mathewhe/aqua_rat huggingface dataset:
Question: A textile manufacturing firm employees 70 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 70 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
(A) 13000
(B) 7000
(C) 10000
(D) 5000
(E) None of these
Rationale: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(69/70)âˆ’150000Ã—(69/70)âˆ’75000.
=>Rs 2,70,000.
Decrease in profit
=>2,75,000âˆ’2,70,000
=>Rs. 5,000.
Answer : D
Answer: (D) 5000
Question: Jeya invested an amount of Rs. 9,500 at the rate of 13% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
(A) 15550
(B) 18450
(C) 13450
(D) 14450
(E) 14650
Rationale: Let the second amount be Rs. x. Then,
(9500 * 13 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100
12350+ 15x= 16800 + 14x
x = 4450
Total investment = 10000 + 4450 = Rs. 14450 .Answer: D
Answer: (D) 14450
Question: In a classroom, 12 students brought apples and 8 students brought bananas. If exactly 10 students brought only one of the two types of fruits, how many students brought both types of fruits?
(A) 5
(B) 6
(C) 7
(D) 12
(E) 14
Rationale: Say x students brought both fruits.
(12 - x) + (8 - x) = 10 --> x = 5.
Answer: A.
Answer: (A) 5
Question: Helen went to the stationers and bought things worth Euro 45, 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) Euro 15
(B) Euro 15.7
(C) Euro 19.7
(D) Euro 39.7
(E) None
Rationale: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [45 - (5 + 0.30)] = Euro 39.70
Answer: Option D
Answer: (D) Euro 39.7
Question: Find the value of 72519 x 9999 = m?
(A) 434539873
(B) 355797990
(C) 435453490
(D) m=725117481
(E) 873430134
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) m=725117481
Question: At a certain university, 69% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
(A) 25
(B) 37.5
(C) 50
(D) 52.5
(E) 75
Rationale: answer is 75%
total women = 69%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured =21%
but question wants to know the percent of men that are tenured
21%/40% = 52.5%
D
Answer: (D) 52.5
Question: Two trains of equal lengths take 12 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 22
(B) 13
(C) 77
(D) 99
(E) 21
Rationale: Speed of the first train = 120/12 = 10 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 10 + 8 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer: B
Answer: (B) 13
Question: It's Valentine's day and Alan has promised to cook his girlfriend Alana her favorite meal: fish fingers and custard. Alana will be arriving in one hour exactly. Alan only has a microwave. The fish fingers take 13 minutes to defrost in the microwave and 6 minutes to cook in the microwave. The custard must be prepared after the fish fingers and takes 24 minutes to cook in the microwave and then 6 minutes to cool sufficiently so as not to burn someone's tongue. It will take Alan 1 minute to plate the food. However, Alan is on his Xbox and really wants to play one more game of his football video game before Alana arrives. What is the maximum length of each half of the match that Alan can play to ensure the meal is ready for Alana's arrival?
(A) 5 min
(B) 6 minutes
(C) 7 minutes
(D) 8 minutes
(E) 10 minutes
Rationale: Alana will arrive in 60 minutes.
The total meal preparation time is 13 (fish finger defrost) + 6 (fish finger cook) + 24 (custard cook) + 6 (custard cool) + 1 (plate time) = 50 minutes.
Alan therefore has 10 minutes (60-50 = 10) to play his football video game.
As football matches have two halves, Alan have select 5 minute halves (10/2 = 5)
ANSWER: A
Answer: (A) 5 min
Question: If X-Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
(A) -4.5.
(B) -2.
(C) -1.7.
(D) -0.667.
(E) 2.5.
Rationale: X-Y = 2X-2Z
Y= -X+2Z---------- 1
X-2Y = 4Z
X-4Z= 2Y--------- 2
Adding equation 1 from equation 2
-2Z= 3Y
Y/Z= -0.667
D is the answer
Answer: (D) -0.667.
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 400. Find the average mark scored by all the three boys?
(A) 384
(B) 192
(C) 207
(D) 269
(E) 208
Rationale: Average mark scored by all the three boys =
[64/100 (400) + 36/100 (400) + 44/100 (400)] / 3
= 192
Answer: B
Answer: (B) 192
Question: A man buys an song for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:
(A) <25
(B) <10
(C) >20
(D) >30
(E) <30
Rationale: C
>20
Let the song be worth $x.
C.P. 90% of $x = $9x/10
S.P. = 110% of $x = $11x/10
Gain = (11x/10 - 9x/10) = $x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer: (C) >20
Question: An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time B will it take to fill the bucket to full capacity?
(A) 7/18
(B) 9/18
(C) 2
(D) 18/7
(E) 18/5
Rationale: Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank B= 60/7 - 6 = 18/7 mins. ANS D.
