mathewhe/aqua_rat huggingface dataset:
Question: The value of 1/(1-x) + 1/ (1+x) + 2/(1+x^2) + 4/(1+x^4)
(A) 8/(1-x^8)
(B) 4x/(1+x^2)
(C) 4/(1-x^6)
(D) 4/(1+x^4)
(E) 4x/(1-x^4)
Rationale: Highlighted part has mistake as the exponent of x must be 4 in last term
CORRECT QUESTION ISThe value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) = ?
Solution is as mentioned below...
one more way that could get the answer in the type of eqn and choices given is to substitute some value for x...
0 would be better as the eq has constant term free of term 'x'..
the Eq gives us 8 as the ans , as also only choice A..
Answer: (A) 8/(1-x^8)
Question: What is the tens digit of 36^5?
(A) 1
(B) 7
(C) 5
(D) 3
(E) 9
Rationale: 36^5 = 6^7
(6^2)=6*6 = 36
(6^3)= 36*6 = .16
(6^4)= .16*6 = ..96
(6^5) = ..96*6 = ..76
(6^6) = ..76*6 = ...56
(6^7) = ....56*6 = ....36
If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...
Continue the pattern up to 6^7 ( dont actually calculate full values) and answer is D: 3
Answer: (D) 3
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 945 what is the least possible value of k?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: 945 = 3*3*3*5*7
Thus k must include numbers at least up to the number 9 so that there are at least three appearances of 3 (that is: 3, 6, and 9).
The answer is C.
Answer: (C) 9
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer?
(A) 2828
(B) 2338
(C) 377
(D) 4266
(E) 288
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266.Answer: D
Answer: (D) 4266
Question: A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 25%. Their gross income from sales for one month increases by what percent?
(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%
Rationale: Let P be the original price and let x be the number of items sold originally.
The original income is P*x.
After the changes, the income is 0.9P*1.25x = 1.125*(P*x), an increase of 12.5%.
The answer is D.
Answer: (D) 12.5%
Question: If $ 5,000 is invested in an account that earns 12% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
(A) $ 4
(B) $ 8
(C) $ 12
(D) $ 16
(E) $ 432
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.12/2)^2= 5412
Amount (SI) = P+PTR/100 = 5000+(5000*1*12/100)=5400
Difference = 5412-5400=12 $
C
Answer: (C) $ 12
Question: If x < 12, then it must be true that...
(A) -x < -12
(B) -x - 2 < 14
(C) -x + 2 < -10
(D) x + 2 < 10
(E) x - 3 < 14
Rationale: A. -x < -12 --> x>12. Not true.
B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.
C. -x + 2 < -10 --> x>12. Not true.
D. x + 2 < 10 --> x<8. Not true, consider x=10.
E. x - 3 < 14 --> x<17. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.
Answer: E.
Answer: (E) x - 3 < 14
Question: If you roll a fair-sided die twice, what is the probability of getting a (4.4) double?
(A) 1/2
(B) 1/4
(C) 1/12
(D) 1/3!
(E) 1/24
Rationale: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(4, 4) = 6
Probability= 6/6*6= 1/6=1/3!
D
Answer: (D) 1/3!
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 17 kmph
(B) 45 kmph
(C) 17 kmph
(D) 19 kmph
(E) 13 kmph
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3)
= 45 kmph.
Answer: B
Answer: (B) 45 kmph
Question: A motorist travel to a place 150 km away at an average speed of 120 km/hr and returns at 30 km/hr.His average speed for the whole journey in km/hr is
(A) 36 km/hr
(B) 37 km/hr
(C) 45 km/hr
(D) 48 km/hr
(E) None of these
Rationale: Explanation:
Average speed will be
2xy/x+y km/hr
= {2(120)(30)}/{120+30} km/hr
= 48 km/hr
Answer: Option D
Answer: (D) 48 km/hr
Question: A can do a work in 7 days B in 12 days and C in 5 days. If they work on it together then in how many days required to complete the work?
