
(E) 8 HOURS 15 MINUTES
Rationale: Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 .
Number of pages typed by Kumar in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 .
Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours
= 8 hours 15 minutes. ANSWER : E
Answer: (E) 8 HOURS 15 MINUTES
Question: If a car had traveled 20 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 km, at what speed did it travel?
(A) 35 kmh
(B) 40 kmh
(C) 50 kmh
(D) 60 kmh
(E) 65 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
60/x - 60/(x + 20) = 1/2
Substitute the value of x from the options. --> x = 40 --> 60/40 - 60/60 = 3/2 - 1 = 1/2
Answer: B
Answer: (B) 40 kmh
Question: SCORE INTERVAL----------------NUMBER OF SCORES
50-59-------------------------- 8
60-69--------------------------10
70-79--------------------------16
80-89--------------------------27
90-99--------------------------18
The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 79 scores?
(A) 39th (80-89)
(B) 40th
(C) 34th
(D) 37th
(E) 35th
Rationale: Total scores= 8+10+16+27+18 = 79, which is odd, therefore the median is the Floor(79/2)+1 = 39th score. And the 39th score is in the 80-89 range, because 50-79 only reference 34 scores.
A
Answer: (A) 39th (80-89)
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 1/2
(B) 10/21
(C) 9/11
(D) 7/11
(E) 11/15
Rationale: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)
=5C2 / 7C2
= (5×42×1)/(7×62×1)
=(5×4)/(7×6)
=10/21
Ans- B
Answer: (B) 10/21
Question: The population of a bacteria colony doubles every day. If it was started 5 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 512
(B) 768
(C) 64
(D) 2048
(E) 4096
Rationale: 2^5(2) = 2^6 = 64
The answer is C
Answer: (C) 64
Question: In one hour a boat goes 22 km long the stream and 12 km against the stream.The speed of the boat in still water is?
(A) 17
(B) 18
(C) 16
(D) 15
(E) 11
Rationale: Speed in still water A = ½ ( 22+12) km/hr A= 17 kmph
Answer: A
Answer: (A) 17
Question: A vessel of capacity 2 litre has 30% of alcohol and another vessel of capacity 6 litre had 45% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 31%.
(B) 71%.
(C) 49%.
(D) 33%.
(E) 51%.
Rationale: 30% of 2 litres = 0.6 litres
45% of 6 litres = 2.7 litres
Therefore, total quantity of alcohol is 3.3 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 33%
D
Answer: (D) 33%.
Question: On an xy-graph, three corners of a
parallelogram are located at (3, 3), (4, – 4),
and (–2, –1). Which of the following points
could be the remaining corner?
(A) (8, 0)
(B) (8, –1)
(C) (–1, 9)
(D) (–3, 6)
(E) (–5, 7)
Rationale: A good way to begin is to draw a picture showing the three points given, including
possible places where a fourth point would form a parallelogram. Here’s what your
picture may look like:
y
A
B
C
(4, –4)
(–2, –1)
(3, 3)
x
This figure shows three possible points for the remaining corner of the parallelogram: A, B,
and C. To find the exact coordinates of these three additional points, choose any of the
given points and count up and over (or down and over) to a second given point. Then,
starting from the third given point, count the same number of steps up and over (or down
and over) and label the point where you end up.
By this method, you find that A = (–3, 6), B = (9, 0), and C = (–1, –8). Only point A is listed
as an answer.
correct answer A)(8, 0)
Answer: (A) (8, 0)
Question: If 9 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
(A) 80
(B) 63
(C) 120
(D) 1008
(E) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 9c2
for vertical 8c2
total parallelogram is 9 c2*8c2=36*28
=1008
ANSWER:D
Answer: (D) 1008
Question: If the prime factorization of the integer q can be expressed as a^2xb^xc^3x−1, where a, b, c, and x are distinct positive integers, which of the following could be the total number of factors of q?
(A) 3j + 4, where j is a positive integer
(B) 5k + 5, where k is a positive integer
(C) 6l + 2, where l is a positive integer
(D) 9m + 7, where m is a positive integer
(E) 10n + 1, where n is a positive integer
Rationale: Straight forward question if you know the formula for number of factors of an integer q=ax∗by∗czq=ax∗by∗cz , where x,y,z≥0 x,y,z≥0 and are integers = (x+1)(y+1)(z+1) including 1 and integer q.
