mathewhe/aqua_rat huggingface dataset:
Question: What is the CP of Rs 100 stock at 6 discount, with 1/5% brokerage?
(A) 99.6
(B) 96.2
(C) 94.2
(D) 98.25
(E) None of these
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-6+1/5
94.2
Thus the CP is Rs 94.2.
ANSWER C
Answer: (C) 94.2
Question: In a survey of parents, exactly 5/6 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?
(A) 12%
(B) 15%
(C) 18%
(D) 20%
(E) 25%
Rationale: Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed.
Mothers without full-time jobs are 1/6*3/5 = 1/10 of all the parents surveyed.
The percent of parents without full-time jobs is 2/20 + 1/10 = 1/5 = 20%
The answer is D.
Answer: (D) 20%
Question: A company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
(A) 6.25
(B) 15
(C) 10
(D) 8
(E) 7
Rationale: Dividend = 12.5*50/100 = 6.25
25 income on investment rs 100
req==>6.25
ANSWER A
Answer: (A) 6.25
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 3, and 4 if each digit can be used only once in each number?
(A) 1776
(B) 1887
(C) 1998
(D) 2332
(E) 2554
Rationale: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(222) + 2(333) + 2(444) = 1998
The answer is C.
Answer: (C) 1998
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 667 sec
(B) 190 sec
(C) 888 sec
(D) 288 sec
(E) 999 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
Answer: B
Answer: (B) 190 sec
Question: The length of the diagonal of a square is 12 cm. Find its area and perimeter.
(A) 31.84 cm
(B) 33.84 cm
(C) 35.84 cm
(D) 38.84 cm
(E) 38.92 cm
Rationale: Diagonal of a square = 12 cm
Area of square = 1/2 (d)²
= 1/2 (12)²
= 1/2 × 12 × 12
= 72
Side of a square = √Area
= √72
= √(2 × 2 × 2 × 3 × 3)
= 2 × 3√2
= 6 × 1.41
= 8.46 cm
Perimeter of square = 4 × 8.46 = 33.84 cm
ANSWER OPTION :B
Answer: (B) 33.84 cm
Question: The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed?
(A) 12
(B) 17
(C) 25
(D) 33
(E) 50
Rationale: Sum of four consecutive odd numbers:
(2a - 3) + (2a - 1) + (2a + 1) + (2a + 3) = 8a
Sum of three consecutive even numbers:
(2b - 2) + 2b + (2b + 2) = 6b
Given 8a = 6b or a/b = 3/4, a and b can be any integers. So, 'a' has to be a multiple of 3 and 'b' has to be a multiple of 4. Possible solutions are: a = 3, b = 4; a = 6, b = 8; a = 9, b = 12 etc
Since 101 < 2b < 200 i.e.
51 <= b < 100
Since b also has to be a multiple of 4, the values that b can take are 52, 56, 60, 64 ... 96
Number of values b can take = (Last term - First term)/Common Difference + 1 = (96 - 52)/4 + 12
Answer:A
Answer: (A) 12
Question: he greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
(A) 15 cm
(B) 25 cm
(C) 35 cm
(D) 42 cm
(E) 45 cm
Rationale: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer: Option C
Answer: (C) 35 cm
Question: The average of five results is 46 and that of the first four is 30. The fifth result is?
(A) 50
(B) 88
(C) 77
(D) 66
(E) 110
Rationale: 5 * 46 â€“ 4 * 30
= 110
Answer: E
Answer: (E) 110
Question: A train travels a certain distance taking 7 hrs in forward journey, during the return journey increased speed 12km/hr takes the times 5 hrs.What is the distance traveled
(A) 210 kms
(B) 30 kms
(C) 60 kms
(D) 90 kms
(E) 80 kms
Rationale: let the speed in the forward journey be x km/hr, also
given time taken in fwd journey = 7 hrs
during return journey
speed=(x+12)km/hr
time=5hrs
nw distance travelled in both the cases is same therefore
forward journey distance=return journey distance
7x=5(x+12)
7x-5x=60
2x=60
x=30km/hr
therefore distance travelled= 30*7=210km
or =5*(30+12)=210km
ANSWER:A
Answer: (A) 210 kms
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
(A) 13
(B) 21
(C) 77
(D) 88
(E) 11
Rationale: 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21'
Answer: B
Answer: (B) 21
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/7
(B) 1/11
(C) 2/7
(D) 2/9
(E) 2/11
Rationale: Explanation: P (getting a prize) = 10/(10+25) = 10/35 = 2/7
Option C
Answer: (C) 2/7
Question: If X = the product of three distinct prime numbers, how many factors does X have besides 1 and itself?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Since X has 3 distinct prime factors, X has a total of 2^3 = 8 factors.