Answer: (D) 18/7
Question: The probability that a number selected at random from the first 100 natural numbers is a composite number is ?
(A) 2/3
(B) 3/5
(C) 3/4
(D) 3/2
(E) 5/2
Rationale: Explanation:
The number of exhaustive events = 100 C₁ = 100.
We have 25 primes from 1 to 100.
Number of favourable cases are 75.
Required probability = 75/50 = 3/2.
Answer is D
Answer: (D) 3/2
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
(A) 17 years
(B) 19 years
(C) 29 years
(D) 10 years
(E) 12 years
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.
Answer: D
Answer: (D) 10 years
Question: If N = 2^0.20 and N^b = 16, b must equal
(A) 3/80
(B) 3/5
(C) 20
(D) 5/3
(E) 80/3
Rationale: 20/100 = 1/5
N = 2 ^ 1/5
N^b = 2^4
(2^1/5)^b = 2^4
b = 20
Answer: C
Answer: (C) 20
Question: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
(A) 27
(B) 29
(C) 40
(D) 89
(E) 22
Rationale: 1/8 - 1/x = 1/10
x = 40
Answer: C
Answer: (C) 40
Question: Cole drove from home to work at an average speed of 30 kmh. He then returned home at an average speed of 90 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
(A) 66
(B) 70
(C) 72
(D) 75
(E) 90
Rationale: Let the distance one way be x
Time from home to work = x/30
Time from work to home = x/90
Total time = 2 hrs
(x/30) + (x/90)= 2
Solving for x, we get x = 45
Time from home to work in minutes= (45)*60/30= 90 minutes
Ans= E
Answer: (E) 90
Question: Five years ago, John’s age was half of the age he will be in 6 years. How old is he now?
(A) 14years
(B) 15years
(C) 16years
(D) 17years
(E) 18years
Rationale: Let John=j,j-5=(j+6)/2,then j=16years
ANSWER:C
Answer: (C) 16years
Question: Two trains of length 180 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 28
(B) 266
(C) 990
(D) 20
(E) 23
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 180 + 280 = 460 m.
The time required = d/s = 460/20 = 23 sec.
Answer: E
Answer: (E) 23
Question: A trader bought a car at 30% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 118
(B) 110
(C) 112
(D) 113
(E) 98
Rationale: Original price = 100
CP = 70
S = 70*(140/100) = 98
100 - 112 = 2%
Answer: E
Answer: (E) 98
Question: If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s>v
ii. u is not equal to v
iii. s > u
(A) None
(B) I only
(C) II only
(D) III only
(E) I and III
Rationale: Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.
Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I and III is always true. As for II: it's not necessarily true, for example 4=2+2.
Answer: E
Answer: (E) I and III
Question: A team of five entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 288
(B) 413
(C) 168
(D) 127
(E) 664
Rationale: Explanation:
5 * 84 = 420 - 7 = 413
Answer:B
Answer: (B) 413
Question: A box contains eight bulbs out of which three are defective. If three bulbs are chosen at random, find the probability that all the three bulbs are defective?
(A) 1/56
(B) 1/22
(C) 1/29
(D) 1/36
(E) 1/12
Rationale: Out of eight, five are good and three are defective. Required probability
= 3C3/8C3
= 1/56
Answer:A
Answer: (A) 1/56
Question: The weight of a glass of jar is 40% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?
(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 2/3
Rationale: Let weight of jar filled with beans = 100 g
Weight of jar = 40 g
Weight of coffee beans = 60 g
Weight of jar and remaining beans = 60 g
Weight of remaining beans = 20 g
Fraction remaining = 20/60 = 1/3
Answer is B.
Answer: (B) 1/3
Question: The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr the distance travelled downstream in 12 minutes is :
(A) 2 km
(B) 2.6 km
(C) 3.6 km
(D) 4 km
(E) None
Rationale: Sol.
Speed downstream = (15 + 3) kmph = 18 kmph.
Distance travelled = [18 * 12/60] km = 3.6 km.
Answer C
Answer: (C) 3.6 km
Question: In a 1000 m race, A beats B by 60 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
(A) 154 m
(B) 176 m
(C) 268 m
(D) 129 m
(E) 218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 60) = 940 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/940 * 1000/900 = 1000/846 So, by the time A covers 1000 m, C covers 846 m.
So in 1000 m race A beats C by 1000 - 846 = 154 m.
Answer:A
Answer: (A) 154 m
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 20 years
(B) 21 years
(C) 22 years
(D) 23 years
(E) 24 years
Rationale: Explanation:
Let the average age of the whole team by x years.
11x – (26 + 29) = 9(x -1)
11x – 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.
Answer D
Answer: (D) 23 years
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) Rs.7
(B) Rs.4
(C) Rs.9
(D) Rs.3
(E) Rs.2
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D
Answer: (D) Rs.3
Question: If (A+B) = 5, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
(A) 16.