Now given, q= a^2xb^xc^3x−1, thus based on the above formula, the number of factors of q including 1 and q = (2x+1)(x+1)(3x-1+1) = 3x(2x+1)(x+1). So we know that the number will be of the form 3x(2x+1)(x+1) , will be an integer and will be true for ALL X. Thus substitute x=1, we get number of factors = 3*3*2 =18 (this eliminates A, as 3 is a factor of 18 and thus can not leave 4 or (4-3=1) as the remainder. Similarly, eliminate C and D).
Now substitute x=2, we get number of factors = 6*5*3 = 90 and this eliminates E as 10 is a factor of 90 and will leave a remainder of 0. Thus B is the only remaining answer choice
ANSWER:B
.
Answer: (B) 5k + 5, where k is a positive integer
Question: Which of the following is closest to 10^140 – 10^30 ?
(A) 10^210
(B) 10^140
(C) 10^150
(D) 10^90
(E) 10^6
Rationale: 10^140 – 10^30
10^30 * (10^110 – 1)
as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^110 – 1) would remain as 10^110.
and 10^30 * 10^110 = 10^140. Answer is B.
Answer: (B) 10^140
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 500 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 3600.
(B) 4860.
(C) 5780.
(D) 5760.
(E) 6380.
Rationale: Efficiency per machine = 500 watt/hr
Efficiency due to increase in wind speed = 500*120% => 600 watt/hr
Production by each machine in 2 hours is 600*2 => 1200 watt
Production by 3 machines => 1200 watt * 3 = 3600 watt
Answer will be (A)
Answer: (A) 3600.
Question: There are 60 people and 3 clubs M, S, and Z in a company. 16 people joined M, 18 people joined S and 11 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Answer E.
key is 'atmost' here.
so 16 people joined M.
18 people joined S and 11 people joined Z. to get maximum people who did not join any club, 11 people who joined Z are among 18 people who joined S.
so 18+16 = 34
60-34 = 26
Answer: (E) 26
Question: P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 1/15
(B) 2/15
(C) 8/15
(D) 9/15
(E) 11/15
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
C
Answer: (C) 8/15
Question: In how many years will a sum of money doubles itself at 12% per annum on simple interest?
(A) 15%
(B) 20%
(C) 10%
(D) 8%
(E) 22%
Rationale: P = (P*12*R)/100
R = 8%
Answer:D
Answer: (D) 8%
Question: If x is an integer, find the minimum value of x such that 0.00001154111 x 10^x exceeds 1000.
(A) 7
(B) 1
(C) 8
(D) 6
(E) 5
Rationale: Considering from the left if the decimal point is shifted by 8 places to the right, the number
becomes 1154.111. Therefore, 0.00001154111 x 10x exceeds 1000 when x has a minimum value of 8.
ANSWER:C
Answer: (C) 8
Question: Find the surface area of a 8 cm x 4 cm x 2 cm brick.
(A) 136 cu cm
(B) 112 cu cm
(C) 164 cu cm
(D) 180 cu cm
(E) None
Rationale: Sol.
Surface area = [2(8 x 4 + 4 x 2 + 8 x 2)]
= (2 x 56)
= 112 cu cm
Answer B
Answer: (B) 112 cu cm
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
(A) 43
(B) 26
(C) 33
(D) 21
(E) 28
Rationale: B
26
Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140 x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer: (B) 26
Question: What is the average of two tenths and five thousandths
(A) 0.2022
(B) 0.3325
(C) 0.1025
(D) 0.2012
(E) 0.2114
Rationale: Explanation:
two tenths = 0.2
Five thousandths = 0.005
The average is (0.2 + 0.005)/2 = 0.1025
Answer: C
Answer: (C) 0.1025
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 8 sec
(B) 6 sec
(C) 2 sec
(D) 9 sec
(E) 3 sec
Rationale: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [110 * 3/55] sec
= 6 sec
Answer: B
Answer: (B) 6 sec
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 5/9
(C) 5/2
(D) 5/1
(E) 5/0
Rationale: Explanation:
Two balls can be picked from nine balls in ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ways.