Besides 1 and itself, X has 6 factors.
The answer is A.
Answer: (A) 6
Question: Sunil purchases two books at Rs. 300 each. He sold one book 10% gain and other at 10% loss. What is the total loss or gain in percentage?
(A) 10% gain
(B) 1% loss
(C) no loss or no gain
(D) 1% gain
(E) 2%
Rationale: tot cost = 300 + 300 = 600
total selling price
300 * 110/100 + 300 * 90/100 = 600
total cost price = total selling price
hence there is neither loss nor gain
ANSWER C
Answer: (C) no loss or no gain
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 22
(A) I, II, and III
(B) I and II only
(C) II and III only
(D) I and III only
(E) II only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: (A) I, II, and III
Question: Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what fraction of all the students are on the honor roll?
(A) 5/9
(B) 3/15
(C) 23/30
(D) 43/60
(E) 53/90
Rationale: for total students take LCM OF FACTIONS=6*5=30
Let female students=x,
so male students=30-x
Now,female stu. on honor roll=5/6(x) and male stu. on honor roll=2/3(30-x)
as given total female stu.=3/5(30)=18
female stu.=(5/6)*18=15
and male stu.=(2/3)*12=8
fraction of honor student=(15+8)/30=23/30.
Correct answer is C.
Answer: (C) 23/30
Question: A man received a cheque. The amount in Rs. has been transposed for paise and vice versa. After spending Rs. 5 and 42 paise, he discovered he now had exactly 6 times the value of the correct cheque amount. What amount he should have received?
(A) Rs 5.30
(B) Rs 6.44
(C) Rs 60.44
(D) Rs 16.44
(E) None of these
Rationale: Explanation :
Option 4 :- on reversal will be 44Rs 16Ps, after spending 5Rs 42Ps, remaining will be around 40rs which is not 6 times 16Rs 44Ps.
Option 3 :- on reversal will lead a smaller value. Hence we can eliminate that as well.
Option 1 :- on reversal is 30Rs 5 Paise, after spending 5Rs 42Ps, remaining will be 24Rs 63Paise, 24Rs63Ps is not 6 times 5Rs30Paise.
Option 2 on reversal is 44Rs 06 Paise, after spending 5Rs 42Ps, remaining will be 38Rs 64Ps, which is 6 times 6Rs 44Paise. Hence Rs 6.44 is the answer.
We need not even consider option 4 and option 3 as reversed number itself is not 6 times the original number. Option 1 when reversed is odd, and when even (5Rs 42Ps) is subtracted from odd, we get a odd number, and an odd number cannot be 6 times another number
Answer : B
Answer: (B) Rs 6.44
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by K percent, which of the following expressions represents the final price of the item?
(A) (10,000z + 100z(x – y) – xyz)/10,000
(B) (A+ Ax/100) - K/100 ( A +Ax/100)
(C) (100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by Y% on Total K/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - K/100 ( A +Ax/100)
B
Answer: (B) (A+ Ax/100) - K/100 ( A +Ax/100)
Question: Which of the following number will completely divide (49^15)-1?
(A) 8 is the number
(B) 6
(C) 22
(D) 12
(E) 14
Rationale: x^n - 1 will be divisible by x+1 only when n is even.
49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8
Answer is A
Answer: (A) 8 is the number
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:15
(C) 18:19
(D) 18:121
(E) 18:112
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11.Answer:A
Answer: (A) 18:11
Question: 4 mat-weaves can weaves 4 mats in 4 days.At the same rate,how many mats would be woven by 8 mat-weaves in 8 days ?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 17
Rationale: Solution
Let the required number of mats be x.
