mathewhe/aqua_rat huggingface dataset:
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is
(A) 35.55 km/hr
(B) 36 km/hr
(C) 71.11 km/hr
(D) 71 km/hr
(E) None of these
Rationale: Explanation:
Total time taken = (160/64 + 160/8)hrs
= 9/2 hrs.
Average speed = (320 × 2/9) km.hr
= 71.11 km/hr.
Answer: C
Answer: (C) 71.11 km/hr
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 18
(B) 19
(C) 19.7
(D) 21
(E) 23
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
C)
Answer: (C) 19.7
Question: An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
(A) 51.6
(B) 51.5
(C) 51.7
(D) 51.1
(E) 51.0
Rationale: Assume total tank capacity = 210 Liters
Now capacity of pipe A = 210/42 = 5 Liters
Capacity of B = 210 / 30 = - 7 Liters
Capacity of C = 210 / 35 = 6 min
Assume tank gets filled in x min after the third pipe got opened.
So x×5+6×(−2)+4x=210x×5+6×(−2)+4x=210
⇒48+4x=210⇒4x=162⇒x=40.5⇒48+4x=210⇒4x=162⇒x=40.5
Total time taken to fill the tank = 40.5 + 12 + 6 = 51.5
Answer:B
Answer: (B) 51.5
Question: If a and b are positive integers and x = 4^a and y = 5^b, which of the following is a possible units digit of xy?
(A) 0
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: The units digit of 4^a is either 4 or 6.
The units digit of 5^b is 5.
4*5 = 20 and 6*5 = 30.
The units digit of xy is 0.
The answer is A.
Answer: (A) 0
Question: In a sequence of 12 numbers, each term, except for the first one, is 12^12 less than the previous term. If the greatest term in the sequence is 12^13, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
(A) −12^11
(B) 0
(C) 12^11
(D) 11·12^11
(E) 12^12
Rationale: there are total 12 terms. andgreatestterm is 12^13. Each term is 12^12 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^12 less than previous one')
Therefore, 12^13 is the first term of the AP and -12^11 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 12^13 + 11*(-12^12)
=> Last term = 12^13 - 11*12^12
=> Last term = 12^12 (12-11) = 12^12
Which is the smallest term.
Hence Ans E it is.
Answer: (E) 12^12
Question: The probability of Sam passing the exam is 1/3. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
(A) 1/24.
(B) 1/2.
(C) 1/3.
(D) 2/3.
(E) 2/5
Rationale: 1/3 *1/m= 1/6 , 1/m = 1/2
Answer B
Answer: (B) 1/2.
Question: In the coordinate plane, one of the vertices of a square is the point (-3, -4). If the diagonals of that square intersect at point (4, 2), what is the area of that square?
(A) 196
(B) 125
(C) 140
(D) 128
(E) 134
Rationale: One point (-3-4), Intersection (4,2) so the distance from the first point -3-4=-7 is the midpoint of the square --> whole side 14, 14*14=196
A
Answer: (A) 196
Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
(A) 4 days
(B) 6 days
(C) 8 days
(D) 12 days
(E) 15 days
Rationale: Explanation:
Suppose A, B and C take x,	x/2	and	x/3	days respectively to finish the work.
Then, 1/X	+	2/X	+	3/X =	1/2
6/X	=	1/2
x = 12.
So, B takes (12/2) = 6 days to finish the work.
ANSWER IS B
Answer: (B) 6 days
Question: You frequently buy a box of dog toys for your 3 puppies to play with. Typically, the toys last 60 days before the dogs bury them all and you have to buy another box. Recently, you've started your own mini-animal shelter and now have 25 total puppies. You've just purchased a new box of dog toys, how many days until they bury all the toys?
(A) 5.6
(B) 9.7
(C) 75
(D) 19.2
(E) 7.2
Rationale: First set up a ratio with all the relevant values and also the unknown variable:
3*60 = 25*x
Now solve by multiplying 3 by 60 and then dividing that product by 25:
3*60 = 180
180/25 = x
x = 7.2
The value of x represents the amount of days it takes 25 puppies to bury the toys in a box.
Answer: E
Answer: (E) 7.2
Question: Two employees X and Y are paid a total of Rs. 572 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.250
(B) s.280
(C) s.290
(D) s.260
(E) s.300
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 572
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 572
⇒ y[12/10 + 1] = 572
⇒ 22y/10 = 572
⇒ 22y = 5720
⇒ y = 5720/22 = 520/2 = Rs.260
D
Answer: (D) s.260
Question: Of the twelve participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 20
Rationale: half are male --> 6 males
half the males are under 18 --> 3 males under 18
same for females --> 3 females above 18
groups of four ( out of which 2 are males below 18 and 2 are females above 18) = 3C2 * 3C2 = 3*3 =9
ANS:D
Answer: (D) 9
Question: 34.	The side surface of a cylinder is rolled with a rectangular plate. If the height of a cylinder tank is 10 feet and the perimeter of the circular base Is 4 feet, what is the area of the rectangular plate?