(B) 8.
(C) 7.
(D) 2.
(E) -1.
Rationale: Given A+B =5
B+C = 9
C+D = 3
(A+B)-(B+C)+(C+D)=(A+D)
=> 5 - 9+3 = -1.
Option E...
Answer: (E) -1.
Question: A club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly A new members into the club. If B is the number of new members brought into the club during the twelfth week, which of the following could be B?
(A)  5^1/12
(B)  3^11 * 5^11
(C)  3^12 * 5^12
(D)  3^11 * 5^12
(E)  60^12
Rationale: At the end of the first week, there are 5 new members;
At the end of the second week, there are 5A new members (since each 5 new members from the previous week brings A new members);
At the end of the third week, there are 5A^2 new members (since each 5A new members from the previous week brings A new members);
...
At the end of the twelfth week, there are 5A^11 new members (since each 5A^10 new members from the previous week brings A new members).
We are given that 5A^11=B. Out of the answers only D yields integer value for A: 5A^11=3^11 * 5^12 --> A=3*5=15.
Answer: D.
Answer: (D)  3^11 * 5^12
Question: Rita was running on a 500 metre track at a rate of 100 metres per minute. One minute after Rita started, Liz started running from the same starting point on the track at 150 metres per minute. What is the shortest time that Liz could run on the track in order to meet up with Rita?
(A) 4 minutes
(B) 3 minutes
(C) 2 minutes
(D) 1.6 minutes
(E) 1 minute
Rationale: we don't need to assume here the direction.we need to find which will take less time
so there are 2 cases
1)both moving in same direction...then time would be 2 minutes
2)both moving in opposite direction then time would be 1.6 minutes
as we need the shortest time it would be the second case
Answer:D
Answer: (D) 1.6 minutes
Question: If 20 liters of chemical X are added to 80 liters of a mixture that is 25% chemical X and 75% chemical Y, then what percentage of the resulting mixture is chemical X?
(A) 28%
(B) 32%
(C) 36%
(D) 40%
(E) 44%
Rationale: The amount of chemical X in the solution is 20 +0.25(80) = 40 liters.
40 liters / 100 liters = 40%
The answer is D.
Answer: (D) 40%
Question: Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has traveled 100km more than the first.the distance
between them.
(A) 800 km
(B) 900 km
(C) 1000 km
(D) 1100 km
(E) 1200 km
Rationale: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 100km
x/50 = x+100 / 60
x= 500
so the distance between A & B is x + x + 100 = 1100 km
Answer is D.
Answer: (D) 1100 km
Question: John is going with 10 friends on a trip to Sidney for spring break. Airfare and hotel costs a total of $12100.00 for the group of 11 friends. How much does each person have to pay for their hotel and airfare?
(A) $1010
(B) $1100
(C) $1110
(D) $1101
(E) $1200
Rationale: Answer= B
The total cost of the trip ($12100.00) divided by 11 equals $1100.00.
Answer: (B) $1100
Question: 6000 - 5000 ÷ 20.00 = ?
(A) 900
(B) 500
(C) 5750
(D) 5000
(E) None
Rationale: Answer
Given expression =6000-5000 ÷ 20.00
= 6000-250
=5750
Correct Option:C
Answer: (C) 5750
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 3?
(A) -1
(B) 0
(C) 4
(D) 2
(E) 3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 3
= x2(x - 2)2 + 3
= (1 + √2)2(1 + √2 - 2)2 + 3
=(√2 + 1)2 (√2 - 1)2 + 3
=[(√2)2 - (1)2]2 + 3
=(2 - 1)2 =1 + 3=4
Correct Option: C
Answer: (C) 4
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
(A) 2160
(B) 2420
(C) 2834
(D) 3150
(E) 3250
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k * 8720 = 2834
The number of valid votes polled in favour of B is 2834.
ANSWER:C
Answer: (C) 2834
Question: If $30,000 interest is invested in x percent simple annual interest for 5 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
(A) 2000x
(B) 3000x
(C) 4500x
(D) 1200x
(E) 1500x
Rationale: 30000*x/100*5 = 1500 x
Answer : E
Answer: (E) 1500x
Question: In what time a sum of money double itself at 3% per annum simple interest?
(A) 33 1/7%
(B) 33 1/3%
(C) 33 1/2%
(D) 33 7/3%
(E) 33 5/3%
Rationale: P = (P*3*R)/100
R = 33 1/3%
Answer: B
Answer: (B) 33 1/3%
Question: Solve the given two equations and find the inequality of X and Y. (a) X^2- 365 = 364 and (b) y- (324) ^(1/2) = (81)^(1/2)
(A) If x>y
(B) If x>=y
(C) If x < y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X= +27, -27
Y= +27
D
Answer: (D) If x<=y
Question: If x/y = 3/z, then 4x^2 =
(A) y/z
(B) xy
(C) y²/z²
(D) 36y²/z²
(E) 15y²/z²
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 4x²:
x/y = 3/z
x = 3y/z
If we substitute 3y/z into the expression for x, we get:
4(3y/z)² = 4(9y²/z²) = 36y²/z².
