mathewhe/aqua_rat huggingface dataset:
Question: The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 60 percent, then the value of T decreases by what percent?
(A) 25%
(B) 33 ¹/₃%
(C) 50%
(D) 66 ²/₃%
(E) 75%
Rationale: We can assign numbers:
lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)
Now increasing S by 50% gives S=4, K remains constant, so T = 2 (6/2=3)
decrease in T= 1, percent decrease in T = (1/4)*100 = 25%
Answer A
Answer: (A) 25%
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 10 m
(B) 16 m
(C) 245 m
(D) 19 m
(E) 225 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30
= 25/2 => 2(150 + x) = 750 => x
= 225 m.
Answer: E
Answer: (E) 225 m
Question: A, B and C rents a pasture for Rs.899. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 279
(C) 267
(D) 255
(E) 552
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 899 = 279
Answer: B
Answer: (B) 279
Question: Two cars start at the same time from opposite ends of a highway that is 500 miles long. One car is riding at 40 mph and the second car is riding at 60 mph. How long after they begin will they meet?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 60+40 = 100 mph
Total distance to be covered = 500 miles.
Time taken would be: 500 miles/100 mph = 5 hours
E is the answer.
Answer: (E) 5
Question: In a hotel we can order two types of varieties, but we can make 5 more varieties in home. One can choose the four varieties with two from hotel as must. Find how many ways one can order.
(A) 14
(B) 10
(C) 56
(D) 28
(E) 29
Rationale: 2c2*5c2=10ways
ANSWER:B
Answer: (B) 10
Question: The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
(A) 2/3
(B) 3/5
(C) 4/7
(D) 5/9
(E) None of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
d = 2n - 1 => d = 9
Hence the fraction is : 5/9
ANSWER:D
Answer: (D) 5/9
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
(A) Rs.12000
(B) Rs.14200
(C) Rs.17520
(D) Rs.13500
(E) Rs.14500
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
ANSWER:D
Answer: (D) Rs.13500
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 153 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1289
(B) 1198
(C) 281
(D) 1224
(E) 282
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 153 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 153 = 3k + 153 => 2k = 306 => k = 153
The initial quantity of water in A = 8k = 8 * 153 = 1224 liters.
Answer: Option D
Answer: (D) 1224
Question: Consider the following sets:
L = {3, 4, 5, 5, 6, 7},
M = {2, 2, 2, 8, 8, 8},
N = {15, 15, 15, 15, 15, 15},
Rank those three sets from least standard deviation to greatest standard deviation.
(A) L, M, N
(B) M, L, N
(C) M, N, L
(D) N, L, M
(E) N, M, L
Rationale: Now we have to compare the standard deviations of Set L and Set M. In Set L, the mean is clearly 5: two of the entries equal 5, so they have a deviation from the mean of zero, and no entry is more than two units from the mean. By contrast, in Set M, the mean is also 5, and here, every number is 3 units away from the mean, so the standard deviation of M is 3. No number in Set L is as much as 3 units away from the mean, so whatever the standard deviation of L is, it absolutely must be less than 3. That means, Set L has the second largest standard deviation, and Set M has the largest of the three. N, L, M in increasing order. Answer = D.
Answer: (D) N, L, M
Question: If two boys starting from same point, walking in the opposite directions with 4km/hr and 2km/hr as average speeds respectively. Then the distance between them after 6 hours is?
(A) 32
(B) 33
(C) 34
(D) 35
(E) 36
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (4Ã— 6) + (2Ã— 6)
= 24+ 12
= 36 Km
Answer:E
Answer: (E) 36
Question: What number has a 5:1 ratio to the number 9?
(A) 45
(B) 50
(C) 88
(D) 52
(E) 12
Rationale: 5:1 = x: 9
x = 45
Answer: A
Answer: (A) 45
Question: Find the odd man out. 362, 482, 551, 263, 344, 284
(A) 362
(B) 482
(C) 551
(D) 344
(E) None of these
Rationale: Explanation :
In all numbers except 344, the product of first and third digits is the middle digit. Answer : Option D
Answer: (D) 344
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 650 resolutions?
(A) 724 m
(B) 704 m
(C) 915.2 m
(D) 278 m
(E) 927 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 650 resolutions.
= 650 * 2 * 22/7 * 22.4 = 91520 cm
= 915.2 m
Answer:C
Answer: (C) 915.2 m
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20
(B) 15
(C) 17
(D) 18
(E) 25
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------
300 ---- 20 years
ANSWER A
Answer: (A) 20
Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 10 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?
