mathewhe/aqua_rat huggingface dataset:
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 731 more than 4times the middle integer. Find the numbers?
(A) 650
(B) 731
(C) 698
(D) 710
(E) 729
Rationale: x + 4 (x + 4) = 731 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 731 + 4 x + 8
x = 723
x + 2 = 725
x + 4 = 727
Check: the smallest is added to four times the largest
723 + 4 * 727 = 3631
four times the middle
4 * 725 = 2900
3631 is more than 2900 by
3631 - 2900 = 731
B
Answer: (B) 731
Question: Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
(A) 27
(B) 26
(C) 25
(D) 24
(E) 23
Rationale: Solution:
We know that the average value is 22 therefore (a+b+c)/3 = 22
so a+b+c = 66
and b = a + 13
therefore a + (a + 13) + c = 66
The least value of c is when c = b
so take c = a + 13
hence, a + (a + 13) + (a + 13) = 66
i.e., a = 40/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+14
a + (a + 13) + (a + 14) = 66
i.e., a= 39/3 = 13
hence, a = 13, b = 26, and c = 27
Answer: A
Answer: (A) 27
Question: All of the stocks on the over-the-counter market are designated by either a 5-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) 2(26^5)
(B) 26(26^4)
(C) 27(26^4)
(D) 26(26^5)
(E) 27(26^5)
Rationale: Number of 4-letter codes: 26 * 26 * 26 * 26 * 26= 26^5
Number of 5-letter codes: 26 * 26 * 26 * 26 * 26 = 26^5
Total Number of codes: 26^5 + 26^5 = 2*(26^5)
Therefore, the answer isA: 2*(26^5).
Answer: (A) 2(26^5)
Question: A pineapple costs Rs 9 each and a watermelon costs Rs. 6 each. If I spend Rs 51 on total what is the number of pineapple I purchased?
(A) 6
(B) 7
(C) 5
(D) 3
(E) 2
Rationale: 5*9 +6 = 51
5 pineapples
Answer : C
Answer: (C) 5
Question: Find the odd man out
3, 7, 15, 27, 63, 127, 255
(A) 7
(B) 15
(C) 27
(D) 63
(E) 54
Rationale: 1*2+1 = 3
3*2+1 = 7
7*2+1 = 15
15*2+1 = 31
31*2+1 = 63
63*2+1 = 127
127*2+1= 255
ANSWER:C
Answer: (C) 27
Question: How many possible ways can 4 girls (Rebecca, Kate, Ashley) go on a date with 4 boys (Peter, Kyle, Sam)?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  24
Rationale: Any one girl can go with 4 boys.
2nd girl can go with remaining 3 boys
3nd girl can go with remaining 2 boys
and 3rd girl can go with remaining 1 boy
4! i.e 24 (E) is the answer
Answer: (E)  24
Question: The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is:
(A) 448
(B) 488
(C) 16748
(D) 548
(E) 560
Rationale: Required number = (L.C.M. of 12, 31, 20, 54) + 8
= 16740+ 8
= 16748.
answer :C
Answer: (C) 16748
Question: One out of every 100 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 50,000
(E) 52,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*100= 10,000 light bulbs are present.
C is the answer
Answer: (C) 10,000
Question: If a job is complete by a and b in z days,b and c in x days and a and c in y days. In how many days that a,b and c can be work simultaneously?
(A) 2(xyz/xy+yz+xz)
(B) xyz/xy+yz+xz
(C) (xy+yz+xz)/xyz
(D) cannot be determined
(E) 2(xy+yz+xz)/xyz
Rationale: Option A is answer.
one day work of a+b,b+c and c+a is 1/z,1/x and 1/y.
That is , 2(a+b+c)=(yz+xz+xy)/xyz.
a+b+c=(yz+xz+xy)/2xyz.(one day work).
Total work done by a,b and c is 2xyz/(xy+yz+xz).
Answer: (A) 2(xyz/xy+yz+xz)
Question: A plane flies 660 km with the wind and 540 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air?
(A) 160 km/h
(B) 180 km/h
(C) 200 km/h
(D) 220 km/h
(E) 240 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 20 km/h
Speed with the wind = (x + 20) km/h
Speed against the wind = (x â€“ 20) km/h
Time = Distance/ Speed
660 / (x+20) = 540 / (x-20)
660(x-20) = 540(x+20)
66x - 1320 = 54x + 1080
12x = 2400
x = 200
Therefore, the speed of the plane in still air is 200 km/h.
