divelab/Sys2Bench huggingface dataset:
Question: Eight children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
Options:
A)600
B)720
C)1440
D)4320
E)4800
Rationale: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 1440.
B is the right answer.
C
Answer: C
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
Options:
A)650
B)656
C)696
D)724
E)756
Rationale: From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
Hence we have the following 3 options.
We can select 5 men ...(option 1)
Number of ways to do this = 7C5
We can select 4 men and 1 woman ...(option 2)
Number of ways to do this = 7C4 × 6C1
We can select 3 men and 2 women ...(option 3)
Number of ways to do this = 7C3 × 6C2
Total number of ways
= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
=
7
×
6
2
×
1
+
7
×
6
×
5
3
×
2
×
1
×
6
=7×62×1+7×6×53×2×1×6
+
7
×
6
×
5
3
×
2
×
1
×
6
×
5
2
×
1
+7×6×53×2×1×6×52×1
=
21
+
210
+
525
=
756
=21+210+525=756
E)
Answer: E
Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)3
B)4
C)5
D)8
E)9
Rationale: Speed in still water = (11 + 5)/2 kmph = 8 kmph.
answer :D
Answer: D
Question: A tank contains 7,500 gallons of a solution that is 6 percent sodium chloride by volume. If 2,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A) 5.18%
B) 6.18%
C) 7.18%
D) 8.18%
E) .7%
Rationale: We start with 7,500 gallons of a solution that is 6% sodium chloride by volume. This means that there are 0.06 x 7,500 = 450 gallons of sodium chloride.
When 2,000 gallons of water evaporate we are left with 5,500 gallons of solution. From here we can determine what percent of the 5,500 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(450/5,500) x 100 = ?
0.081 x 100 = ?
= 8.18%
Answer is D.
Answer: D
Question: If 20 men can build a water fountain 56 metres long in 7 days, what length of a similar water fountain can be built by 35 men in 3 days?
Options:
A)40 m
B)42 m
C)47 m
D)49 m
E)50 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 7: 3 : : 56 : x
Therefore (20 x 7 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/140=42
Hence, the required length is 42 m.
Answer : B
Answer: B
Question: Everyone shakes hands with everyone else in a room. Total number of handshakes is 78. Number of persons=?
Options:
A)13
B)12
C)11
D)15
E)16
Rationale: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2
So n(n-1)/2 = 78 OR n(n-1)=156 OR n=13
Answer is (A)
Answer: A
Question: A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number R of tickets sold by the male members of the association
Options:
A)50
B)56
C)58
D)62
E)66
Rationale: Given that, Total average R sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.
(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C.
Answer: C
Question: In the new budget the price of rise rose by 5%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
Options:
A)7.5%
B)9.1%
C)4.76%
D)12.6%
E)15%
Rationale: Reduce in consumption = R/(100+R) *100% = 5/105 *100 =4.76%
Answer is C
Answer: C
Question: A wholeseller cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 30% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 20% 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)78%
B)56%
C)99.33%
D)14.109%
E)79%
Rationale: Anyways, one can infer that he 'steals' 30% from suppliers and then charges 20% extra to customers
So basically 1.3 * 1.2 = 1.56
Given that 1 is start point, we get 21% more
Hence answer is B
Answer: B
Question: how many seconds are there in a year ?
Options:
A)31536000
B)21536000
C)11536000
D)None
E)cannot be determined
Rationale: Solution:
== Mathematical Answer ==
Mathematical Answer = number of seconds in a minute * number of minute in an hour * number hour in a day * number of day in year
60 * 60 * 24 * 365 = 31536000
Answer A
Answer: A
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Options:
A)1
B)2
C)4
D)5
E)6
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: A
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Options:
A)Rs.1000
B)Rs.600
C)Rs.800
D)Rs.400
E)Rs.700
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
ANSWER:D
Answer: D
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
Options:
A)0.65
B)3.3
C)0.3
D)0.4
E)0.6
Rationale: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350
R1 - R2 = 0.3%.Answer: C
Answer: C
Question: When a number is added to another number the total becomes 33 1⁄3 per cent of the second number. What is the ratio between the first and the second number?
Options:
A)3 : 7
B)7 : 4
C)7 : 3
D)Data inadequate
E)None of these
Rationale: Let the first and second numbers be x and y respectively.