(A)  100%
(B)  80%
(C)  75%
(D)  66+2/3%
(E)  55%
Rationale: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
B
Answer: (B)  80%
Question: The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
(A) 18
(B) 19
(C) 20
(D) 21
(E) 46
Rationale: l2 + b2 = 41.
Also, lb = 20.
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
Answer:A
Answer: (A) 18
Question: The triplicate ratio of 3:5 is?
(A) 27:125
(B) 1:62
(C) 1:34
(D) 3:64
(E) 5:64
Rationale: 3^3: 5^3 = 27:125
ANSWER:A
Answer: (A) 27:125
Question: A bag marked at $80 is sold for $68. The rate of discount is?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Rate of discount = 12/80 * 100 = 15%
Answer is B
Answer: (B) 15%
Question: A certain sum of money at simple interest amounted Rs.780 in 5 years at 4% per annum, find the sum?
(A) 337
(B) 268
(C) 198
(D) 650
(E) 168
Rationale: 780 = P [1 + (5*4)/100]
P = 650'
Answer:D
Answer: (D) 650
Question: In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate?
(A) 100
(B) 50
(C) Cannot be determined
(D) 105
(E) 25
Rationale: Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position.
Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points.
Answer: (C) Cannot be determined
Question: A train passes a station platform in 30 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) 150 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)/30 = 15
--> x + 300 = 450
x = 150m.
Answer : A.
Answer: (A) 150 m
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,10). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 2/3
(E) 2/5
Rationale: The area of the right triangle is (1/2)*4*10 = 20.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/20 = 2/5
The answer is E.
Answer: (E) 2/5
Question: Baby Isabel plays with blocks. Each block is 4.5 inches tall. She has a collection of 33 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
(A) 67.19"
(B) 90.9"
(C) 106.34"
(D) 120.5"
(E) 148.5"
Rationale: 4.5"*33=148.5". Answer is E.
Answer: (E) 148.5"
Question: P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 130 days, in how many days can R alone complete the remaining work?
(A) 50 days
(B) 83.6 days
(C) 100 days
(D) 150 days
(E) 80 days
Rationale: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 380 days
P works for 60 days--> 60/200 work done => 30%
Q works for 130 days--> 130/250 work done => 52%
22% work left ... R alone will take 22% * 380 = 83.6 days
Answer is (B)
Answer: (B) 83.6 days
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 54° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 15%
(B) 25%
(C) 30%
(D) 35%
(E) 72%
Rationale: ANSWER:A 54° divided by 360° equals 0.15, therefore the sector is equal to 15% of the total
Answer: (A) 15%
Question: What will come in place of the x in the following Number series? 18, 22, X, 46 ,78, 142
(A) 35
(B) 56
(C) 30
(D) 87
(E) 98
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30
Answer: (C) 30
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets Q did Irwin score?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored Q= 2 11-point baskets in my opinion.
Answer C
Answer: (C) 2
Question: A batsman scored 80 runs which included 2 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets?
(A) 45%
(B) 500/11
(C) 75%
(D) 55%
(E) 35%
Rationale: Explanation :
Number of runs made by running,
=>80−(2×4+2×6).
=>80−20
=>60
Hence, the required percentage is:-
=>60/80*100
=>75%
Answer : C
Answer: (C) 75%
Question: The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ?
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: S.I. = 1680, R = 4% T = 5 years
Principal = (100 *1680)/ (5*4) = 8400
So P = 8400
Rate = (100 *1680)/ (8400 * 4) = 5%
ANSWER:A
Answer: (A) 5%
Question: If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. If x is positive, y must be positive
III. Both x and y are positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: The best way to approach such questions is to plug in values for x and y
Given: x-y=8
III. Both x and y are positive:
Let x=10 and y=2
x-y=8
But,
Let x=6 and y=-2
x-y=8
Therefore, NOT TRUE
II. If x is positive, y must be positive
Let x=10 and y=2
x-y=8
But,
Let x = 6 and y=-2
x-y=8
Therefore, NOT TRUE
I. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'A'
Answer: (A) I only
Question: 4 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 5 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?
(A) 3/24
(B) 3/4
(C) 15/24
(D) 18/24
(E) 21/24
Rationale: Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*3*2*1*1=18
and total possible outcomes =4!=24
probability of the favourable outcome= 3/4. B
Answer: (B) 3/4
Question: Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually.
(A) 812
(B) 712
(C) 412
(D) 512
(E) 612
Rationale: Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.
therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612.
