divelab/Sys2Bench huggingface dataset:
Question: How many different 4 letter combinations can be created from the letters M,N,O, and P?
Options:
A)4
B)16
C)32
D)96
E)256
Rationale: This is a case of number of arrangements possible with repetition.
Thus you have 4 options each for the 1st,2nd,3rd and 4th letter giving you a total of 4*4*4*4 = 256 number of possible combinations.
Answer : E
Answer: E
Question: If an integer n is to be chosen at random from the integers 1 to 86, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)55/86
E)3/4
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 86, there are 43 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (43 + 12)/96
=55/86
Ans isD
Answer: D
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 130 kilometers?
Options:
A)8.5 gallons
B)7.5 gallons
C)6.5 gallons
D)5.5 gallons
E)4.5 gallons
Rationale: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 130 kilometers?
130 / 20 = 6.5 * 1 gallon = 6.5 gallons correct answer C
Answer: C
Question: When the positive integer j is divided by 9, the remainder is 5. What is the remainder when 3j is divided by 9?
Options:
A)0
B)1
C)3
D)4
E)6
Rationale: Lets take the number as j
when j is divided by 9 the remainder is 5 hence j can be written as
j=9k +5
Multiplying by 3 will give
3j = 27k + 15
we can also write
3j = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: E
Question: Out of 250 students of a college, 160 play football, 90 play cricket and 50 neither play football nor cricket. How many students play both football and cricket?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Explanation :
Solution: n(A) = 160, n(B) = 90, n(A U B) = 250-50 = 200.
Required number => n(A ^ B) = n(A) +n(B) - n(A U B) = 160+90-200 = 250-200 = 50.
Answer : C
Answer: C
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
Options:
A)67%
B)45%
C)25%
D)70%
E)50%
Rationale: C
C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Question: Frederick invested Rs.14000 in a business which he jointly owns with two other persons (James and Greg). If his share of a profit of Rs.1500 is Rs.600 and Greg's share is Rs.300, what is James' capital?
Options:
A)15500
B)12500
C)1270
D)12505
E)12540
Rationale: 600 + 300 = 900
1400 - 900 = 500
600 ---- 15000
500 ---- ? => 12500
ANSWER:B
Answer: B
Question: The probability that A speaks truth is 2/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)17/35
B)18/37
C)18/39
D)18/33
E)18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 2/5 * 4/7 + 3/5 * 3/7
= 17/35
Answer:A
Answer: A
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
Options:
A)20
B)98
C)37
D)26
E)17
Rationale: Explanation:
Let the numbers be a, b and C. Then,
a2 + b2 + c2 = 138 and (ab + bc + ca) = 131
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
138 + 2 * 131 = 400
(a + b + c) = âˆš400 = 20
Answer:A
Answer: A
Question: Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 4 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)2
B)5
C)6
D)4
E)1
Rationale: Let the leak can empty the full tank in x hours 1/2 - 1/x = 1/4
=> 1/x = 1/2 - 1/4 = 1/4
=> x = 4. Answer:D
Answer: D
Question: Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 15% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?
Options:
A)Six hours and 30 minutes.
B)Seven hours and 30 minutes.
C)Eight hours and 20 minutes.
D)Nine hours and 15 minutes.
E)Ten hours and 20 minutes.
Rationale: Speed of second train= 50*85/100= 42.5
Time= toral distance /total speed
705/ (50+42.5)= 705/92.5= 7.___
B is the answer
Answer: B
Question: If (A+B) = 4, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
Options:
A)16.
B)8.
C)7
D)2.
E)-2
Rationale: Given A+B = 4 => A = 4 - B --> Eq 1
B+C = 9
C+D = 3 => D = 3 - C --> Eq 2
Then Eqs 1 + 2 => A + D = 4 - B + 3 - C
=> 7 - (B+C)
=> 7 - 9 = -2.
Option E...
Answer: E
Question: An eccentric casino owner decides that his casino should only use chips in $3 and $7 denominations. Which of the following amount cannot be paid out using these chips?
Options:
A)$27
B)$24
C)$23
D)$25
E)$21
Rationale: Yes, the number of 3 or/and 7 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but D can be represented as the sum of a multiple of 3 and a multiple of 7:
A. $27 = 7*3 + 3*2
B. $23 = 7*2 + 3*3
C. $24 = 7*3 + 3*1
E. $21 = 7*3
Answer: D.
