divelab/Sys2Bench huggingface dataset:
Question: It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options:
A)16^2+1
B)12
C)(2^96+1)
D)24
E)4^4+6
Rationale: Explanation:
Let 2^32 = x. Then, (2^32 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(2^32)3 + 1] = (x^3 + 1) = (x + 1)(x^2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
C
Answer: C
Question: Evaluate: 50 - 12÷4×2 =
Options:
A)44
B)54
C)16
D)27
E)30
Rationale: According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right
12÷4×2 = 3 × 2 = 6
Hence
50 - 12÷4×2 = 50 - 6 = 44
correct answer A)44
Answer: A
Question: I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price?
Options:
A)$2000
B)$2500
C)$2400
D)$3120
E)$1540
Rationale: 115% of cost - 110% of cost = $120
5% of cost = $120
cost = 120*100/5 = $2400
Answer is C
Answer: C
Question: In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together?
Options:
A)6!/2!
B)3!*3!
C)4!/2!
D)4! *(3!/2!)
E)3!*3!/2
Rationale: In the word ABROAD , there are 3 vowels - 2 A's and O
Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: D
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 690, what is the least possible value of n?
Options:
A)10
B)11
C)12
D)13
E)23
Rationale: 690 = 2 * 3 * 5 * 23
so the least value forNcan be 23.
E
Answer: E
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Options:
A)15000
B)15002
C)15029
D)15329
E)15012
Rationale: Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A
Answer: A
Question: In how many ways letters of the word RSCUPERATE be arranged?
Options:
A)357898
B)654326
C)865453
D)545778
E)302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: E
Question: A cistern is filled by pipe A in 10 hours and the full cistern can be leaked out by an exhaust pipe B in 15 hours. If both the pipes are opened, in what time the cistern is full?
Options:
A)50hrs
B)30hrs
C)70hrs
D)80hrs
E)90hrs
Rationale: time taken to full the cistern=(1/10-1/15)hrs
=1/30
=30hrs
ANSWER:B
Answer: B
Question: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x
II. y/7 is an integer
III. The cube root of x is an integer
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: Given 91*x=8*y
It can be equal when x = 8 or -8
and y = 91 or -91
So Statement (I) y < x if we take x = -8 and y =-91
but y > x if we take x = 8 and y = -91, so (I) is not true always
Statement (2) in any case
91/7 or -91/7 is an integer that is 13 or -13. So it is true
Statement (3) cube root of 8 or -8 is 2 and -2 respectively. So it is true always.
answer is E
Answer: E
Question: The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?
Options:
A)432
B)376
C)299
D)276
E)396
Rationale: 2(3x + x) = 88
l = 36 b = 11
lb = 36 * 11
= 396
E
Answer: E
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
Options:
A)25 days
B)24 days
C)22 days
D)27 days
E)21 days
Rationale: B
24 days
B = 1/8 – 1/2 = 1/24 => 24 days
Answer: B
Question: A man invests Rs. 8,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Options:
A)Rs. 1200
B)Rs. 1300
C)Rs. 1500
D)Rs. 4000
E)None of these
Rationale: Explanation :
Interest on Rs.8000 at 5% per annum = ( 8000 × 5 × 1) / 100 = Rs. 400
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (8000 + x) × 6 × 1/100.
=> 400 + 2x/25 = (8000 + x) × 6 × 1/100.
=> 40000 + 8x = (8000 + x) × 6.
=> 40000 + 8x = 48000 + 6x.
=> 2x=8000.
=> x=4000.
Answer : D
Answer: D
Question: For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 8 of whom are females, by how much does the index for the females exceed the index for the males in the group?
Options:
A) 0.05
B) 0.0625
C) 0.2
D) 0.25
E) 0.6
Rationale: Index for females = (20-8)/20 = 3/5 = 0.6
Index for males = (20-12/20 = 2/5 = 0.4
Index for females exceeds males by 0.6 - 0.4 = 0.2
Answer: C
Answer: C
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?
Options:
A)Rs.2038
B)Rs.2073
C)Rs.2000
D)Rs.2027
E)Rs.2022
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 2288
for 114.4 ---> 100 ; 2288 ---> ?
Required price = (2288 * 100)/114.4 = 20 * 100 = Rs.2000.
Answer:C
Answer: C
Question: There are three foam generators in the factory, each of the first two can generate 10 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
Options:
A)128
B)132.
C)146.
D)154.
E)166.
Rationale: Let the foam generators capacity be -
A = 10 lit/hr
B = 10 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 38 lit ( 10 + 10 + 18 ) ; since in 1 and 1/2 hr they will generate 38 + 19 => 57 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 10 lit/hr
C = 18 lit/hr
Total foam generation in 2 hour will be 56 litres {2 (10+18)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 10 => 15 litres
So, total foam generated will be 128 Litres ( 57 + 56 + 15 ) ; hence answer will be (A)
Answer: A
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
Options:
A)80%
B)105%
C)120%
D)112%
E)138%
Rationale: 0,112R = x/100*0.1R
Answer D
Answer: D
Question: 30 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?