(A) 420/177
(B) 420/179
(C) 410/87
(D) 90/14
(E) 77/56
Rationale: Person ( A ) ( B ) ( C ) (A+B+C)
Time - ( 7 ) ( 12 ) ( 5 )
Rate - (60) (35) ( 84 ) (179)
Work - (420) (420) (420) (420)
therefore A+B+C requires (420/179) days to complete entire work
= 420/179
Answer is B
Answer: (B) 420/179
Question: 2, 6, 12, 20, 30, 42, 56, ?
(A) 84
(B) 37
(C) 72
(D) 35
(E) 86
Rationale: C
72
The pattern is 1 × 2, 2 × 3, 3 × 4, 4 × 5, 6 × 7, 7 × 8,....
Answer: (C) 72
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 338
(B) 277
(C) 160
(D) 882
(E) 232
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: (D) 882
Question: The sum of a number and its reciprocal is one-eighth of 34. What is the product of the number and its square root?
(A) 8
(B) 27
(C) 32
(D) 42
(E) 52
Rationale: Let the number be x. Then,
x + 1/x = 34/8
8x2 - 34x + 8 = 0
4x2 - 17x + 4 = 0
(4x - 1)(x - 4) = 0
x = 4
required number = 4 * √4 = 4 * 2 = 8.
ANSWER:A
Answer: (A) 8
Question: A man covers a certain distance C in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?
(A) 200 km
(B) 50 km
(C) 20 km
(D) 60 km
(E) 80 km
Rationale: Not really. When you solve the 2 equation above, you get,
6T-4/3 = 5R/6 from simplifying equation 1
4T-2=R/2 from simplifying equation 2
You can now multiply equation 2 by 5 to get
5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance C= R*T=20*3=60 km.D
Answer: (D) 60 km
Question: Which number is the odd one out?
159
642
693
537
289
582
(A) 916
(B) 345
(C) 895
(D) 642
(E) 624
Rationale: D
642
In the rest there is the same difference between each digit, eg: 6 (Ã¢â‚¬â€œ2) 4 (Ã¢â‚¬â€œ2)2
Answer: (D) 642
Question: sue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 4 how many does he have left?
(A) 2
(B) 5
(C) 6
(D) 4
(E) 8
Rationale: 4 D
Answer: (D) 4
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2
(B) 5
(C) 7
(D) 5
(E) 8
Rationale: Explanation:
|-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: Option A
Answer: (A) 2
Question: 11^9 - 11^2 is approximation of which of the following?
(A) 9^7
(B) 9^8
(C) 9^9
(D) 11^9
(E) 9^10
Rationale: => Since 9^2 is a small number compared to 11^9, it can be disregarded. Thus, 11^9-11^2=11^9 is derived and the answer is D.
Answer: (D) 11^9
Question: (?) + 3699 + 1985 - 2047 = 31111
(A) 27460
(B) 27474
(C) 27485
(D) 27490
(E) 27495
Rationale: x + 3699 + 1985 - 2047 = 31111
x + 3699 + 1985 = 31111 + 2047
x + 5684 = 33158
x = 33158 - 5684 = 27474.
B)
Answer: (B) 27474
Question: A man takes
5
5 hours
45
45 min in walking to a certain place and riding back. He would have gained
2
2 hours by riding both ways. The time he would take to walk both ways is
(A) 11 hrs
(B) 8 hrs 45 min
(C) 7 hrs 45 min
(D) 9 hrs 20 min
(E) 8 hrs
Rationale: Explanation:
Solution 1Given that time taken for riding both ways will be 22 hours lesser than the time needed for waking one way and riding back.
Therefore,
time needed for riding one way = time needed for waking one way - 22 hours
Given that time taken in walking one way and riding back =5=5 hours 4545 min
Hence, the time he would take to walk both ways
=5=5 hours 4545 min + 22 hours
=7=7 hours 4545 min
Answer is C
Answer: (C) 7 hrs 45 min
Question: Henry completes a piece of work in 640 days, Rose completes the same work in 960 days. If both of them work together, then the number of days required to complete the work is?