The answer is C.
Answer: (C) 200 km/h
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 2 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 240
(C) 289
(D) 270
(E) 927
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 2 = 240
Answer: B
Answer: (B) 240
Question: A man sells a horse for Rs.1400 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 2270
(B) 2990
(C) 1540
(D) 8600
(E) 7710
Rationale: CP = SP + 1CP = SP - g
1400 + x = 980 - 2x
3x = 420 => x = 140
CP = 1400 + 140 = 1540
Answer: C
Answer: (C) 1540
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 176
(B) 500
(C) 278
(D) 270
(E) 279
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer:B
Answer: (B) 500
Question: A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 298 m
(B) 225 m
(C) 208 m
(D) 988 m
(E) 299 m
Rationale: Speed = 90 * 5/18 =25/1 m/sec
Length of the train = speed * time = 25 * 9
= 225 m
Answer:B
Answer: (B) 225 m
Question: What is the probability of having 53 Fridays in an ordinary year
(A) 1/5
(B) 1/6
(C) 1/7
(D) 1/8
(E) 1/9
Rationale: 1/7 because 53 friday in ordinary year then 53*7=371 (53/371=1/7)
ANSWER:C
Answer: (C) 1/7
Question: Two girls started running simultaneously around a circular track of length 1200 m from the same point at speeds of 30 km/hr and 50 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 50
(B) 51
(C) 52
(D) 53
(E) 54
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 1200 / (30 + 50)5/18 = 1200* 18 / 80 * 5 = 54 seconds.
Answer:E
Answer: (E) 54
Question: Two whole numbers whose sum is 72 cannot be in the ratio
(A) 3 : 4
(B) 3 : 5
(C) 4 : 5
(D) 5 : 7
(E) None
Rationale: Sol.
The sum of the ratio terms must divide 72. So, the ratio
cannot be 3 : 4.
Answer A
Answer: (A) 3 : 4
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 66√3 cm2
(B) 74√3 cm2
(C) 64√3 cm2
(D) 64√5 cm2
(E) 14√3 cm2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;
Answer:D
Answer: (D) 64√5 cm2
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.
(A) 22
(B) 88
(C) 27
(D) 40
(E) 11
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500∗2/25=40seconds
Answer: C
Answer: (C) 27
Question: 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275
(A) 147
(B) 149
(C) 268
(D) 2696
(E) 2976
Rationale: Explanation:
Let 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275
Then, 63 * 15 / 5 + X = 61 + 275
63 * 3 + X = 336
189 + X = 336
X = 147
ANSWER: A
Answer: (A) 147
Question: The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive?
(A) 2.5
(B) 3.00
(C) 3.25
(D) 3.75
(E) 4.0
Rationale: For first 0.25 miles 34 cents.
So the person is left with 1.24-0.34 = 0.9
So the person can travel next (90/6) times 1/5 miles
i.e 15 *1/5 miles = 3 miles.
SO total distance is 3 + 0.25 = 3.25 miles(C)
Answer: (C) 3.25
Question: In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
(A) 4! x 9!
(B) 4! x 2!
(C) 4! x 5!
(D) 4! x 6!
(E) 7! x 9!
Rationale: Explanation:
The word EDUCATION is a 9 letter word, with none of the letters repeating.
The vowels occupy 3rd,5th,7th and 8th position in the word and the remaining 5 positions are occupied by consonants
As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the afore mentioned 4 places and the consonants can occupy1st,2nd,4th,6th and 9th positions.
The 4 vowels can be arranged in the 3rd,5th,7th and 8th position in 4! Ways.
Similarly, the 5 consonants can be arranged in1st,2nd,4th,6th and 9th position in5! Ways.
Hence, the total number of ways = 4! × 5!
Answer: C) 4! x 5!
Answer: (C) 4! x 5!
Question: The average of first 6 prime numbers is?