(A) 24
(B) 34
(C) 28
(D) 40
(E) 14
Rationale: Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both you can multiply them together to find the area, 40. (Correct answer D)
Answer: (D) 40
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 5
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits G of the larger integer?
(A) G=2
(B) G=5
(C) G=8
(D) G=10
(E) G=11
Rationale: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: (A) G=2
Question: When a certain number X is divided by 63, the remainder is 27. What is the remainder when X is divided by 8?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: When a certain number X is divided by 63, the remainder is 27. What is the remainder when X is divided by 8?
Putting a value say x = 27 we get remainder as 27 when divided by 63.
When 27 divided by 8 we get 3 as remainder.
B is the answer.
Answer: (B) 3
Question: There is a square with sides of 12. What is the circumference of the biggest circle that can be cut out of this square?
(A) 75.4
(B) 31.42
(C) 36
(D) 18.85
(E) 37.7
Rationale: Circumference of a circle = C=2Ï€r
Square is 12 wide, so circle's diameter would be 12, and radius would be 6
C=2Ï€6 which is approximately 37.7
Answer is E
Answer: (E) 37.7
Question: The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
(A) 31
(B) 36
(C) 51
(D) cannot be determined
(E) None of these
Rationale: Age of the teacher = (37 × 15 – 36 × 14) years
= 51 years.
Answer C
Answer: (C) 51
Question: A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 1/3 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?
(A) x/3
(B) x/2
(C) 2x/3
(D) 3x/2
(E) 2x
Rationale: x/(x+y) = 1/3
3x = x+y
2x = y
y = 2x
Answer E
Answer: (E) 2x
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.4528
(B) s.4520
(C) s.5436
(D) s.4530
(E) s.4521
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 6
= Rs.5436
Answer:C
Answer: (C) s.5436
Question: The ratio, by volume, of soap to alcohol to water in a certain solution is 2:40:70. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
(A) 500
(B) 600
(C) 650
(D) 700
(E) 720
Rationale: soap:alcohol
Initial ratio soap:alcohol: water --> 2:40:70
Initial soap:alcohol = 2/40 =2:40
after doubled soap:alcohol =2* 2/40 = 4:40
Initial soap:water = 2/70=2:70
after halved soap:water: 1/2 * 2/70 = 1/70 = 1:70
After soap: alcohol:water --> 4:40:280-->1:10:70
given alcohol 100 cubic centimeter.
ratio is 10:100:700(1:10:70)
For 100 cubic centimeter of Alcohol --- 700cubic cm water is required.
Answer-D
Answer: (D) 700
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 130 sq cm. Find the area of the square?
(A) 482
(B) 268
(C) 260
(D) 480
(E) Cannot be determined
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: E
Answer: (E) Cannot be determined
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 63. By how much do the two digits differ?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  7
Rationale: Given that (10a + b) - (10b + a) = 63 --> 9a - 9b =63 --> a - b = 7.
Answer: E.
Answer: (E)  7
Question: Ken and Shen are workers in a department that has a total of 10 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
(A) 2/45
(B) 1/45
(C) 11/45
(D) 12/45
(E) 1/45
Rationale: Probability = 2c2/10c2
= 1/45
Answer B
Answer: (B) 1/45
Question: If 12 carpenters working 6 hours a day can make 460 chairs in 24 days, the no. of chairs made by 18 carpenters in 36 days each working 8 hours a day will be:
(A) 1380
(B) 920
(C) 1320
(D) 1260
(E) None of these
Rationale: Explanation :
no of work hour days by carpenters is 460/(12*6*24)
now no chair is 460*18*36*8/(12*6*24)=1380
Answer : A
Answer: (A) 1380
Question: 9 - 3 ÷ 1/3 + 2 = ?
(A) 2
(B) 3
(C) 6
(D) 9
(E) 12
Rationale: 9 - 3 1/3 + 2
=9-3÷1/3+2
=9-(3X3) +2
=9-9+2
=2
CORRECT ANSWER : A
Answer: (A) 2
Question: A man has Rs. 448 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
(A) 45
(B) 60
(C) 75
(D) 84
(E) 95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 448
16x = 448
x = 28.