More weaves,More mats (Direct Proportion)
More days,More mats (Direct Proportion)
∴ 4 × 4 × x = 8 × 8 × 4 ⇔ x = (8x8x4)/(4x4)= 16. Answer D
Answer: (D) 16
Question: When positive integer x is divided by positive integer y, the remainder is 8. If x/y = 76.4, what is the value of y?
(A) 20
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: When positive integer x is divided by positive integer y, the remainder is 8 --> x=qy+8;
x/y=76.4 --> x=76y+0.4y (so q above equals to 76);
0.4y=8 --> y=20.
Answer: A.
Answer: (A) 20
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values V are within three standard deviations of the mean?
(A) 0
(B) 1
(C) 3
(D) 6
(E) 7
Rationale: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.B
Answer: (B) 1
Question: If the number of 89n,870, where n represents the thousands digit, is a multiple of 9, then the value of n could be which of the following?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Divisibility rule of 9: The sum of the digits must be divisible by 9
i.e 8+9+n+8+7+0 = multiple 9
or, 32 + n = multiple of 9.
If n=4, 32 + n =36,which is a multiple of 9.
Hence answer is D.
Answer: (D) 4
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3443, how much was it in the beginning?
(A) 4264
(B) 2776
(C) 4400
(D) 2871
(E) 881
Rationale: X * (95/100) * (85/100) = 3443
X = 4264
Answer:A
Answer: (A) 4264
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 177 m
(B) 166 m
(C) 776 m
(D) 150 m
(E) 176 m
Rationale: Speed=(60 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 9) m = 150 m.
Answer:D
Answer: (D) 150 m
Question: If r = 2^4 * 5^2 * 7 and s = 2 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?
(A) 2 * 5
(B) 2^2 * 5
(C) 2^3 * 5^2
(D) 2*3*5*7
(E) 2^3 * 3^2 * 5^2 * 7
Rationale: GCD = product of prime factors raised to the least power = 2 * 5
The answer is A.
Answer: (A) 2 * 5
Question: A company produces 72000 bottles of water everyday. If a case can hold 10 bottles of water .How many cases are required by the company to hold its one day production
(A) 2000
(B) 4500
(C) 5000
(D) 7200
(E) 9000
Rationale: Number of bottles that can be held in a case =10
Number of cases required to hold 72000 bottles = 72000/10=7200 cases.
So the answer is D =7200
Answer: (D) 7200
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 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 in this range.
Answer: A
Answer: (A) None
Question: The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs.110.Find the banker's discount and the banker’s gain?
(A) Rs.111
(B) Rs.120
(C) Rs.121
(D) Rs.125
(E) None
Rationale: Solution
T.D	=	√P.W x B.G
B.G	= (T.D)² / P.W
= Rs(110x110/1100)
= Rs.11.
B.D	= (T.D + B.G)
= Rs(110+11)
= Rs.121.
Answer C
Answer: (C) Rs.121
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.
(A) Rs.18000
(B) Rs.17000
(C) Rs.18500
(D) Rs.17500
(E) None of these.
Rationale: The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
ANSWER:B
Answer: (B) Rs.17000
Question: The marks obtained by Polly and Sandy are in the ratio 4:5 and those obtained by Sandy and Willy are in the ratio of 5:2. The marks obtained by Polly and Willy are in the ratio of...?
(A) 2:1
(B) 3:2
(C) 4:3
(D) 5:4
(E) 6:5
Rationale: Polly : Sandy = 4:5
Sandy : Willy = 5:2
Polly : Sandy : Willy = 4:5:2
Polly : Willy = 4:2 = 2:1
The answer is A.
Answer: (A) 2:1
Question: A bus trip of 550 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: The time is the distance/speed. The time difference is 1 hour.
550/V - 550/(V+5) = 1
550(V+5) - 550V = (V)(V+5)
2750 = (V)(V+5)
50*55 = (V)(V+5)
V = 50 mph
The answer is C.
Answer: (C) 50
Question: If q is an integer greater than 6, which of the following must be divisible by 3?