Then, x + y = 10⁄3y
or, x = 7⁄3y
∴ x : y = 7 : 3
Answer C
Answer: C
Question: The area of playground is 5900 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
Options:
A)a) $144
B)b) $150.50
C)c) $165
D)d) $158.60
E)e) $160.70
Rationale: total volume * unit cost = total cost
or, 5900 * 0.01 * 2.8 = total cost = 165=C
Answer: C
Question: A crate of apples contains 1 bruised apple for every 30 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
Options:
A)270
B)360
C)480
D)600
E)840
Rationale: as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.75x=12
x=1200/75=16
thus total number of bruised apples =16
total number of apples =30*16=480
ANSWER:C
Answer: C
Question: A businessman wants to label folders with numbers using digit stickers only. If the businessman uses 1,335 stickers, how many folders have been numbered? (The numbers of the folders are consecutive and the number of the first folder is 1).
Options:
A)392
B)395
C)398
D)481
E)484
Rationale: For the first 9 folders we need 9 stickers.
For the next 90 we need 2 stickers each or 180 stickers.
For the next 900 folders we need 3 stickers each.
The first 99 folders correspond to 189 stickers.
Subtract 189 from the total number of stickers (1,335).
This leaves 1,146 stickers for folders that use 3 stickers each. So, divide 1,146 by 3 to get 382 folders.
Add 99 folders to 382 folders to get the total number of folders, 481.
Answer: D
Answer: D
Question: The length of a rectangle i s two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)149
C)148
D)17
E)143
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: A
Question: David paid $5,000 for 100 shares of stock X and $3,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/6 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
Options:
A)A loss 3 times as much
B)A loss 2 times as much
C)A Gain of 1.67 times as much.
D)A loss 1.5 times as much
E)A Gain of 2 times as much.
Rationale: A = 5000; B = 3000; Profit = (3/6)*3000 = 1500
After prices are reversed:
A = 3000; B =5000; Profit = (3/6)*5000 =2500
2500 --> Gain of 1.67 times 1500
Answer: C
Answer: C
Question: Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 265 barrels of oil?
Options:
A)2
B)3
C)4
D)5
E)180
Rationale: Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 265 barrels they will take a bit less than 265 mins which will be more than 4 hrs but less than 5 hrs.
Answer (D)
Answer: D
Question: The cost price of a particular amount of articles is same as the number of articles. Selling price of the articles comes out to be 20. Over the whole transaction 25% is gained. What is X?
Options:
A)16
B)77
C)15
D)18
E)161
Rationale: Explanation:
According to the question let n be the number of articles.
=> Cost price of n articles = n
=> Selling price of n articles = 20
=> Profit % = 25%
=> Profit % = (SP - CP)/CP X 100
Putting the values in the formula
(20-n)/n x 100 = 25
=> 5n/4 = 20
=> n = 16
ANSWER: A
Answer: A
Question: In a certain town, there are five times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
Options:
A)1 to 4
B)1 to 3
C)1 to 2
D)3 to 4
E)5 to 6
Rationale: Town state: 5 times the whole town or country
then ratio will be 5(times)/6 total(times)
So the answer is 5/6.
E
Answer: E
Question: A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 3 and 5 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
Options:
A)Per month, with savings of $(2a + 2b)
B)Per month, with savings of $(2a - 2b)
C)The two options would cost an equal amount.
D)Per project, with savings of $(2a + 2b)
E)Per project, with savings of $(2a - 2b)
Rationale: Per Project, company will pay as follows:
For 3 hours work = a+2b
For 5 hours work = a+4b
Total = 2a+6b
Per Month, company will pay for 8 hours work = a+5b
Total per contract - total per month
3a+5b - (a+7b)
2a-2b
Since a>b Amount 3a+5b(per contract amount) > a+7b (per project amount) by 2a-2b.
Hence per month payment will be cheaper by 2a-2b .
OA B
Answer: B
Question: 3x<2y<0 which of the following is the greatest?
Options:
A)2x+3y
B)-(3x+y)
C)2x-y
D)x+y
E)0
Rationale: Plugging in -1 for both x and y we get
A. 2x+3y =-5
B. -(3x+y) =4
C. 2x-y =1
D. x+y =-2
E. 0 =0
Answer: B
Answer: B
Question: In the parking lot there are 44 vehicles, 24 of them are buses, and the rest are cars. The color of 24 vehicles is red, of which 18 are buses. How many cars can be found in the parking lot which are not colored red?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: The number of cars is 44-24 = 20.