Answer: D
Question: If 5^27 * 4^14 = 2 * 10^n, what is the value of n?
Options:
A)11
B)21
C)22
D)23
E)27
Rationale: My attempt:
5^(27) * 4^(14) = 2*10^p
5^(27) * 2 ^ (28) = 2 * (2*5)^p
5^(27) * 2 ^ (28) = 2 * 2^(p) * 5^(p)
5^(27) * 2 ^ (28) = 2^(p+1) * 5^(p)
=> (p+1) = 28
=> p = 27
Answer: 27 (E)
Answer: E
Question: If y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer, then y must be
Options:
A)21
B)10
C)61
D)72
E)14
Rationale: 31360= 8*8*7*7*5*2, so we need one 5 and one 2 to make it a square of a number. so 5*2= 10
Ans: B
Answer: B
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 34 minutes, then the slower pipe alone will be able to fill the tank in
Options:
A)144 mins
B)140 mins
C)136 mins
D)132 minw
E)None of these
Rationale: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/34
=>4/x=1/34
x=34∗4=136mins
Option C
Answer: C
Question: The average height of 35 boys in a class was calculated as 181cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
Options:
A)178.27 cm
B)179.29 cm
C)978.29 cm
D)178.89 cm
E)176.29 cm
Rationale: Calculated average height of 35 boys = 181 cm.
Wrong total height of 35 boys = 181 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 181 cm - (166 cm - 106 cm)/35
= 181 cm - 60 /35 cm
= 181 cm - 1.71 cm = 179.29 cm.
Answer: B
Answer: B
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 7'o clock.
Options:
A)36sec
B)62sec
C)66sec
D)64sec
E)76sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
So, 36sec at 7'o clock.
ANSWER:A
Answer: A
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)8
B)18
C)15
D)20
E)25
Rationale: 1500 ---- 270
100 ---- ? => 18%
ANSWER B
Answer: B
Question: If x -5 > -3 and x - 3 < 4, the value of x must be between which of the following pairs of numbers?
Options:
A) -3 and 10
B) -3 and 4
C) 2 and 7
D) 3 and 4
E) 3 and 10
Rationale: Let’s isolate x in each inequality.
x - 5 >-3
x > 2
Next we simplify x – 3 < 4.
x – 3 < 4
x < 7
We know that x is greater than 2 and less than 7.
The answer is C.
Answer: C
Question: In X game of billiards, X can give Y 20 points in 45 and he can give Z 30 points in 45. How many points can Y give Z in X game of 100?
Options:
A)30
B)20
C)25
D)40
E)50
Rationale: X scores 45 while Y score 40 and Z scores 30.
The number of points that Z scores when Y scores 100 = (100 * 30)/25 = 60.
In X game of 100 points, Y gives (100 - 60) = 40 points to C.
D
Answer: D
Question: A tap can fill a tank in 10 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)5hr 45min
B)6hr 30min
C)4hr
D)3hr 25min
E)2hr 10min
Rationale: Time taken by one tap to fill the half tank = 5 hr
part filled by the 4 taps in 1hour = 4*1/6 = 2/3
Remaining part = 1-1/2 = 1/2
2/3:1/2::1:x
x = 3/4hr = 45min
Total time taken = 5hr 45min
Answer is A
Answer: A
Question: How many different number-plates for cars can be made if each number-plate contains four of the digits 0 to 9 followed by a letter A to Z, assuming that repetition of digits is allowed?
Options:
A)2.6 * 10^4
B)2.6 * 10^5
C)26 * 10^5
D)26 * 10^4
E)30 * 10^4
Rationale: With repetition, we have simply:
(number of digits from 0000 to 9999)times×26 = 10 * 10 * 10 * 10 * 26
= 10^4 * 26
= 2.6 * 10^5
Ans- B
Answer: B
Question: If 216 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
Options:
A)36
B)14
C)20
D)18
E)22
Rationale: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (216 *4/24) = 36
ANSWER:A
Answer: A
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Options:
A)17 kmph
B)50 kmph
C)11 kmph
D)19 kmph
E)16 kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120
= 12x/120 = x/10 Average speed
= (2x + 3x)/(x/10)
= 50 kmph.
Answer: B
Answer: B
Question: Adidas company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options:
A) 16
B) 64
C) 256
D) 576
E) 4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
Adidas company has four empty trucks that will head out in the morning, all four to the same destination. Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: C
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 130 mangoes.