(A) 384
(B) 385
(C) 386
(D) 387
(E) 388
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 640 × 960/1600 = 384 days
Answer is A
Answer: (A) 384
Question: What are the next two letters in the following series and why?
W A T N T L I T F S _ _
*Hint : Look into the title of the Riddle
(A) A and W
(B) A and E
(C) B and W
(D) A and C
(E) S and W
Rationale: A
A and W.
The letters are the first letters of the words in the question. Thus, the next two letters are A and W.
Answer: (A) A and W
Question: Which is the least number that must be subtracted from 1256 so that the remainder when divided by 7, 12, 16 is 4?
(A) 242
(B) 232
(C) 236
(D) 240
(E) 244
Rationale: First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}
The largest such number less than or equal to 1256 is 336x3+4 or 1012
To obtain this you need to subtract 244.
E
Answer: (E) 244
Question: An outlet pipe empties a tank which is full in 8 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 4 hours longer. Find the capacity of the tank.
(A) 8600 litres
(B) 200 litres
(C) 12800 litres
(D) 11520 litres
(E) 13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 8*60 = 480 liters/hour;
Net outflow rate when both pipes operate would be x-480 liters/hour.
Capacity of the tank = x*8 hours = (x-480)*(8+4) hours
8x=(x-480)*12 --> x=1440 --> capacity = 8x = 11520 liters.
Answer: D.
Answer: (D) 11520 litres
Question: The sum of three consecutive numbers is 87. The greatest among these three number is:
(A) 26
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: Let the numbers be x, x + 1 and x + 2
Then,
x + (x + 1) + (x + 2) = 87
3x = 84
x = 28
Greatest number, (x + 2) = 30.
ANSWER:D
Answer: (D) 30
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 1/5
(B) 11 1/4
(C) 11 1/9
(D) 11 1/2
(E) 11 1/1
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer:B
Answer: (B) 11 1/4
Question: Simplify (3^y + 3^y) (2^y + 2^y + 2^y)
(A)  4^4y * 3^3y
(B)  12^y+1
(C)  16^y + 9^y
(D)  12^y
(E)  6^y+1
Rationale: E
(3^y + 3^y) (2^y + 2^y + 2^y)
(2*3^y)(3*2^y)
6*6^y=6^(y+1)..
Answer: (E)  6^y+1
Question: A painting at an art gallery is framed such that the area of the square frame is 2/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 10, what is the area of the painting inside the frame?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b
Area of painting = a^2 and we know that the area of the frame is (2/3) of that of the painting so
Area of frame = (2/3) * a^2
Area of Frame + Painting = a^2 + (2/3)*a^2 = (5/3)*a^2 which is equal to b^2
Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2
so, b * sqrt2 = 10
so, b = 5 * sqrt2
b^2 = 50
we know that b^2 = (5/3)*a^2
so, a^2 = (3/5)*b^2 = (3/5)*50 = 30
And area of painting = a^2 = 30
So, answer will be C.
Answer: (C) 30
Question: In a room filled with 6 people, all 6 people have exactly 1 sibling in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 3/5
(B) 4/5
(C) 5/6
(D) 5/12
(E) 7/12
Rationale: The 6 people consist of three sets of 2 siblings.
The number of ways to choose 2 people is 6C2 = 15.
The number of ways to choose 2 from the first group of siblings is 2C2 = 1.
The number of ways to choose 2 from the second group of siblings is 2C2 = 1.
The number of ways to choose 2 from the third group of siblings is 2C2 = 1.
The number of ways to choose 2 people who are siblings is 1+1+1 = 3.
The number of ways to choose 2 people who are not siblings is 15-3=12.
P(the two people are not siblings) = 12/15 = 4/5
The answer is B.
Answer: (B) 4/5
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.3 km long?