The required probability = (5 * 4) = 20/36 = 5/9
Answer:B
Answer: (B) 5/9
Question: A water tank is one-third 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) 6 min.to empty
(B) 9 min.to empty
(C) 5 min.to empty
(D) 4 min.to empty
(E) 7 min.to empty
Rationale: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 1/3
part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15
so, the tank will be emptied in 5 min
Answer: C
Answer: (C) 5 min.to empty
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 11 1/5%
(B) 11 8/9%
(C) 11 1/9%
(D) 13 1/9%
(E) 11 4/9%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer:C
Answer: (C) 11 1/9%
Question: If an apple orchard has 10,000 apples on its trees, and every day half of the apples on the trees are harvested, how many will still be on the trees after 4 days?
(A) 500 apples
(B) 625 apples
(C) 1000 apples
(D) 1250 apples
(E) 1500 apples
Rationale: 10000/(2^4)=10000/16=625
The answer is B.
Answer: (B) 625 apples
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:5
(C) 1:4
(D) 1:1
(E) 1:8
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: (A) 1:2
Question: Dacid obtained 96, 95, 82, 87 and 92 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 67
(B) 26
(C) 87
(D) 26
(E) 90
Rationale: Average
= (96+95+82+87+92)/5
= 452/5 = 90.
Answer: E
Answer: (E) 90
Question: The sum of ages of Aswin ,Sachin and Sumesh is 93 years.10 years ago ratio of their age was 2:3:4.what is the present age of sachin.
(A) 19
(B) 21
(C) 31
(D) 41
(E) 51
Rationale: Solution:Sum of the present ages of Aswin ,Sachin and Sumesh=93
Sum of the ages of Aswin ,Sachin and Sumesh 10 years ago=93- 10*3=63
Age of sachin 10 years ago=(3/(2+3+4)) * 63 = 21.
Present age of Sachin=21+10=31
Answer C
Answer: (C) 31
Question: After giving a discount of rs.50 the shopkeeper still gets a profit of 20%,if the cost price is rs.180.find the markup %?
(A) 0.5
(B) 0.6
(C) 0.48
(D) 0.65
(E) 0.45
Rationale: cost price=180
s.p=180*120/100=216
disc=50
so...mark price=216+50=266......
mark up%=266-180/180=86/180=.48 or 48%
ANSWER:C
Answer: (C) 0.48
Question: Rocky is 22 and his brother Ronnie is 25 years old. How many years ago was the ratio of their ages 2:5 ?
(A) 20 years
(B) 2 years
(C) 10 years
(D) 22 years
(E) 24 years
Rationale: let be x years ago....
so, (22-x)/(25-x)=2/5........solve it.
x=20years
ANSWER:A
Answer: (A) 20 years
Question: If the operation # is defined for all a and b by the equation a@b =(a*b)-1, then 2#(3#1) =
(A) 4
(B) 2
(C) 3
(D) 1
(E) 5
Rationale: work within the parenthesis first so solve (3#1) first
(3#1)=(3*1)-1=2
now take 2 plug back into equation and solve the rest
(2#2)=(2*2)-1=3
so 3 is the answer....this question is merely testing order of operations
remember PEMDAS
Option C is answer
Answer: (C) 3
Question: A ballet instructor has decided to divide her next class into equal groups. Unfortunately, the number of students doesn't divide equally by the group size that she wanted. It turns out that in order for the groups to be equal, she must increase her group size by one and cut three children from the roster. Which of the following can describe the initial number of students in the class and the instructor's initial group size (in the order Students; group size)?
(A) 82; 5.
(B) 54; 9.
(C) 27; 4.
(D) 15; 6.
(E) 35; 7.
Rationale: Option E) Initially 35 students then reduced to 32 students; and Initially a group size of 7 increased to a group size of 8 fits the requirement.
32 / 8 = 4 groups of students
Answer: (E) 35; 7.
Question: Evaluate 25% of 450 + 45% of 250
(A) 225
(B) 242
(C) 252
(D) 262
(E) 272
Rationale: Explanation:
= (25/100) * 450 + (45/100) * 250
= 225
Option A
Answer: (A) 225
Question: xy=1 then what is (7^(x+y)^2) / (7^(x-y)^2)
(A) 2401
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
7^4 = 2401
Answer A
Answer: (A) 2401
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 9 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
(A) 15
(B) 12
(C) 9
(D) 6
(E) 3
Rationale: A+P+G= 9*2
A=2G
P=3G
3G+2G+G= 9*2
G= 9*2/6= 3
A= 3*2=6
Difference = 6-3=3
'E' is the answer
Answer: (E) 3