(A) 10.11
(B) 11.11
(C) 12.11
(D) 6.83
(E) 14.11
Rationale: Sum of 6 prime no. = 41
Average = 41/6 = 6.83
ANSWER: D
Answer: (D) 6.83
Question: A train passes a station platform in 50 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) 177 m
(B) 176 m
(C) 450 m
(D) 187 m
(E) 186 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 50 = 15
x + 300 = 750
x = 450 m.
Answer: C
Answer: (C) 450 m
Question: X, Y and Z can do a work in 6 , 9 and 10 days respectively. They completed the work and got Rs.775. What is the share of Y?
(A) 250
(B) 240
(C) 260
(D) 230
(E) 245
Rationale: The ratio of their working rates = 1/6 : 1/9 : 1/10 = 15 : 10 : 6.
Since, they work together, the share of y
= 10/31 * 775 = Rs.250
Answer: A
Answer: (A) 250
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
(A) 1/6
(B) 1/3
(C) 1/5
(D) 1/1
(E) 1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer: C
Answer: (C) 1/5
Question: A certain bus driver is paid a regular rate of $18 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: For 40 hrs = 40*18=720
Excess = 976-720=252
For extra hours =.75(18)=13.5+18=31.5
Number of extra hrs =252/31.5=8
Total hrs =40+8=48
Answer D 48
Answer: (D) 48
Question: In a group of cows and chickens, the number of legs was 16 more than twice the number of heads. The number of cows was:
(A) 8
(B) 7
(C) 10
(D) 12
(E) 14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 16 more than twice the number of heads.
Therefore, 2 × (x + y) + 16 = 4x + 2y.
or, 2x + 2y + 16 = 4x + 2y.
or, 2x + 16 = 4x [subtracting 2y from both sides].
or, 16 = 4x – 2x [subtracting 2x from both sides].
or, 16 = 2x.
or, x = 8 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
Correct Answer:A)8
Answer: (A) 8
Question: Calculate the cost of e yards of cloth given that the cost of f yards of said cloth is g rupees?
(A) Rs.(e*f)
(B) Rs.(g*f)
(C) Rs.(eg/f)
(D) Rs.(g/f)
(E) Rs.(e/f)
Rationale: Cost of f yards = Rs. g.
Cost of 1 yard = Rs.	g/f
Cost of e yards = Rs.(g/f)* e= Rs.(eg/f)
Answer is C.
Answer: (C) Rs.(eg/f)
Question: Calculate the area of a triangle, if the sides are 13 cm, 12 cm and 5 cm, what is its area?
(A) 36 cm2
(B) 35 cm2
(C) 30 cm2
(D) 32 cm2
(E) 31 cm2
Rationale: The triangle with sides 13 cm, 12 cm and 5 cm is right angled, where the hypotenuse is 13 cm.
Area of the triangle = 1/2 * 12 * 5 = 30 cm2
Answer: C
Answer: (C) 30 cm2
Question: There are 100 students in a class. If 14% are absent on a particular day, find the number of students present in the class.
(A) 43
(B) 36
(C) 86
(D) 129
(E) 11
Rationale: Number of students absent on a particular day = 14 % of 100
i.e., 14/100 × 100 = 14
Therefore, the number of students present = 100 - 14 = 86 students.
Answer:C
Answer: (C) 86
Question: If x/6 and x/15 are integers, then x must be divisible by -
(A) 12
(B) 18
(C) 30
(D) 45
(E) 60
Rationale: Factors of 6 2 and 3
factors of 15 are 3 and 5
So number is 2*3*5 = 30
ANSWER:C
Answer: (C) 30
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 140 units?
(A) 50 hours
(B) 40 hours
(C) 17.5 hours
(D) 12 hours
(E) 8 hours
Rationale: Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 140 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 140 units is '7 times' 20, we need '7 times' more TIME.
(2.5 hours)(7 times) = 17.5 hours
Final Answer:
[Reveal]Spoiler:
C
Answer: (C) 17.5 hours
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $16. If the shop keeper has a order of 200 articles, how much profit he will get?