The correct answer is choice (D).
Answer: (D) 36y²/z²
Question: If the sum of the first n positive integers is S, what is the sum of the first n positive integers divisible by 3, in terms of S ?
(A)  S/2
(B)  S
(C)  2S
(D)  3S
(E)  4S
Rationale: Answer is D
Given sum of 1 2 3.....n = S
sum of 3 , 6 , 9 ....3n = 3[sum(1 2 3....n) ] = 3S
Answer: (D)  3S
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters K long?
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 3
Rationale: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m=K, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Answer: (B) 1
Question: 20 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
(A) 144
(B) 131
(C) 330
(D) 390
(E) 445
Rationale: there are 20 business exec and in each handshake 2 business execs are involved.
hence 20C2=190
Also, each of 20 exec will shake hand with every 7 other chairmen for total of 140 handshake.
total=190+140=330
ANS: C
Answer: (C) 330
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 21 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 225
(B) 240
(C) 288
(D) 267
(E) 211
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 21)m = 315 m. Let the length of the platform be x meters. Then, (x + 315)/36 = 15 ==> x + 315 = 540 ==> x = 225 m.Answer: A
Answer: (A) 225
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +B +2C?
(A) 6A+7.
(B) 5A+1.
(C) 5A-5.
(D) 6A-5.
(E) 6A-7.
Rationale: B = A-1
C= A-2
Putting these values in 2A +B +2C we get 5A-5
C is the answer
Answer: (C) 5A-5.
Question: The average weight of 7 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
(A) 76 kg
(B) 77 kg
(C) 75.5 kg
(D) Data inadequate
(E) None of these
Rationale: total weight increases = 7 × 1.5 = 10.5 kg
so the weight of new person = 65 + 10.5 = 75.5 kg
Answer C
Answer: (C) 75.5 kg
Question: A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 7 letters in its codes, and all letters can be repeated in any one code?
(A) A.17576
(B) B.456976
(C) C.11881376
(D) D.308915776
(E) E.8353082582
Rationale: The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = 676
# for 3 letters : 26 * 26*26 =17576
# for 4 letters : 26 * 26*26*26 =456976
# for 5 letters : 26 * 26*26*26*26 =11881376
# for 6 letters : 26 * 26*26*26*26*26 =308915776
# for 7 letters : 26 * 26*26*26*26*26*26 =8031810176
The total : By adding all of them , 26+676+17576+456976+11881376+308915776+8031810176
=8353082582
E
Answer: (E) E.8353082582
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'5" tall, which of the following is the median height of the children?
(A) 2'5"
(B) 2'6"
(C) 3'3"
(D) 3'4"
(E) 4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'5"+2'5")/2 = 2'5"
Ans:Option A
Answer: (A) 2'5"
Question: When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/2 of the remaining balance, what will be the final balance in her bank account?
(A) 300
(B) 375
(C) 450
(D) 500
(E) 575
Rationale: As per the question 200=2a/5
thus- a which is the total amount =500
The amount thus left =300
She then deposited 1/2 of 300=150
total amount in her account =450
Answer C
Answer: (C) 450
Question: Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
(A) 48
(B) 24
(C) 38
(D) 36
(E) 35
Rationale: Explanation:
Less Cogs more turns and less time less turns
Number of turns required=80 Ã— Ã— = 24 times
ANSWER IS B
Answer: (B) 24
Question: A store sells a certain product at a fixed price per unit. At the product's current price, A units cost a total of exactly $300. If the price were lowered by $5 from its current value, then A + 2n units would cost exactly $300; if the price were raised by $5, then A – n units would cost exactly $300. What is the value of A?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p a pa = 300
p-5 a+2n (p-5)(a+2n) = 300
p+5 a-n (p+5)(a-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So a = 20 satisfies all equations!!
Answer: (C) 20
Question: The average weight of 46 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?
(A) 51 1⁄23
(B) 52 15/23
(C) 52 15⁄3
(D) 43.42
(E) None of these
Rationale: Total weight of 46 students
= 46 × 52 = 2392 kg
Total weight of 5 students who leave
= 5 × 48 = 240 kg
Total weight of 5 students who join
= 5 × 54 = 270 kg
Therefore, new total weight of 46 students
= 2392 – 240 + 270 = 2422
⇒ New average weight = 2422⁄46 = 52 15/23 kg
Answer B
Answer: (B) 52 15/23