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 168 sec
(D) 344 sec
(E) 2 mins 44 sec
Rationale: D = 25 * 60 + 1300 = 2800 m
T = 2800/60 * 18/5 = 168 sec
ANSWER:C
Answer: (C) 168 sec
Question: Find the odd man out
1, 3, 10, 21, 64, 129, 356, 777
(A) 10
(B) 21
(C) 64
(D) 356
(E) 384
Rationale: 1*2+1=3,3*3+1=10,10*2+1=21,21*3+1=64,64*2+1=129,129*3+1=388 but here it placed with 356, so it is wrong. starts with x*2+1,next x*3+1 alternately changes
ANSWER:D
Answer: (D) 356
Question: If 2 persons can do 2 times of a particular work in 2 days, then, 7 persons can do 7 times of that work in
?
(A) 3 days
(B) 7 days
(C) 9 days
(D) 2 days
(E) 15 days
Rationale: That is, 1 person can do one time of the work in 2 days.
Therefore, 7 persons can do 7 times work in the same 2 days itself.
Option 'D'
Answer: (D) 2 days
Question: There are 10 periods in each working day of a school. In how many ways can one organize 9 subjects such that each subject is allowed at least one period?
(A) 16329600
(B) 16356789
(C) 16324600
(D) 15679892
(E) None of these
Rationale: 9 subjects can be arranged in 10 periods in 10P9 ways.
Remaining 1 period can be arranged in 9P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (10p9 x 9P1)/2! = 16329600
ANSWER:A
Answer: (A) 16329600
Question: 19 balls are numbered 1 to 19. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
(A) 2/9
(B) 4/19
(C) 6/29
(D) 8/39
(E) 10/49
Rationale: P(1st ball is even) = 9/19
P(2nd ball is also even) = 8/18
P(both balls are even) = 9/19 * 8/18 = 4/19
The answer is B.
Answer: (B) 4/19
Question: A survey reveals that the average income of a company’s customers is $50,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
(A)  $27,500
(B)  $43,750
(C)  $37,500
(D)  $42,500
(E)  $50,000
Rationale: let x be the average of 40 customers
40*x + 10* 75000 = 50*50000
solving this we have x= 43750
Answer is B.
Answer: (B)  $43,750
Question: The LCM of two numbers is 2310 and HCF is 26. If one of the numbers is 210. Then what is the other number ?
(A) 715
(B) 825
(C) 286
(D) 582
(E) 465
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 26 / 210 = 11*26 = 286
ANSWER :C
Answer: (C) 286
Question: In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)
(A) 1:2
(B) 3:5
(C) 1:1
(D) 3:7
(E) 2:4
Rationale: C
1:1
This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up.
Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method.
Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + …
Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + …
Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + …
Number of girls = C
(using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms)
The proportion of boys to girls is 1 : 1.
Answer: (C) 1:1
Question: The average of 9 observations was 5, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 45
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Explanation:
1 to 9 = 9 * 5 = 45
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 45 = 45
Option A
Answer: (A) 45
Question: Find the numbers which are in the ratio 3:2:1 such that the sum of the first and the second added to the difference of the third and the second is 16?
(A) 4,3,22
(B) 4,4,22
(C) 9,3,32
(D) 9,6,12
(E) 12,8,4
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:1
Given, (a + b) + (c - b) = 16
=> a + c = 16
=> 3x + x = 16 => x =4
a, b, c are 3x, 2x, x
a, b, c are 12, 8, 4.
Answer:E
Answer: (E) 12,8,4
Question: The least number of five digits which is exactly divisible by 12,15 and 18 is :
(A) 10010
(B) 10015
(C) 10020
(D) 10080
(E) None of these
Rationale: Solution
Least number of 5 digits is 10000. L.C.M. of 12, 15 and 18 is 180.
On dividing 1000 by 180, the remainder is 100.
∴ Required number = 10000 + (180 - 100) = 10080. Answer D
Answer: (D) 10080
Question: If a, b are integers and |a-b|=10, which of the following is the smallest possible value of ab?
(A) -16
(B) 0
(C) -25
(D) 7
(E) 40
Rationale: a=5, b=-5. Hence, the answer is C.
Answer: (C) -25
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (7; 9),
what is the maximum possible area of C?
(A)  6
(B)  9
(C)  24
(D)  32
(E)  64
Rationale: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
E
Answer: (E)  64
Question: The cost of hiring a bus is shared equally by all passengers. The bus has seats for 40 passengers and the total bill comes to Rs.70.37. How many seats went unoccupied?