(A) A)200
(B) B)2000
(C) C)1500
(D) D)1200
(E) E)600
Rationale: Total money after selling articles = 200*16 = 3200
cost price = 200*10 = 2000
profit = 1200
correct option is D
Answer: (D) D)1200
Question: There are 50 people in a certain community who belong to the local golf club, tennis club or both clubs. If 1 as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
(A) 1) 4
(B) 2) 7
(C) 3) 17
(D) 4) 21
(E) 5) 27
Rationale: x -> Golf Club
x -> Tennis Club
y -> both
x+x-y = 50
2x - y =50
multiples of 2 greater than 50
52
54-4=50
IMO (A)
Answer: (A) 1) 4
Question: A customer pays 65 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) A)$50
(B) B)$60
(C) C)$70
(D) D)$85
(E) E)$90
Rationale: Let x be the original price.
x - 20 = 65
x - 20 + 20 = 65 + 20
x + 0 = 85
x = 85
correct answer is D)$85
Answer: (D) D)$85
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1642
(B) 1640
(C) 1632
(D) 2789
(E) 6386
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025
=1640
Answer:B
Answer: (B) 1640
Question: The average of six number is 3.95. The average of two of them is 3.4, while the average of the other two is 3.62. what is the average of the remaining two number ?
(A) 4.5
(B) 4.6
(C) 4.7
(D) 4.83
(E) None of these
Rationale: solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.4 × 2) + (3.62 ×2)]
=23.70 -(6.8 + 7.24) = 23.70 - 14.04 = 9.66.
∴ Required average =9.66/2 = 4.83 Answer D
Answer: (D) 4.83
Question: A began business with Rs.27000 and was joined afterwards by B with Rs.54000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
(A) 9
(B) 6
(C) 7
(D) 8
(E) 2
Rationale: 27*12 : 54*x = 2: 1
x = 3
12 -3 = 9
Answer: A
Answer: (A) 9
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 6w widgets.
(A) 4
(B) 36
(C) 8
(D) 10
(E) 12
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 36 days to doing 6w widgets.
Answer : B
Answer: (B) 36
Question: james works in a bakery. He made cookies that cost $2 and made $200. How many customer did he have?
(A) 200 customers
(B) 85 customers
(C) 250 customers
(D) 100customers
(E) 170 customers
Rationale: A cookie costs $2 adding another one is $4. 200 divided by 3 is 50 x 2 is 100. He had 100 customers. The correct answer is D.
Answer: (D) 100customers
Question: The product of a and b is equal to 11 more than twice the sum of a and b. If b = 7, what is the value of b - a?
(A) 2
(B) 5
(C) 7
(D) 24
(E) 35
Rationale: Given: ab = 2(a + b) + 11 and b = 7
Hence 7a = 2a + 14 + 11
5a = 25, a = 5
(A potential trap. Do not get excited here. We need to find b - a, not a)
b - a = 7 - 5 = 2
Correct Option: A
Answer: (A) 2
Question: In year Y imported machine tools accounted for 20 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 15x
(B) 13x
(C) 12.5x
(D) 14x
(E) 14.5x
Rationale: Sales of imported tools = 20% of the total sales = 0.20*{total} = {total}/5;
Sales of Japanese tools = 40% of the sales of imported tools = 2/5*{total}/5 = 2{total}/25
Since the sales of of Japanese tools was x, then 2{total}/25 = x -->2{total} = 25 x
{total} = 25x/2 =12.5 x
Answer: C
Answer: (C) 12.5x
Question: In how many ways can the integer 84 be expressed as a product of two different positive integers?
(A) 10
(B) 8
(C) 5
(D) 4
(E) 2
Rationale: 84=(2^2)*3*7
Since 84 is not a perfect square, no of ways=4
Answer D
Answer: (D) 4
Question: In measuring the sides of a rectangle, one side is taken 8% in excess, and the other 7% in deficit. Find the error percent in the area calculated from these measurements.
(A) 0.11%
(B) 0.7%
(C) 0.44%
(D) 0.6%
(E) 0.8%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (27/25) x (40/43) y = (913/909 )(xy)
Error In measurement = (913/909)xy- xy = (4/909)xy
Error percentage = [(4/909)xy (1/xy)100] % = (11/25) % = 0.44%.
Answer is C.
Answer: (C) 0.44%
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 4.6, what is the value of C?