(A) Q(Q+1)(Q-4)
(B) N(N+2)(N-1)
(C) N(N+3)(N-5)
(D) N(N+4)(N-2)
(E) N(N+5)(N-6)
Rationale: Now take Q = 3k , Q = 3k+1 Q = 3k+2..put in all the choices. If by putting all the values of Q we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: (A) Q(Q+1)(Q-4)
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 122.9 m
(B) 127.5 m.
(C) 122.2 m
(D) 222.9 m
(E) 12289 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000
= 127.5 m.
Answer:B
Answer: (B) 127.5 m.
Question: How many integers are between 7 and 120/9, inclusive?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 10
Rationale: 120/9 = 13.xx
We are not concerned about the exact value of 120/9 as we just need the integers.
The different integers between 7 and 120/9 would be 7, 8, 9, 10, 11, 12,13
Total number of integers = 7
Option C
Answer: (C) 7
Question: The salary of a worker is first increased by 15% and afterwards reduced by 15%. What is the net change in the worker's salary?
(A) 5.25% increase
(B) 5.25% decrease
(C) 2.25% increase
(D) 2.25% decrease
(E) no change
Rationale: Let x be the original salary.
The final salary is 0.85(1.15x) = 0.9775x
The answer is D.
Answer: (D) 2.25% decrease
Question: In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 25 and the slope of line segment AC is 4/3, what is the length of AB?
(A) 12
(B) 18
(C) 20
(D) 28
(E) 40
Rationale: Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3
Change in Vertical Direction = 4x = AB
Change in Horizontal Direction = 3x = BC
AB^2 + BC^2 = 25^2
16x^2 + 9x^2 = 625
25x^2 = 625
x^2 = 25
x = 5
Therefore AB = 5*4 = 20
Answer: C
Answer: (C) 20
Question: An express traveled at an average speed of 120 km/hr, stopping for 3 min after every 90 kn. How long did it take to reach its destination 600 km from the starting point?
(A) 5 hrs 21 min
(B) 4 hrs 21 min
(C) 6 hrs 41 min
(D) 5 hrs 15 min
(E) 4 hrs 34 min
Rationale: D
6 hrs 21 min
Time taken to cover 600 km = 600/120 = 5 hrs.
Number of stoppages = 600/90 - 1 = 5
Total time of stoppages = 3 * 5 = 15 min
Hence, total time taken = 5 hrs 15 min.
Answer: (D) 5 hrs 15 min
Question: The set X = {10,11,12,13}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
(A) 9/16
(B) 7/16
(C) 5/16
(D) 5/8
(E) 3/8
Rationale: The total number of x and y pairs is 4*4=16.
There are five pairs such that x / y is an integer.
The probability that x / y is an integer is 5/16.
The answer is C.
Answer: (C) 5/16
Question: A passenger sitting near the window in a train moving at 45 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 75 metres?
(A) a)50km/h
(B) b)52km/h
(C) c)45km/h
(D) d)60km/h
(E) e)70km/h
Rationale: im getting A
3 secs to pass a 75 mts train , therefore speed = 25 meters/sec
to convert m/s to km/hrs multiply by 3.6
25*3.6 = 90
so its 90-45 = 45 .
C
Answer: (C) c)45km/h
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 3.5 years
(B) 4 years
(C) 4.5 years
(D) 5 years
(E) 5.5 years
Rationale: Time = (100 x 81)/(450 x 4.5) = 4 years.
Answer: Option B
Answer: (B) 4 years
Question: Find last two digits of the following expression (201*202*203*204*246*247*248*249)^2
(A) 33Q76
(B) 76
(C) 20
(D) 27
(E) 200
Rationale: To find the last two digits of a product take the last two digits in each number and multiply. 01*02*03......48*49 (use onscreen calculator)
this gives 76. So 762762 = 576 So last two digits are 76
Answer:B
Answer: (B) 76
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of four metre is left from all sides of the boundary of the garden. What is the length of the garden?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 4 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 Ã— 2) + 4 + 4 = 30 meter
Answer is E.