The number of red cars is 24-18=6.
The number of cars which are not red is 20-6=14.
The answer is D.
Answer: D
Question: If a certain sample of data has a mean of 23.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)15.0
D)23.5
E)26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 23-7.5=15.5or more than 23+7.5=30.5.
Answer: C.
Answer: C
Question: Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: 134-132=2
46-44=2
x-12=2
x=14
ANSWER:A
Answer: A
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
Options:
A)18
B)20
C)25
D)28
E)31
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Answer: B
Question: A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
Options:
A)153mph
B)253mph
C)353mph
D)453mph
E)553mph
Rationale: The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
correct answer B)253mph
Answer: B
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many year younger than A
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Explanation:
Given that A+B = 13 + B + C
=> A ? C = 13 + B ? B = 13
=> C is younger than A by 13 years
Answer: Option C
Answer: C
Question: If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
6 = 36
7 = 42
Then 42 = ?
Hint: Its a logic Riddle not a mathematical riddle
Options:
A)7
B)2
C)3
D)4
E)5
Rationale: A
1
As stated
7=42 => 42=7
Answer is A
Answer: A
Question: what is the angle between the hands of a clock when time is 8:40?
Options:
A)65deg
B)75deg
C)45deg
D)15deg
E)100deg
Rationale: Angle between two hands =
40h - 11/2 m = 40*8 - 40*11/2 = 320 - 220 = 100deg
ANSWER:E
Answer: E
Question: 32,0.2,160,15,0.5,30,28,0.7,?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: (32,0.2,160),(15,0.5,30),(28,0.7,?)
32 / 0.2 = 160,
15 / 0.5 = 30
28 / 0.7 = 40
ANSWER:B
Answer: B
Question: If 3^k is a divisor of the product of all even integers between 2 and 30 (inclusive), what is the maximum value of k?
Options:
A)4
B)6
C)10
D)13
E)14
Rationale: since the Q tells us 3k3k is a divisor of the product of all even integers between 2 and 30 (inclusive)
the Q basically asks us power of 3 in the product..
lets see the even multiples of 3 from 2 to 30..
6*12*18*24*30..
3^5(2*4*6*8*10)..
or 3^6*2*4*2*8*10..
ans 6
ANSWER:B
Answer: B
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 8, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 15?
Options:
A)1
B)2
C)5
D)19
E)20
Rationale: When positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1
values of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}
Similarly,
When n is divided by 8, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 13, 21, 29, 37, 45, 53, 61........}
combining both the sets we get
n={13, 37, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 15 or 15x
in case of n=13 p=2
so for min value of p, we take min value of n.
B is the answer.
Answer: B
Question: In a certain country, 60 percent of the population likes basketball, and 33 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
Options:
A)20%
B)33%
C)40%
D)55%
E)67%
Rationale: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 33 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 33/60 = 55%, or choice D.
Answer: D
Question: At Pat's Pet Shop, 25 cups of bird seed are used every 5 days to feed 20 parakeets. How many cups of bird seed would be required to feed 15 parakeets for 7 days?
Options:
A)35.25
B)15
C)64
D)104
E)26 1/4
Rationale: Let's go step-by-step.
25 cups are used over a 5 day period, which means 5 cups a day. This feeds 20 parakeets, which means each parakeet needs 1/4 of a cup every day.
For 15 parakeets, we need 15*1/4 cups = 3 3/4 cups a day. Over 7 days, we need 26 1/4 cups. Choice E.
Answer: E
Question: What is the greatest possible common divisor of two different positive integers which are less than 144?
Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?
Options:
A)143
B)142
C)72
D)71
E)12
Rationale: First of all, what is the greatest common divisor of 143 and 142? It is 1. You are looking for the common divisor. 142 and 143 will have no common divisor except 1.
Think:
2 and 3 have GCD (greatest common divisor) of 1
2 and 4 have GCD of 2.
3 and 4 have GCD (greatest common divisor) of 1
So if you were to select 2 numbers less than 5 with the greatest GCD, you need to select 2 and 4, not 3 and 4.
