divelab/Sys2Bench huggingface dataset:
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625.
The answer is B.
Answer: B
Question: The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.180 and Rs.120 respectively. What is the sum and the time?
Options:
A)Sum = Rs.380 and Time = 4 years
B)Sum = Rs.400 and Time = 6 years
C)Sum = Rs.320 and Time = 4 years
D)Sum = Rs.360 and Time = 5 years
E)None of these
Rationale: Explanation :
BD = Rs.180
TD = Rs.120
R = 10%
F = BD ×TD/(BD – TD)=180×120/(180–120)=180×120/60=Rs. 360
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒180 = (360×T×10)/100
⇒180 = 36 × T
⇒ T = 180/36 = 5 years Answer : Option D
Answer: D
Question: The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 80, then 1/m + 1/n is equal to
Options:
A)1/35
B)3/35
C)5/37
D)4/63
E)None
Rationale: Answer
We have, m x n = 6 x 210 = 1260
âˆ´ 1/m + 1/n = (m + n)/mn = 80/1260 = 4/63
Correct Option: D
Answer: D
Question: If f(x) = 2x − √x and g(x) = x^2, what is f(g(3))?
Options:
A)-4
B)8
C)17
D)32
E)15
Rationale: g(x) = x²
g(3) = 3² = 9
So, f(g(3)) = f(9)
f(x) = 2x − √x
So, f(9) = 2(9) − √9
= 18 - 3
= 15
= E
Answer: E
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 45km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
Options:
A)8.95km/hr
B)26.7km/hr
C)27.7km/hr
D)37.9km/hr
E)8.45km/hr
Rationale: average speed = (2*45*20)/45+20 km/hr
=27.7 km/hr
Answer (C)
Answer: C
Question: 4539,1513,378.25,75.65,12.60 ?
Options:
A)1.2
B)6.87
C)1.8
D)4.68
E)9.87
Rationale: Explanation :
Terms are continuously divided by 3 ,4, 5,6 and so on
4539
4539 Ã· 3 = 1513
1513 Ã· 4 = 378.25
378.25 Ã· 5 =75.65
75.65 Ã· 6= 12.60
12.60Ã·7=1.80
Answer : Option C
Answer: C
Question: If 2A = 3B = 4C, find A : B : C
Options:
A)2 : 4 : 5
B)5 : 3 : 1
C)3 : 2 : 1
D)7 : 3 : 2
E)6 : 4 : 3
Rationale: Let 2A = 3B = 4C = x
So, A = x/2 B = x/3 C = x/4
The L.C.M of 2, 3 and 4 is 12
Therefore, A : B : C = x/2 × 12 : x/3 × 12 : x/4 = 12
= 6x : 4x : 3x
= 6 : 4 : 3
Answer is E
Answer: E
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Options:
A)2277
B)28886
C)5550
D)2678
E)2681
Rationale: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year
= 66600/12 = 5550
Answer: C
Answer: C
Question: A square has a side 5 centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let x be the side of the smaller square and y be the side of the larger square. The statement "A square has a side 5 centimeters shorter than the side of a second square" may be formulated by
x = y - 5
The area of the smaller square is equal to x 2 = (y - 5) 2 and the area of the larger square is equal to y 2
The statement "the area of the larger square is four times the area of the smaller square" may be formulated by
y 2 = 4 (y - 5) 2
Write the above equation so that the right side is equal to 0
y 2 - 4 (y - 5) 2 = 0
The left side is made up of the difference of two squares and can be easily factored as follows
[ y - 2 (y - 5) ] [ y + 2 (y - 5) ] = 0
Solve for y to find
y = 10 and y = 10 / 3.
We now use the equation x = y - 5 to find x
y = 10 and x = 5
For the second solution y = 10 / 3, x is negative and cannot be accepted as the length of the side of a square must be positive.
Answer A
Answer: A
Question: . A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)16 2/3%
B)20%
C)18%
D)25%
E)35%
Rationale: 900 ---- 180
100 ---- ? => 20%
ANSWER:B
Answer: B
Question: The simple interest on a sum of money will be Rs.1000 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Options:
A)8981
B)3799
C)1200
D)2693
E)2000
Rationale: P --- 10 ---- 1000
P --- 5 ----- 500
3P --- 5 ----- 1500
------
=> 2000
Answer: E
Answer: E
Question: In a 80 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
Options:
A)3 seconds
B)12 seconds
C)10 seconds
D)18 seconds
E)28 seconds
Rationale: B runs 56 m in 7 sec.