Hence, total number of notes = 3x = 84
Answer: Option D
Answer: (D) 84
Question: Out of first 20 natural numbers , one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/65
(B) 17/29
(C) 17/21
(D) P(EᴜP) =17/20
(E) 17/212
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D
Answer: (D) P(EᴜP) =17/20
Question: There are 9 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 1296
(B) 720
(C) 1,060
(D) 1,520
(E) 1,980
Rationale: Answer is E. Can somebody tell me what answer I may have found if I had added the 9C2 and 9C2 (36+36=72)?
I'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?
A
Answer: (A) 1296
Question: 125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 12 liters
(B) 32 liters
(C) 41 liters
(D) 50 liters
(E) 34 liters
Rationale: Milk = 3/5 * 125 = 75 liters
Water = 50 liters
75 : (50+P) = 3:4
150 + 3P = 400 => P = 50
50 liters of water are to be added for the ratio become 3:4.
Answer:D
Answer: (D) 50 liters
Question: Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
(A) 8/38
(B) 8/32
(C) 8/35
(D) 8/31
(E) 6/38
Rationale: Explanation:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35
ANSWER: C
Answer: (C) 8/35
Question: A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find A's share.
(A) Rs. 3240
(B) Rs. 2520
(C) Rs. 2880
(D) Rs. 3360
(E) None of these
Rationale: Explanation:
Let C's investment = Rs. x
B's investment = Rs. (x - 3000)
A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)
Now, (A + B + C)'s investment = Rs. 72000
=> x + (x - 3000) + (x + 3000) = 72000
=> 3x = 72000
=> x = 24000
Hence, A's investment = Rs. 27000
B's investment = Rs. 21000
C's investment = Rs. 24000
Ratio of the capitals of A, B and C
= 27000 : 21000 : 24000
= 9 : 7 : 8
A's share = Rs. [(9/24) × 8640] = Rs. 3240
Answer: Option A
Answer: (A) Rs. 3240
Question: P runs 25% faster than Q so P gives Q a ten meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.25V = (D-10) / V
D=1.25D-12.5
0.25D=12.5
D=50 meters.
The answer is A.
Answer: (A) 50
Question: 5.005/4.004 =
(A) 1.05
(B) 1.50015
(C) 1.501
(D) 1.5015
(E) 1.25
Rationale: 5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25
The answer is E.
Answer: (E) 1.25
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?
(A) 28
(B) 27
(C) 12
(D) 37
(E) 01
Rationale: Explanation:
16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Answer: (D) 37
Question: Jim is now twice as old as Fred, who is nine years older than Sam. Four years ago, Jim was four times as old as Sam. How old is Jim now?
(A) 40
(B) 44
(C) 48
(D) 52
(E) 56
Rationale: J = 2F = 2(S+9) = 2S+18
J-4 = 4*(S-4)
(2S+18)-4 = 4S-16
S = 15 and so J = 48
The answer is C.
Answer: (C) 48
Question: If a = 0, b = 0, and (a^2)b = a, then which of the following MUST equal a?
(A) 1/(b^2)
(B) 0
(C) b
(D) b^2
(E) b^2 – 2b +1
Rationale: A=0
B=0
A^2b-A=0
A (Ab-1)=0
Since A =0 then
Ab-1=-1
Ab=0
Ans:B
Answer: (B) 0
Question: What is the difference between local value & face value of 3 in the numeral 65793?
(A) 8453
(B) 8956
(C) 8991
(D) 0
(E) 10000
Rationale: (Local value of 3) - (Face value of 3)
= (3 - 3) = 0
D
Answer: (D) 0
Question: If x and y are both odd prime numbers andx < y, then how many different positive integer factors does2xyhave?
(A)  3
(B)  4
(C)  6
(D)  12
(E)  8
Rationale: x and y are both odd prime numbers- It means either x or y is not 2
and since prime numbers have only two factors - 1 and the number itself
x and y each will have (1+1)= 2 factors
Hence 2xy will have (1+1)(1+1)(1+1)= 8 factors
E is the answer
Answer: (E)  8
Question: It takes 50 identical printing machines 8 hours to print 500,000 posters. How long would it take 40 of these machines to print the same total?
(A) 10 hr
(B) 12 hr
(C) 12 hr 24 min
(D) 12 hr, 40 min
(E) 13 hr, 20 min
Rationale: 50 machines finish the job in 8 hours. We do not have to take care of the 500'000 posters, it does not matter.
40 machines means, 20% less of capacity and therefore 20% longer to work for a certain job.
8 * 1.2 = 9 hr, 36 min
Answer A	..