Options:
A)14.4
B)120
C)50.4
D)60
E)90
Rationale: 30% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/30)*100 = 120 square feet
Answer: Option B
Answer: B
Question: There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?
Options:
A)10
B)20
C)40
D)60
E)120
Rationale: Method 1:
Take the first amateur. He plays a game with each of the other four i.e. 4 games.
Now take the second one. He has already played a game with the first one. He plays 3 games with the rest of the 3 amateurs i.e. 3 more games are played.
Now take the third amateur. He has already played a game each with the first and the second amateur. Now he plays 2 games with the remaining 2 amateurs so 2 more games are played.
Now go on to the fourth amateur. He has already played 3 games with the first 3 amateurs. He just needs to play a game with the last one i.e. 1 more game is played.
The last amateur has already played 4 games.
Total no of games = 4+3+2+1 = 10
Method 2:
Each person is one participant of 4 games. So there are in all 4*5 = 20 instances of one participant games. But each game has 2 participants so total number of games = 20/2 = 10
Answer: A.
Answer: A
Question: If 28a+30b+31c=425.
then a+b+c=?.a,b,c are natural numbers
Options:
A)14
B)8
C)6
D)9
E)2
Rationale: have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*6 + 31*7..
hence values of a,b and c are 1, 6 and 7 respectively..
a+b+c=14
ANSWER:A
Answer: A
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
Options:
A)88hours
B)38hours
C)78hours
D)28hours
E)48hours
Rationale: 2/7 - 1/x
= 1/4
x = 28
Answer:D
Answer: D
Question: What is the place value of 3 in the numeral 53468?
Options:
A)3000
B)30
C)3
D)330
E)300
Rationale: place value of 3 = 3 * 1000 = 3000
Answer is A
Answer: A
Question: A child is playing with letter blocks (a playing cube in which an english letter is written). Before leaving the child to play on her own, her mon arranged 5 blocks into the word APPLE. How many different 6 letter words can the child make with these 5 blocks (Words need not have a meaning.She is just a child!) ?
Options:
A)2!
B)3!
C)4!
D)5!
E)6!
Rationale: There are 6 letter blocks to be arranged. Note that the letter P occurs twice. 2 'P' blocks can be arranged only in one way, since the two blocks are exactly the same(PP is same as PP). So we can consider PP as one letter and proceed to find the arrangement of 4 letters, A, PP, L, E. These four blocks can be arranged in 4! ways. So answer is C. 4!.
Answer: C
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $30 to ship a certain package, which of the following was the weight of the package, in pounds?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: Let the weight of the package be X.
2X + 6= 30
X = 12
The answer is D.
Answer: D
Question: Williams works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 8 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
Options:
A)3/7
B)5/7
C)6/7
D)1/7
E)4/7
Rationale: First notice the number of months for which he worked - March to Sept i.e. 7 months
Avg of monthly totals in tips for months other than August = x
Tips in August = 8x
Total tips for all months = 6*x + 8x = 14x
Tips for August/Total tips for all months = 8x/14x = 4/7
Answer : E
Answer: E
Question: If four coins are tossed, the probability of getting two heads and two tails is
Options:
A)3/8
B)6/11
C)2/5
D)4/5
E)5/11
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer : A
Answer: A
Question: If 0.75: x :: 5:9, then x is equal to:
Options:
A)1.12
B)1.16
C)1.2
D)1.35
E)None of these
Rationale: Explanation:
(x * 5) = (0.75 *9)
X=6.75/5 = 1.35
Answer: D
Answer: D
Question: By investing in 16 2/3% stock at 64, one earns Rs. 1500. The investment made is:
Options:
A)Rs. 5640
B)Rs. 5760
C)Rs. 7500
D)Rs. 8600
E)Rs. 9600
Rationale: To earn Rs.	50/3	, investment = Rs. 64.
To earn Rs. 1500, investment = Rs.64 x	3/50x 1500	= Rs. 5760.
ANSWER :B
Answer: B
Question: A grocery purchased cereal at 40% of its list price and sold it for 90% of its list price. What is its percent gain?
Options:
A)30
B)65
C)75
D)110
E)125
Rationale: Cost = 40% of List Price = .4*LSale = 90% of List Price = .9*LGain Ratio = (Sale - Cost) / Cost = (.9*L - .4*L) / .4*L = .5*L / .4*L = 1.25Gain Percent = 100 * Gain Ratio = 100 * 1.25 = 125% = Answer E
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 720 grams per kg, what is his percent?
Options:
A)15%
B)25%
C)38.9%
D)45%
E)35%
Rationale: Explanation:
720 --- 280
100 --- ? => 38.9%
Answer: C
Answer: C
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)240
B)288
C)665
D)199
E)261
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec
= 4 min
Answer: A
Answer: A
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
Options:
A)123
B)480
C)266
D)1251
E)121
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480Answer: B
Answer: B
Question: A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw
Options:
A)64
B)128
C)132
D)222
E)None of these
Rationale: Explanation:
From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that
at least one black ball should be there.
Hence we have 3 choices
All three are black
Two are black and one is non black
One is black and two are non black
Total number of ways
= 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because 6 are non black]
=1+[3×6]+[3×(6×5/2×1)]=1+18+45=64
Option A
Answer: A
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then JUMP?