Now think: 143 = 11 * 13
The greatest possible divisor it will have with another number less than 144 will be either 11 or 13. Let's move on.
142 = 2*71
The greatest possible divisor it can have with another number less than 144 can be 71 (say, if the other selected integer is 71)
Do you think another number less than 144 could have a GCD of greater than 71? No because when you split a number into two factors, one of them will be at least 2. If it is greater than 2, the other factor will obviously be less than 71.
Answer: D
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
Options:
A)3/7
B)1/4
C)1/5
D)1/7
E)2/5
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
A
Answer: A
Question: The present worth of a certain sum due sometimes hence is Rs.1600 and the true discount is Rs.160.The banker's gain is
Options:
A)Rs.16
B)Rs.24
C)Rs.20
D)Rs.12
E)None
Rationale: Solution
B.G
Given,T.D = 160, P.w= 1600	= (T.D)² / P.W
= Rs(160 x 160 / 1600)
= Rs.16.
Answer A
Answer: A
Question: The length of a rectangular field is 7/5 its width. If the perimeter of the field is 288 meters, what is the width of the field?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 288, 2(7/5)W + 2W = 288
Solve the above equation to find: W = 60 m and L = 84 m.
correct answer B)60
Answer: B
Question: A clock shows the time as 11 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
Options:
A)45 minutes
B)55 minutes
C)35 minutes
D)25 minutes
E)40 minutes
Rationale: there are 7 hours in between 11 a.m. to 6 p.m.
7*5=35 minutes.
ANSWER:C
Answer: C
Question: In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.08 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?
Options:
A)1-0.06^10
B)1-0.92^10
C)(1-0.94)^10
D)0.06
E)1-10*0.06
Rationale: ans B.
Prob that light will not turned off = 0.92^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: B
Question: |x+3| – |4-x| = |8+x| How many X solutions will this equation have?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: X=|x| = x when x >= 0 (x is either positive or 0)
|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,
|0| = 0 = -0 (all are the same)
So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.A
Answer: A
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 10 days starting with sunday is
Options:
A)280
B)285
C)290
D)855
E)275
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/10)=(8550/10)=855
Answer: Option D
Answer: D
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)0
B)1
C)10
D)19
E)2
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
ANSWER:D
Answer: D
Question: Set R has a mean of 14 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){13,15}
B){18,19}
C){11,19}
D){15,19}
E){14,25}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 14,the values (13,15) are closer than others.
Hence Answer : A
Answer: A
Question: 90, 180, 12, 50, 100, 200, ?, 2, 50, 4, 25, 2, 6, 30, 3
Options:
A)130
B)150
C)180
D)100
E)220
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
50*4=200
2*50=100 ans is 100
ANSWER:D
Answer: D
Question: Tom planted vegetables in a rectangular garden that was 23 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
Options:
A)155 sq. ft.
B)156 sq. ft.
C)161 sq. ft.
D)168 sq. ft.
E)179 sq. ft.
Rationale: area of garden is 23 x 15 = 345 sq. ft.
1/3 x 345 = 115 sq. ft. for corn
1/5 x 345 = 69 sq. ft. for peas
115 + 69 = 184 sq. ft. used
345 - 184 = 161 sq. ft. left over
correct answer C
Answer: C
Question: What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)?
Options:
A)less than -100,000
B)-2500
C)0
D)2500
E)more than 100,000
Rationale: One of the terms is (50-50) so the product is 0.
The answer is C.
Answer: C
Question: The factorial expression 9!/2! is not divisible by which of the following integers?
Options:
A)3
B)5
C)6
D)7
E)None of these
Rationale: 9!/2! => 9 x 8 x7 x 6 x 5 x 4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 5
(C) 6 Can divide 12
(D) 7 can divide 7,21,28
Hence answer will be (E)
Answer: E
Question: When a natural number N is successively divided by 1,2,3,4 the remainders are 5,6,7,8. What will be the sum of the remainders if the order of the division is reversed?
Options:
A)11
B)12
C)10
D)2
E)7
Rationale: 1 2 3 4
5 6 7 8
leave the top right- most number 8
start with bottom right-most number 5
8*3+7=31
31*2+6=68
68*1+5=73
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 10
Hence, the correct option is C
Answer: C