Options:
A)360
B)380
C)400
D)406
E)433
Rationale: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 130 mangoes = 130*3.33 = 433.
Answer E
Answer: E
Question: A committee of three people is to be chosen from four teacher-student pairs. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)24
C)26
D)30
E)32
Rationale: Each pair can send only one representative to the committee. Let's see in how many ways we can choose 3 pairs (as there should be 3 members) out of 4 to send only one representatives to the committee: 4C3=4.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: E.
Answer: E
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)09 2/3
B)10 2/3
C)11 2/3
D)12 2/3
E)16 2/3
Rationale: B
10 2/3
2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer: B
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?
Options:
A)236
B)127.5
C)267
D)268
E)281
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
Question: Joe invested a certain sum of money in a simple interest bond whose value grew to $460 at the end of 3 years and to $560 at the end of another 5 years. What was the rate of interest in which he invested his sum?
Options:
A)3%
B)4%
C)5%
D)6%
E)7%
Rationale: In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $460 - $60 = 400.
The interest rate is $20/$400 = 5%
The answer is C.
Answer: C
Question: 3(1/2) + 5(1/5) + ? + 2(1/4) = 11(1/3)
Options:
A)11/60
B)13/60
C)23/60
D)29/60
E)None of these
Rationale: Explanation:
3(1/2) + 5(1/5) + ? + 2(1/4) = 11(1/3)
=> ? = 11(1/3) - [3(1/2) + 5(1/5) + 2(1/4)]
= 34/3 - [7/2 + 26/5 + 9/4]
= 34/3 - 219/20 = 23/60
Answer: Option C
Answer: C
Question: A number x is 11 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)90.9
C)91.7
D)11%
E)1%
Rationale: Say y=1 and x=11.
Then y=1 is less than x=11 by (11-1)/11*100=10/11*100=90.9%.
Answer: B.
Answer: B
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/3
B)1/8
C)1/4
D)1/1
E)1/2
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: A
Question: In the coordinate plane, a circle centered on point (-3, -4) passes through point (-1, 1). What is the area of the circle?
Options:
A)9π
B)18π
C)29π
D)37π
E)41π
Rationale: r^2=(-3+1)^2+(-4-1)^2=4+25=29
Area of circle=πr^2=29π
Answer : C
Answer: C
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)17%
C)15%
D)11%
E)12%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: A
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
Options:
A)20:15:16
B)20:15:15
C)20:15:12
D)20:15:14
E)20:15:11
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: C
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Options:
A)50 kmph
B)60 kmph
C)40 kmph
D)70 kmph
E)80 kmph
Rationale: A
Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer: A
Question: There is a circle of radius 2. What is the perimeter of the biggest rectangle that can be cut out of this circle?
Options:
A)4âˆš8
B)4âˆš5
C)2âˆš6
D)16
E)5
Rationale: The largest rectangle to be cut out of a circle would be a square, with a diagonal of 4 (Radius*2 2*2=4)
Using the Pythagorean theorem a^2+b^2=c^2; in a square this is 2a^2 because this is a right triangle/half of a square, so 2a^2=4^2
2a^2=16
a^2=8
a=âˆš8
Area of a square = side * 4 so perimeter= 4âˆš8
Answer is A
Answer: A
Question: Yearly subscription to professional magazines cost a company $940.00. To Make a 20% cut in the magazine budget, how much less must be spent?
Options:
A)654
B)752
C)656
D)657
E)658
Rationale: total cost 940
940*20/100=188
so the cut in amount is 188
the less amount to be spend is 940-188=752
ANSWER:B
Answer: B
Question: 24 * 22 = ? / 8
Options:
A)4224
B)2224
C)5374
D)2434
E)4254
Rationale: A
4224
?/8 = 24*22
? = 24 * 22 * 8
? = 4224
Answer: A
Question: The speed of a boat in still water in 30 km/hr and the rate of current is 7 km/hr. The distance travelled downstream in 36 minutes is:
Options:
A)18.4 km
B)20.6 km
C)21.4 km
D)1111 km
E)22.2 km
Rationale: Explanation:
Speed downstream = (30 + 7) = 37 kmph
Time = 36 minutes = 36/60 hour = 3/5 hour
Distance travelled = Time × speed = (3/5)×37 = 22.2 km
Answer: Option E
Answer: E
Question: The speed of a train is 90 kmph. What is the distance covered by it in 15 minutes?