Answer is E.
Answer: (E) 612
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers R are there between 6* + 2 and 6* + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes R in this range.
Answer: A.
Answer: (A) None
Question: The simple interest on a sum of money will be Rs.800 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 2261
(B) 1600
(C) 1200
(D) 2699
(E) 2771
Rationale: P --- 10 ---- 800
P --- 5 ----- 400
3P --- 5 ----- 1200
------
=> 1600
Answer: B
Answer: (B) 1600
Question: If y is the smallest positive integer such that 630 multiplied by y is the square of an integer, then y must be
(A) 20
(B) 50
(C) 60
(D) 70
(E) 140
Rationale: 630 = 2*3^2*5*7
To be perfect square, we need to multiply by at least 2*5*7 = 70.
The answer is D.
Answer: (D) 70
Question: If 15 students in a class average 80% on an English exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?
(A) 83%
(B) 83 1⁄2%
(C) 84%
(D) 85%
(E) 86 2⁄3%
Rationale: The average percentage = (15 x 80% + 10 x 90%)/25
= (15 x 80% + 10x 80% + 10x10%) / 25 ......(as 90% = 10% + 80% )
=(25x80% + 10x10%)/25
= 80% + 10x10%/25
= 80% + 4%
= 84%
ANSWER:C
Answer: (C) 84%
Question: A shopkeeper first raises the price of Jewellery by x% then he decreases the new price by x%. After such up down cycle, the price of a Jewellery decreased by Rs. 21025. After a second up down cycle the Jewellery was sold for Rs. 484416. What was the original price of the jewellery.2
(A) Rs. 5,26,000
(B) Rs. 6,00,625
(C) Rs. 525625
(D) Rs. 5,00,000
(E) None of these
Rationale: Solution: Let the initial price = Rs. 10000P
price after first increment = 10000P + 100xP.
price after first decrement = 10000P + 100xP - (100Px+Px2) = 10000P - Px2.
Now, total decrement,
Px2 = 21025 .............. (1)
price after second increment,
10000P - Px2 + 100xP - Px3/100
price after second increment,
10000P - P2 + 100xP - P3/100 - 100xP + Px3/100 - Px2 + Px4/10000
= 10000P -2Px2+Px2/10000 = 484416 ............... (2)
on solving equation equn (1) and (2), We get
x = 20.
substituting back we get,
P = 52.5625
Therefore
Answer: Option C
Answer: (C) Rs. 525625
Question: The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?
(A) 1000
(B) 1500
(C) 2000
(D) 3000
(E) 4000
Rationale: Let monthly income of A = a
monthly income of B = b
monthly income of C = c
a + b = 2 × 5050 .... (Equation 1)
b + c = 2 × 6250 .... (Equation 2)
a + c = 2 × 5200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
=> a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)
=> 2a = 2(5050 + 5200 - 6250)
=> a = 4000
i.e., Monthly income of A = 4000
Answer is E.
Answer: (E) 4000
Question: An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 9 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?
(A) 9 and 6/7 pounds
(B) 10 and 1/10 pounds
(C) 10 and 2/5 pounds
(D) 11 pounds
(E) 124/13 pounds
Rationale: Solution: Average weight = Total weight/number of packages. The total weight on Tuesday was 6 * (9 and 2/3 pounds), or 58 pounds. The total weight on Wednesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 58, or 124 pounds. The average is 124 pounds/13 packages.
Correct answer: E
Answer: (E) 124/13 pounds
Question: If w/x = 2/3 and w/y = 6/15, then (x + y)/y =
(A) 4/5
(B) 6/5
(C) 7/5
(D) 8/5
(E) 9/5
Rationale: W/X = 2/3=>x=3/2w and W/Y = 6/15=>y=15/6w
(X+Y)/Y = (3/2w+15/6w)/15/6w = 4w/(15/6W) = 8/5
Correct Option: D
Answer: (D) 8/5
Question: How many unique positive odd integers less than 110 are equal to the product of a positive multiple of 5 and an odd number?
(A) 4
(B) 6
(C) 11
(D) 12
(E) 15
Rationale: The Question basically asks how many positive odd integers less than 110 are odd multiples of 5
So we have 5,15,25,35,45,.. and 105
=11
Ans C
Answer: (C) 11
Question: A cycle is bought for Rs.670 and sold for Rs.780, find the gain percent?