(A) 6
(B) 5.2
(C) 4
(D) 3
(E) 2
Rationale: If A+B=4.6
assuming A and B are positive then A*B<10 (they could be either 1,2,3,4)
therefore
A*B=C
2*B=C
A+B=4.6
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=2.6 --> C=5.2 (ANSWER B)
Answer: (B) 5.2
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 6 cm
(B) 4 cm
(C) 8 cm
(D) 3 cm
(E) 9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer:E
Answer: (E) 9 cm
Question: A train 420 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 36 sec
(B) 16 sec
(C) 17 sec
(D) 88 sec
(E) 12 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 420 * 2/35 = 36 sec
Answer:A
Answer: (A) 36 sec
Question: If a square mirror has a 20-inch diagonal, what is the approximate perimeter T of the mirror, in inches?
(A)  40
(B)  60
(C)  80
(D)  100
(E)  120
Rationale: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter T must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
Answer: (B)  60
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
(A) 35
(B) 39
(C) 48
(D) 50
(E) 52
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: (C) 48
Question: A certain company had a total annual expenditure of 1.89∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
(A) $20,000
(B) $25,000
(C) $35,000
(D) $40,000
(E) $45,000
Rationale: Given: Total annual expenditure of 1.89∗10^7 on employee salaries
Total employees = 420
Observe that 420*4 = 1890
Therefore try to bring the numerator in terms of 1890
Average salary = (1890*10^4) /420 = 4.5*10^4 = 45,000
Option E
Answer: (E) $45,000
Question: Which of the following must be an integer if the integer x is divisible by both 18 and 24?
(A) x/252
(B) x/189
(C) x/126
(D) x/108
(E) x/72
Rationale: the integer has to be multiple of LCM of 18 and 24, which is 72..
so x/126 will be an integer
ans E
Answer: (E) x/72
Question: Factory X's bulbs work for over 5000 hours in 78% of cases, whereas factory Y's bulbs work for over 5000 hours in 65% of cases. It is known that factory X supplies 90% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
(A) 76.4%
(B) 76.7%
(C) 77.4%
(D) 75%
(E) 73.9%
Rationale: For X, 90% of 78% will work.
For Y, 10% of 65% will work. *10% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.90(0.78) = .702
0.10(0.65) = 0.065
The combined probability then is 70.2 + 6.5 = 76.7%
ANS B
Answer: (B) 76.7%
Question: Positive Integer A gives the remainder of 32 when divided by another positive Integer B. If A/B = 147.64, what is the value of B?
(A) 96
(B) 75
(C) 48
(D) 50
(E) 12
Rationale: .64 of B = Remainder
.64 of B = 32
B = (32 *100) / 64= 50.
D
Answer: (D) 50
Question: There are three motor's are available in the office,namely P,Q,& R.Its power consumption is different.Ratio of the power consumption of 3 different motor's 3:4:5.Total power consumption of 3 motor's are 1250 units.Then find out the power consumption of motor R?
(A) 655.50 UNITS
(B) 258.54 UNITS
(C) 566.29 UNITS
(D) 520.84 UNITS
(E) 634.25 UNITS
Rationale: Ratio of the power consumption of 3 different motor's 3+4+5=12.
Power consumption of motor R= 5/12*1250 = 520.84 UNIT Answer: D
Answer: (D) 520.84 UNITS
Question: There is a total of 90 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/3 and the probability that it will be green is 1/5. What is the probability that the marble will be either red or blue?
(A) 1/3
(B) 3/5
(C) 7/15
(D) 11/30
(E) 17/30
Rationale: P(red or blue) = 1 - P(white) - P(green) = 15/15 - 5/15 - 3/15 = 7/15
The answer is C.
Answer: (C) 7/15
Question: A can finish a work in 18days and B can do the same work in half the time taken by A. Then, working together what part of the same work they can finish in a day?
(A) 1/2
(B) 1/3
(C) 1/6
(D) 2/5
(E) 2/9
Rationale: 1days work of A+B = (18+9)/18*9 = 1/6
Answer is C
Answer: (C) 1/6
Question: The perimeter of one face of a cube is 24 cm. Its volume will be:
(A) 216cm3
(B) 400cm3
(C) 250cm3
(D) 625cm3
(E) None of these
Rationale: Explanation:
Edge of cude = 24/4 = 6 cm
Volume = a*a*a = 6*6*6 = 216 cm cube
Option A
Answer: (A) 216cm3