Hi reto,
since you are looking time for 40 machines it is 25% less so will take 25% more ..
ans 8*1.25=10 hrs..
A)
Answer: (A) 10 hr
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 735, Krishan has ?
(A) s. 4335
(B) s. 2330
(C) s. 1190
(D) s. 1620
(E) s. 2680
Rationale: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 735 : N
&there N = 289 x 735 / 49
= Rs. 4335
Answer :A
Answer: (A) s. 4335
Question: A number consists of two digits. The sum of the digits is 9. If 63 is subtracted
from the number, its digits are interchanged. Find the number.
(A) 27
(B) 36
(C) 81
(D) 72
(E) 18
Rationale: Let the ten's digit be x. Then, unit's digit = (9 - x).
Number = l0x + (9 - x) = 9x + 9.
Number obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.
therefore, (9x + 9) - 63 = 90 - 9x =>	18x = 144 =>	x = 8.
So, ten's digit = 8 and unit's digit = 1.
Hence, the required number is 81.
Answer is C.
Answer: (C) 81
Question: Renuka bought an electric cooker at 90% of the regular price. She paid $360 for the cooker. What was the regular price?
(A) $250
(B) $400
(C) $450
(D) $550
(E) $650
Rationale: Regular price = 360/90*100 = 400
Answer : B
Answer: (B) $400
Question: 8269Ã—9998=?
(A) 85432864
(B) 82673462
(C) 86985434
(D) 68954365
(E) 65486954
Rationale: 8269Ã—(10000-2)
82690000-16538=82673462
answer B
Answer: (B) 82673462
Question: The marks obtained by Vijay and Amith are in the ratio 2:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:8
(B) 3:1
(C) 6:5
(D) 3:2
(E) 3:5
Rationale: 2:5
3:2
-------
6:15:10
6:10
3:5
Answer: E
Answer: (E) 3:5
Question: Insert the missing number.
2, 6, 12, 20, 30, (....)
(A) 22
(B) 38
(C) 42
(D) 66
(E) 19
Rationale: Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6.
So, the next number is 6 x 7 = 42.
Answer: C) 42
Answer: (C) 42
Question: In a two digit number it is known that its unit's digit exceeds its ten's digit by 4 and that the product of the given number and the sum of its digits is equal to 208, What is the number ?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: xy is 2 digit no.
y-x=4;
(10x+y)*(2x+4)=208;
sub y=x+4;
we get 26
ANSWER:C
Answer: (C) 26
Question: 9x^2+3px+6q divided by 3x+1 leave reminder -3/4 and qx^2+4px+7 is exactly divisible by x+1, then find the values of p and Q
(A) 7/4,0
(B) 8/4,0
(C) 9/4,0
(D) 7/4,1
(E) 7/4,2
Rationale: 1st quadration eqn gives remainder -3/4 on dividing by 3x+1.so, eqn-(-3/4) is divisible by 3x+1 means eqn+3/4 has a roo x=-1/3.so,on putting x=-1/3 in the 1st eqn,1-p+6q+3/4=0 that is 6q-p=-7/4.2nd quad eqn is divisible by x+1.so x=-1 is root of that eqn.on putting x=-1,eqn=0.so,
q-4p+7=0.on comparing two linear eqns in p and 2,we get p=7/4 and q=0.
ANSWER:A
Answer: (A) 7/4,0
Question: A man gets a simple interest of Rs.200 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) s.156
(B) s.226
(C) s.300
(D) s.356
(E) s.410
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 2 years on Rs.P = Rs.200
(P)(2)(5)/100 = 200
P = 2000
C.I on Rs.2P i.e., Rs.4000 at 5% p.a in two years
=4000{ [1 + 5/100]^2 - 1}
= 4000(41/ 400)
= Rs.410
Answer:E
Answer: (E) s.410
Question: The length of rectangle is thrice its breadth and its perimeter is 80 m, find the area of the rectangle?
(A) 360
(B) 376
(C) 299
(D) 276
(E) 111
Rationale: 2(3x + x) = 80
l = 36 b = 10
lb = 36 * 10
= 360
A
Answer: (A) 360
Question: Rs.240 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 388
(B) 266
(C) 120
(D) 299
(E) 180
Rationale: 4x 5x 6x
100 50 25
400x + 250x + 150x = 24000
x = 30
6x = 180
Answer: E
Answer: (E) 180
Question: A and B complete a work in 3 days. A alone can do it in 9 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.99 days
(C) 2.99 days
(D) 2.98 days
(E) 2.25 days
Rationale: 1/3 + 1/9 = 4/9
9/4 = 2.25 days
Answer: E
Answer: (E) 2.25 days