=> B runs 80 m in 7/56*80 = 10 seconds
Since A beats B by 7 seconds, A runs 80 m in (10-7) = 3 seconds
Hence, A's time over the course = 3 seconds
ANSWER:A
Answer: A
Question: A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year
A).	B)
C) D)
Options:
A)Rs. 5624.32
B)Rs.5423
C)Rs.5634
D)Rs.5976
E)Rs.5376
Rationale: 5% is the rate of interest. 20% of the interest amount is paid as tax.
i.e 80% of the interest amount stays back.
if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.
The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.
= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32
The amount at the end of 3 years = 5000 + 624.32 = 5624.32 Answer: A
Answer: A
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)8
C)7
D)4
E)1
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer:A
Answer: A
Question: A shopkeeper sells 500 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
Options:
A)12
B)27
C)29
D)50
E)41
Rationale: SP per metre = 18000/500 = Rs. 36 Loss per metre = Rs. 5 CP per metre = 36+ 5 = Rs. 41.Answer: E
Answer: E
Question: An empty pool being filled with water at a constant rate takes 6hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?
Options:
A)5hr 30min
B)5hr 20min
C)4hr 48min
D)3 hr 12min
E)2hr 40 min
Rationale: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours =3 hours 12 minutes.
Answer: D.
Answer: D
Question: How many meters are there in 660 centimeters?
Options:
A)6.6 meters
B)660 meters
C)600 meters
D)6.5 meters
E)6 meter
Rationale: Solution:
1 meter = 100 centimeters
Just divide 660 by 100
660 Ã· 100 = 6.6, so there are 6.6 meters in 660 centimeters
Option A
Answer: A
Question: Consider a Number 3.1n2
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
Options:
A)1
B)2
C)3
D)4
E)3
Rationale: In this ques we are given the thousandth digit as 2, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 2, the hundreth digit has to go up by 0, and correspondingly, the tenth digit should remain same.i.e 0-9.say 1
A
Answer: A
Question: If x and y are integers and x=50y + 39, which of the following must be odd?
Options:
A)xy
B)x + y
C)3X-1
D)X+2Y
E)3x+1
Rationale: x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
D: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, stop here.
C: EVEN ...E - EVEN
Answer D
Answer: D
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?
Options:
A)72
B)80
C)120
D)150
E)100
Rationale: Answer: Option E
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% OF X= 48+2/3 OF 48
80/100 X=80
X=100
Answer: E
Question: In the Bombay Stock Exchange there are 45% female employees and thus the number of male employees is exceeded by 72. Hence the total no. of employees in the BSE is:
Options:
A)540
B)720
C)800
D)550
E)None
Rationale: Solution: Female employees = 45%
Male employees = 55%
Difference = 55 - 45 = 10%
→ 10% = 72
→ 1% = 72 /10
→ 100 = 7.2 * 100 = 720.
Answer: Option B
Answer: B
Question: Find the simple interest on the Rs. 2000 at 25/4% per annum for the period from 4th Feb 2005 to 18th April 2005
Options:
A)Rs 25
B)Rs 30
C)Rs 35
D)Rs 40
E)None of these
Rationale: Explanation:
One thing which is tricky in this question is to calculate the number of days.
Always remember that the day on which money is deposited is not counted while the day on which money is withdrawn is counted.
So lets calculate the number of days now,
Time = (24+31+18) days = 73/365 years = 1/5 years
P = 2000
R = 25/4%
S.I. = =2000×25 /4×5×100=25
Option A
Answer: A
Question: A man is 18 years older than his son. In eight years, his age will be twice the age of his son. The present age of this son is
Options:
A)5 years
B)10 years
C)15 years
D)20 years
E)25 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+18.
=> 2(x+8) = (x+18+8)
=> 2x+16 = x+26
=> x = 10 years
Answer: Option B
Answer: B
Question: Calculate 73196 ÷ ? = 631
Options:
A)101
B)116
C)119
D)116
E)32
Rationale: Answer
Let 62976/X = 631
Then X = 62976/631 =116
Option: D
Answer: D
Question: The angles of a triangle are in the ratio 2: 6 : 4. Find the measurement of the 3 angles of triangle.
Options:
A)90°
B)60°
C)20°
D)30°
E)80°
Rationale: If the ratio of the three angles is 2:6:4, then the measures of these angles can be written as 2x, 6x and 4x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
2x + 6x + 4x = 180
Solve for x
12x = 180
x =15
The measures of the three angles are
2x =2 x15=30°
6x = 6 × 15= 90°
4x = 4 × 15 = 60°
B
Answer: B
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,715 minutes earlier? (Assume standard time in one location.)
Options:
A)6:23
B)6:24
C)6:27
D)6:30
E)6:32
Rationale: 6:27minus 2,880,715in any way must end with 2, the only answer choice which ends with 2 is E.