Options:
A)15
B)66
C)22.5
D)52
E)42
Rationale: 90 * 15/60 = 22.5 kmph
Answer:C
Answer: C
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.08. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fourth day it is overdue?
Options:
A)$0.62
B)$0.70
C)$0.80
D)$0.90
E)$1.00
Rationale: 1st day fine - 0.08
2nd day fine - 0.08*2 = 0.16 (as doubling gives lower value)
3rd day fine - 0.16*2 = 0.32 (as doubling gives lower value)
4th day fine - 0.32 + 0.3 = 0.62 (as doubling gives higher value we add 0.3 this time)
Answer: A.
Answer: A
Question: A sock drawer contains 4 socks, each one a different solid color. The colors of the socks are green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
Options:
A)12
B)15
C)6
D)36
E)42
Rationale: Since the order in which we select the socks does not matter we can use combinations.
We can select 2 socks from 4 socks in 4C2 ways.
4C2 = 6
Answer : C
Answer: C
Question: The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 9:7. The marks obtained by Polly and Willy are in the ratio of...?
Options:
A)9:8
B)11:10
C)13:12
D)15:14
E)17:16
Rationale: Polly : Sandy = 5:6 = 15:18
Sandy : Willy = 9:7 = 18:14
Polly : Sandy : Willy = 15:18:14
Polly : Willy = 15:14
The answer is D.
Answer: D
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)5
B)8
C)9
D)5
E)1
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold W was 25,200, how many of them were sold at full price?
Options:
A)21,000
B)19,800
C)16,500
D)15,800
E)8,700
Rationale: Given:
The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.
Approach:
The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.
Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.
Working Out:
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
Substituting values in the equation, we get
5,400 + 5x + x = 25,200
x= 3,300
Tickets sold at full price = 5x = 16,500
Answer: Option C
Answer: C
Question: In how many ways can 3 postcards can be posted in 5 postcards?
Options:
A)50
B)120
C)125
D)130
E)100
Rationale: First card can go into any of the five boxes, Second can go into any of the five boxes.
Third card also can go into any of the five boxes
Number of ways=5*5*5=125 ways
Answer:C
Answer: C
Question: If a/b = 1/7, b/c = 3, c/d = 2/3, d/e = 2 and e/f = 1/2, then what is the value of abc/def ?
Options:
A) 72/21
B) 27/85
C) 34/47
D) 13/81
E) 16/21
Rationale: Say a = 1. Then:
a/b = 1/7 --> b = 7;
b/c = 3 --> c = 7/3;
c/d = 2/3 --> d = 7/2;
d/e = 2 --> e = 7/4;
e/f = 1/2 --> f = 7/2.
abc/def = (1*7*7/3)/(7/2*7/4*7/2) = 16/21.
Answer: E.
Answer: E
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 12 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 4 days?
Options:
A)3
B)5
C)6
D)9
E)12
Rationale: Explanation: If six computers require 12 days to process the data, thats
a total of 72 computer-days the product of 6 and 12. If you change the number
of computers or the number of days, 90 will have to remain the product, whether
that means 72 days of one computer or one day with 72 computers.
In 4 days, the number of computers is:
4c = 72
c = 18
18 computers is 12 more than the 6 that it took to do the job in 12 days, so
the correct choice is (E).
Answer: E
Question: Find a sum for 1st 5 prime no.'s?
Options:
A)23
B)28
C)30
D)32
E)34
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)3944
B)2882
C)2999
D)2667
E)2121
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer: A
Answer: A
Question: If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?
Options:
A)105
B)109
C)119
D)218
E)288
Rationale: Solution:
Since 95 bags contain wheat 9975 kg
Therefore, 1 bag contains wheat (9975 ÷ 95) kg
= 105 kg
ANSWER IS A
Answer: A
Question: An assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
Options:
A)40
B)44
C)48
D)52
E)56
Rationale: The time to produce the first 60 cogs is 60/30 = 2 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / 3 hours = 40 cogs per hour.
The answer is A.
Answer: A
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 44 years, was replaced by a new person. Find the age of the new person?
Options:
A)18
B)56
C)12
D)17
E)14
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 44 + Q
=> Q = 14
Answer:E
Answer: E