Answer: (E) 30
Question: A work can be finished in 16 days by 30 women. The same work can be finished in 10 days by sixteen men. The ratio between the capacity of a man and a woman is
(A) 3:1
(B) 4:3
(C) 2:3
(D) 2:1
(E) 2:4
Rationale: Work done by 30 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×30)
Work done by 16 men in 1 day = 1/10
Work done by 1 man in 1 day = 1/(10×16)
Ratio of the capacity of a man and woman =1/(10×16) : 1/(16×30) = 1/10 : 1/30
= 1/1 :1/3 = 3:1
Option A
Answer: (A) 3:1
Question: If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?
I. (a+c)/(b+d) < c/d
II. (a+c)/(b+d) < a/b
III. (a+c)/(b+d) = a/b +c/d
(A) None
(B) I only
(C) II only
(D) I and II
(E) I and III
Rationale: If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?
Since the numbers are positive we can safely cross-multiply. So, we are given that ad<bcad<bc.
I. a+cb+d<cda+cb+d<cd = ad+cd<bc+cd
ad+cd<bc+cd= cdcd cancels out: ad<bc. This is given to be true.
II. a+cb+d<aba+cb+d<ab = ab+bc<ab+adab+bc<ab+ad= ab
ab cancels out: bc<ad bc<ad. Opposite what is given, thus this option is not true.
III. a+cb+d=ab+cda+cb+d=ab+cd. From I we already know that a+cb+d<cda+cb+d<cd, thus when we add a positive value (abab) to (cdcd)we make the right hand side even bigger.Thus a+cb+d=ab+cda+cb+d=ab+cd cannot be true.
Answer: B.
Answer: (B) I only
Question: For a road work, a contractor was given a deadline to complete the work in 25 days. Hence, he employed a certain number of workers to accomplish the job. But from the very first day 9 workers were absent and the remaining workers could finish the work in 40 days. What number of workers did the contractor hired in the beginning?
(A) 20
(B) 30
(C) 24
(D) 16
(E) 19
Rationale: Explanation :
Let the number of workers initially hired be x.
Hence, x workers can complete the work in 25 days and (x-9) workers can complete the work in 40 days.
Now, the number of men and the amount of work are in direct proportion and number of men and number of days in indirect proportion.
x*25 = (x 9)*40
25x = 40x 360
15x = 360
x = 24
Answer : C
Answer: (C) 24
Question: A particular library has 150 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 108 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 40
(B) 60
(C) 80
(D) 100
(E) 120
Rationale: The total number of books is 150.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 108 books, thus the number of un-returned books is 150-108 = 42 books.
0.35x = 42
x = 120
The answer is E.
Answer: (E) 120
Question: It rained on exactly 7 of the days during Jane's summer holiday trip. On
each day that it rained, it rained either in the morning or the afternoon
but not both. There were exactly 5 afternoons when it did not rain and
exactly 6 mornings when it did not rain. How many days did the trip
last?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let M be the number of days it rained in the morning; A - the number of
days it rained in the afternoon; and let N be the number of days when it did not rain.
We have M + A = 7 (days when it rained); M + N = 5 (afternoons when it did not
rain); and A + N = 6 (mornings when it did not rain). Adding the equations we get
2(M + A + N) = 18, M + A + N = 9.
correct answer C
Answer: (C) 9
Question: The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median Q income in the community be in 2 years?
(A)  $50,000
(B)  $60,000
(C)  $60,500
(D)  $65,000
(E)  Cannot be determined
Rationale: Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean Q is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
Answer: (E)  Cannot be determined
Question: An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 44$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?
(A) 52
(B) 75
(C) 92
(D) 136
(E) 150
Rationale: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (44 - 40)/(40 - 36) = 4/4 = 1/1 = Number of MicroTron stocks/Number of Dynaco stocks
So for every 1 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/1)th i.e. 300/2 = 150 must be Dynaco stock.
Answer (E)
Answer: (E) 150
Question: The simple form of the ratio 2/3:2/5 is?
(A) 5:6
(B) 5:1
(C) 5:7
(D) 5:3
(E) 1:3
Rationale: 2/3 : 2/5 = 10:6
=5:3
Answer:D
Answer: (D) 5:3