(A) 70%
(B) 20%
(C) 16%
(D) 19%
(E) 80%
Rationale: Explanation:
670 ---- 110
100 ---- ? => 16%
Answer: C
Answer: (C) 16%
Question: John paid a sum of money for purchasing 30 pens, which he recovered in full when he sold 20 of them. What was his percentage of profit or loss per pen?
(A) 50%
(B) 60%
(C) 40%
(D) 30%
(E) 45%
Rationale: A
50%
If the sum he paid whilst purchasing 30 pens = A,
Then the Cost Price of each pen = A/30.
Since the amount he got whilst selling 20 pens is also = A
Then the Selling Price of each pen = A/20.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/20 - A/30 = A/60.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (A/60) / (A/30) x 100 = 50%
Answer: (A) 50%
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 3 km?
(A) 1.5
(B) 1.75
(C) 2.0
(D) 2.25
(E) 2.5
Rationale: The swimmer can swim against the current at a speed of 4-2 = 2 km/h.
The time it will take is 3/2 = 1.5 hours.
The answer is A.
Answer: (A) 1.5
Question: Bradley owns b video game cartridges. If Bradley’s total is one-half the total owned by James and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) (16/3)b
(B) (17/4)b
(C) (13/4)b
(D) (19/12)b
(E) (7/12)b
Rationale: b = Bradley’s total
2b = James’s total
(1/4)b = Charlie’s total
Add each total
b + 2b+ (1/4)b = 3b + (1/4)b = = (13/4b)
Answer : C
Answer: (C) (13/4)b
Question: If n is a prime number greater than 19, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 19, square it and see what would be the remainder upon division of it by 12.
n=23 --> n^2=529 --> remainder upon division 529 by 12 is 1.
Answer: B.
Answer: (B) 1
Question: Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
(A) 2a2 – ab + 3b2
(B) (a – b)(2a – 3b) + 4ab
(C) (a – b)2 + (a2 + ab + 2b2)
(D) (a + b)2 + (a2 + 2b2 – 3ab)
(E) (a + b)(a – b) + (2a2 – ab + 4b2)
Rationale: The other parts are equal to 34.
Answer E
Answer: (E) (a + b)(a – b) + (2a2 – ab + 4b2)
Question: David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
(A) 75
(B) 37
(C) 26
(D) 97
(E) 27
Rationale: Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5
= 75.
Answer: A
Answer: (A) 75
Question: If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
(A) Saturday
(B) Sunday
(C) Monday
(D) Friday
(E) Thursday
Rationale: The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005.
So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday (1 day before to 6th March, 2005).
Answer is B.
Answer: (B) Sunday
Question: Sum of two number is 50 & sum of three reciprocal is 1/12 so find these two numbers
(A) 30 & 29
(B) 30 & 26
(C) 30 & 24
(D) 30 & 22
(E) 30 & 20
Rationale: Sol : x+y = 50 .....(1) x=50-y ....(2)
1x+1y=1121x+1y=112 ⇒y+xxy=112⇒12(y+x)=xy⇒y+xxy=112⇒12(y+x)=xy ...(3)
put (2) in (4)
⇒⇒ 12(y+50-y)=(50-y)y
⇒⇒ 12y+600-12y=50y-y2y2
⇒⇒ y2y2-50y+600=0
⇒⇒ y2y2-30y-20y+600=0
⇒⇒ y(y-30)-20(y-30)=0
⇒⇒ (y-20) (y-30)=0
y=20 or y=30
if y=20 then x = 30
or y=30 then x = 20
two numbers are 30 & 20
Answer:E
Answer: (E) 30 & 20
Question: John is going with 7 friends on a trip to Paris for spring break. Airfare and hotel costs a total of $5600.00 for the group of 8 friends. How much does each person have to pay for their hotel and airfare?
(A) $500
(B) $600
(C) $650
(D) $680
(E) $700
Rationale: Answer= E
The total cost of the trip ($5600.00) divided by 8 equals $700.00.
Answer: (E) $700
Question: A can do a piece of work in 6days, and B can do it in 5days. If C, who can do the work in 12days, joins them, how long will they take to complete the work?
(A) 2days
(B) 3.5days
(C) 2.2days
(D) 4days
(E) 5.7days
Rationale: A,B, and C do the work in = 6*5*12/6*5+5*12+6*12 = 360/162= 2.2 days
Answer is C
Answer: (C) 2.2days
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 35 days
(B) 48 days
(C) 64 days
(D) 24 days
(E) 36 days
Rationale: B
48 days
B = 1/16 – 1/24 = 1/48 => 48 days
Answer: (B) 48 days