Answer: E.
Answer: E
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)708 m
B)704 m
C)774 m
D)714 m
E)744 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm
= 704 m
Answer:B
Answer: B
Question: Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 3 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?
Options:
A)4
B) 8
C) 12
D) 18
E) 24
Rationale: x rate = k/6
y rate = k/3
k/6 + k/3 = 12k / T
solving T = 24
Answer E
Answer: E
Question: In Town X, 64 percent of the population are employed, and 44 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)55%
C)29%
D)40%
E)52%
Rationale: answer b
male-employed - 64%
female-employed-20%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
20/64 =29 C
Answer: C
Question: If R is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, R, 0, 1, 3, K, 7}?
I. -1.5
II. -2
III. 0
Options:
A) I only
B) II only
C) III only
D) I and III only
E) None
Rationale: The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E
Answer: E
Question: An investment of $100 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $100 increased to $400 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?
Options:
A)16
B)20
C)18
D)24
E)30
Rationale: In 12 years the investment quadrupled (from $100 to $400).
Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $400 to $800).
Therefore, 12+6=18 years are needed $100 to increase to $800.
Answer: C.
Answer: C
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)26
B)89
C)76
D)27
E)23
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10
= 89 sec.
Answer:B
Answer: B
Question: Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other?
Options:
A)1.5 hours
B)1.27 hours
C)1.73 hours
D)2 hours
E)1.69 hours
Rationale: The cars travel (145+150=295) miles in one hour.
500 miles/295 miles/hour= 1.69 hours
Answer is E
Answer: E
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHM', if repetition of letters is not allowed?
Options:
A)690
B)504
C)740
D)760
E)780
Rationale: The word 'LOGARITHM' has 9 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 9P3
=
9
×
8
×
7
=
504
Option B
Answer: B
Question: 10, 14, 26, 42, 70, ?
Options:
A)86
B)98
C)114
D)126
E)136
Rationale: Each term of the series, except the first two terms, is 2 more than the sum of the preceding two terms.
Answer : C.
Answer: C
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 60%?
Options:
A)800
B)882
C)772
D)652
E)271
Rationale: Cost price = Rs.500
profit = 60% of 500 = Rs.300
Selling price = Cost price + Profit
= 500 + 300 = 800
Answer:A
Answer: A
Question: A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 30% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
Options:
A)20%
B)43%
C)99.33%
D)75.109%
E)47%
Rationale: Anyways, one can infer that he 'steals' 10% from suppliers and then charges 30% extra to customers
So basically 1.1 * 1.3 = 1.43
Given that 1 is start point, we get 43% more
Hence answer is B
Answer: B
Question: Fox jeans regularly sell for $10 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
Options:
A)9%
B)10%
C)11%
D)12%
E)40%
Rationale: x discount on Pony jeans, (0.22-x) discount on Fox jeans.
Set the equation: 3*10(0.22-x)+2*18x=9 --> x=0.4=40%
Answer: E.
Answer: E
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
A)39
B)37
C)342
D)288
E)261
Rationale: 400*(90/100)*(95/100) = 342
Answer: C
Answer: C
Question: John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
Options:
A)6
B)9
C)36
D)120
E)144
Rationale: First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 4 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways = 4*3*3*2*2*1*1 = 144 ways
E
Answer: E
Question: A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
Options:
A)200, 360,162
B)200, 460,160
C)200, 360,160
D)200, 360,138
E)200, 360,129
Rationale: Explanation:
let ratio be x.
Hence no. of coins be 5x ,9x , 4x respectively
Now given total amount = Rs.206
=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206
we get x = 40
=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160
Answer: C)
Answer: C
Question: If (A-B-C+D = 18) and (A+B-C-D = 4), what is the value of (B-D)^2?
Options:
A)49.
B)8.
C)12.
D)16.
E)64.
Rationale: EQ1: A - B - C + D = 18
EQ2: A + B - C - D = 4
(1) Subtract EQ1 from EQ2
A - B - C + D = 18
- A +B - C - D = 4
------------------------
-2B + 2D = 14
(2) Simplify
-B + D = 7
B - D = -7
(B-D)^2 = (-7)^2 = 49
My answer: A
Answer: A
Question: A vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away?
Options:
A)24
B)26
C)28
D)30
E)32
Rationale: Let x be the original number of apples.
On day one, the vendor throws away (0.4)(0.4)x=0.16x.
The remaining apples are (0.6)(0.4)x = 0.24x.
On day two, the vendor throws away (0.5)(0.24)x=0.12x.
The vendor throws away a total of 0.16x + 0.12x = 0.28x.
The vendor throws away 28 percent of the apples.
The answer is C.