(A) 13
(B) 11
(C) 9
(D) 7
(E) 5
Rationale: As the bill of Rs 70.37 is equally divided, it is only possible when 31 passengers shared the bill.
70.37/31= 2.27
Also
70.37 is not fully divisible by 27,29,33.
so 40-31=9 seats went unoccupied.
ANSWER:C
Answer: (C) 9
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 80 km apart both 3 and 6 hours after start, then find the distance between the two stations.
(A) 240 km
(B) 230 km
(C) 220km
(D) 180km
(E) 200km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+80+ 80
2(R+S ) = R+S +160
R+S = 160
Hence distance between XY is R+S+ 80 = 160 +80 =240
Answer : A
Answer: (A) 240 km
Question: Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 30% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
(A) 47%
(B) 59%
(C) 71%
(D) 83%
(E) 95%
Rationale: Let x be the number of new biographies added to the library.
Let b be the original number of biographies, so the original number of books was 5b.
0.3(5b+x) = b+x
0.5b = 0.7x
x = 0.71b
The answer is C.
Answer: (C) 71%
Question: 2 dice are tossed. What is the probability that the total score is a prime no. is?
(A) 1/13
(B) 5/12
(C) 3/11
(D) 4/13
(E) 5/13
Rationale: 5/12
B
Answer: (B) 5/12
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
(A) 1/48
(B) 1/42
(C) 1/46
(D) 1/47
(E) 1/43
Rationale: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer: B
Answer: (B) 1/42
Question: By the how much is two-fifth of 200 greater than three -fifths of 25?
(A) 15
(B) 3
(C) 5
(D) 30
(E) 65
Rationale: Reqd no. = 2â„5 Ã— 200 - 3â„5 Ã— 25
= 80 - 15 = 65
Answer E
Answer: (E) 65
Question: What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5?
(A)  94
(B)  99
(C)  26
(D)  73
(E)  None of the Above
Rationale: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -10
Thus 2xy +5 = x^2 + y^2 - 10
x^2 + y^2 -2xy = 15
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 94
Thus the answer is A
Answer: (A)  94
Question: A can run 1.5 km distance in 2 min 20 seconds, while B can run this distance in 2 min 30 sec. By how much distance can A beat B?
(A) 90 m
(B) 100 m
(C) 120 m
(D) 180 m
(E) 190 m
Rationale: A takes time 2.20 minutes=140sec
B takes time 2.30 minutes=150sec
diffrence= 150-140=10sec
now we are to find distance covered in 10 sec by B
150sec=1500m
1sec=10m
10sec=10x10=100m
ANSWER:B
Answer: (B) 100 m
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 25 pages.
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(25/2.5)=10 hrs
ANSWER:B
Answer: (B) 10
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 14 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 30
(B) 45
(C) 60
(D) 90
(E) 105
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/5x + 2/3x + 14
x - 13/15x = 14
2/15x = 14 => so x = (15/2)*14 = 105Km
Answer E
Answer: (E) 105
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
(A) 24%
(B) 74%
(C) 69%
(D) 64%
(E) 54%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: (D) 64%
Question: If b is a positive integer, then 3^b + 3^(b) =
(A) 3^(b + 1)
(B) 2^(b + 1)
(C) 2(3^b)
(D) 2b^(b + 1)
(E) 3(2^b)
Rationale: If b is a positive integer,3^b+3^b=2(3^b)
option C is answer
Answer: (C) 2(3^b)
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: Q=7 is the correct answer.
Good solution Buneul.B
Answer: (B) 7
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 33 what is the value of a1 ?
(A) 1
(B) 6
(C) 13
(D) 16
(E) 21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 33
a4 = 29
a3 = 23
a2 = 18
a1 = 13 <<<< Ans C
Answer: (C) 13
Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 55 kg
(C) 80 kg
(D) 85 kg
(E) 25 kg
Rationale: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (60 + 20) kg = 80 kg.
Answer: C
Answer: (C) 80 kg