Answer: C
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?
Options:
A)700
B)750
C)780
D)800
E)820
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
D
Answer: D
Question: A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
Options:
A)8p
B)pq
C)pq + 27
D)-p
E)(p - q)^6
Rationale: A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject.
B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject.
C. Hold.
D. since p is a perfect cube, -p will also be a perfect cube. reject.
E. (p-q)^6, is a perfect cube, so reject.
By elimination C is the answer.
Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube.
ANSWER:C
Answer: C
Question: find value for x from given equation? x + 1 = -3
Options:
A)1
B)-4
C)-3
D)-5
E)5
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Answer: B
Question: If n is a positive integer, which of the following is a possible value of |71 - 5n| ?
Options:
A)7
B)5
C)19
D)15
E)20
Rationale: When 71>5n, then |71- 5n| = 71- 5n = (70-5n) + 1 = {multiple of 5} + 1
When 71<=5n, then |71 - 5n| = -(71- 5n) = (5n-70) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.
Answer: C
Answer: C
Question: SI on a certain sum of money for 3 yrs at 8 percent /annum is 1/2 the CI on Rs.4000 for 2 yrs at 10 percent/ annum. The sum placed on SI is?
Options:
A)Rs. 1600
B)Rs. 1650
C)Rs. 1750
D)Rs. 1800
E)Rs. 1900
Rationale: C.I.
= Rs. 4000 x 1 +	10 2	- 4000
100
= Rs. 4000 x	11	x	11	- 4000
10	10
= Rs. 840.
Sum = Rs. 420 x 100 = Rs. 1750.
3 x 8
C
Answer: C
Question: The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals?
Options:
A)1/40
B)8/75
C)75/4
D)2/15
E)75/6
Rationale: (1/a)+(1/b)=(a+b)/ab=40/300=2/15
ANSWER:D
Answer: D
Question: The length of a rectangle is four times its width. If the area is 100 m2 what is the length of the rectangle?
Options:
A)50 m
B)40 m
C)80 m
D)20 m
E)70 m
Rationale: Let L be the length and W be the width of the rectangle. Hence
L = 4 W
We now use the area to write
100 = L ? W
Substitute L by 4 W in the equation above
100 = 4 W ? W = 4 W2
Solve for W and find L
4 W2 = 100
W2 = 25 , W = 5 and L = 4 W = 20 m
correct answer D
Answer: D
Question: There are 15 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl or 2 boys are selected ?
Options:
A)100
B)105
C)115
D)120
E)125
Rationale: n(s) = sample space = 25C3 = 2300
E = event that 1 girl and 2 boys are selected
n(E) = we have to select 2 boys from 15 or 1 girl from 10
= 15C2 + 10C1
= 115
Ans - C
Answer: C
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Options:
A)30000
B)66000
C)53000
D)20000
E)45000
Rationale: D
20000
Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: D
Question: In a plastic company, 14 men working 8 hrs per day complete a piece of work in 12 days. To complete the same work in 6 days, working 14 hours a day, the number of men required is :
Options:
A)16
B)8
C)12
D)20
E)22
Rationale: Explanation :
Solution: Let the required number of men be x.
Less days, more men (Indirect proportion)
more working hrs per day, less men (Indirect proportion)
days 6 : 12
} : : 14 :x
working hrs 14 : 8
.'. 6*14*x = 12*8*14 \
=> x =16.
Answer : A
Answer: A
Question: Five friends, Peter, Eric, Melyssa, Tony, and Carl, are pooling their money to buy a $1300 item. Peter has twice as much money as Melyssa. Tony has $60 more than Peter. Carl has 20% more than Tony and Eric has twice as much as Peter. If they put all their money together and spend the $1300, they will have $38 left. How much money does Peter have?
Options:
A)$300
B)$270
C)$320
D)$350
E)$220
Rationale: P= 2M ; T= P+60 ; C= 1.2(T); P=(E/2)
P+M+T+C+E-1300=38
P+0.5P+P+60+1.2(P+20)+2P = 1338
P+0.5P+P+60+1.2P+24+2P = 1338
P+0.5P+P+1.2P+2P+84 = 1338
P+0.5P+P+1.2P+2P = 1254
5.7P = 1254
P=220
Answer:E
Answer: E
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 30% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
Options:
A)$16,830
B)$17,820
C)$18,000
D)$19,800
E)$21,780
Rationale: 10000 seats --> Full Price : Half Price = 7000 : 3000
Price when all seats are filled = 14000 + 3000 = 17000
100 seats are unsold --> Loss due to unfilled seats = 30 + 2*70 = 170
Revenue = 17000 - 170 = 16830
Answer: A
Answer: A