Options:
A)200
B)210
C)220
D)230
E)240
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
JUMP=(10+21+13+16)*4= 240
ANSWER:E
Answer: E
Question: A drought decreased the amount of water in city X’s reservoirs from 118 million gallons to 96 million gallons. If the reservoirs were at 79 percent of total capacity before the drought began, approximately how many million gallons were the reservoirs below total capacity after the drought?
Options:
A)67
B)58
C)54
D)46
E)32
Rationale: let T be the total capacity of the reservoir.
Now we can equate before cases i.e 79/100(T) = 118.
Lets take approximate values for easy calculation 80/100(T) = 120 => T = 150 MG.
We need to subtract total - after drought case = 150 - 96 = 54 MG..
Option C is correct answer...
Answer: C
Question: Evaluate : 986 x 237 + 986 x 863
Options:
A)986000
B)968000
C)978000
D)987000
E)None of them
Rationale: 986 x 137 + 986 x 863 = 986 x (137 + 863) = 986 x 1000 = 986000.
Answer is A.
Answer: A
Question: The class mean score on a test was 50, and the standard deviation was 15. If Jack's score was within 2 standard deviations of the mean, what is the lowest score he could have received?
Options:
A)20
B)31
C)45
D)90
E)89
Rationale: 1SD from the mean ranges from 35 to 65, where 65 is within SD above the mean and 35 within 1SD below the mean
2SD=15 TWICE=30 from the the mean, which is 80 to 20, where 80 is within 2 SD above the mean AND 20 is within 2 SD below the mean.
Answer = A
Answer: A
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8100. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Options:
A)2177
B)2876
C)4500
D)2981
E)6100
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8100 = 32400 ----(2)
(2)-(1) i.e. May - Jan = 400
Salary of May is Rs.6500
Salary of January = Rs.6100.Answer: E
Answer: E
Question: 256, 225, 196, 169, 144, ?
Options:
A)49
B)64
C)81
D)121
E)100
Rationale: Explanation :
The pattern is 16^2, 15^2, 14^2, 13^2, 12^2, ...
So next number is 11^2 = 121
Answer : Option D
Answer: D
Question: In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks Z are made of cotton?
Options:
A)100
B)80
C)60
D)50
E)25
Rationale: I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks Z has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A.
Answer: A
Question: A certain junior class has 3000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
Options:
A)1/40000
B)1/3600
C)9/2000
D)1/60
E)1/15
Rationale: Let's see
Pick 60/3000 first
Then we can only pick 1 other pair from the 800
So total will be 60 / 800 *3000
Simplify and you get 1/40000
Answer is A
Answer: A
Question: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 630,000 different outfits, then for how many garments does Dave have exactly five choices?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 630,000 = 63*10,000 = 63*5^4*2^4
Dave has exactly 5 choices for four garments.
The answer is E.
Answer: E
Question: A sum amounts to Rs.4410 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
Options:
A)Rs.4000
B)Rs.5000
C)Rs.4500
D)Rs.4800
E)Rs.5800
Rationale: CI=4410,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
4410=P[21/20]^2
4410[20/21]^2
4000
ANSWER:A
Answer: A
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?
Options:
A)1/3
B)2/3
C)2/5
D)3/5
E)4/5
Rationale: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3.
Hence, B is the correct answer.
Answer: B
Question: In store A there are 50 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
Options:
A)3:16.
B)2:3.
C)5:3.
D)3:4.
E)2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
50x : 40x
5X:4X
Price :
4y:3y
Total revenue
20xy : 12xy
5:3
Answer is C
Answer: C
Question: The side of a cube is 15 m, find it's surface area?
Options:
A)1350
B)1750
C)1150
D)1450
E)1570
Rationale: Surface area = 6 a(power)2 sq. units
6 a(power)2 = 6 × 225 = 1350 m(power)2
Answer is A.
Answer: A
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 on the committee. In how many ways can it be done?
Options:
A)784
B)365
C)452
D)251
E)756
Rationale: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756
Ans: E
Answer: E
Question: A train 220 m long is running with a speed of 59 kmph.. In what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going
Options:
A)8 sec
B)10 sec
C)12 sec
D)14 sec
E)15 sec
Rationale: Explanation:
Speed of the train relative to man = (59 + 7) kmph
= 66 ×5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man = Time taken by it to cover 220 m
at (55/3) m / sec = (220 ×3/55) sec = 12 sec
Answer: Option C
Answer: C
Question: A train 500m long takes 10 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
Options:
A)175kmph
B)150kmph
C)162kmph
D)145kmph
E)100kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
500/[(x+5)*5/18] = 10
10(x+5) = 1800
x = 175kmph
Answer is A
Answer: A
Question: The average age of applicants for a new job is 20, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
Options:
A)8
B)16
C)17
D)18
E)34
Rationale: Minimum age = Average - 1 Standard deviation = 20 - 8 = 12
Maximum age = average + 1 Standard deviation = 20+ 8 = 28
Maximum number of different ages of the applicants = 28 - 12 + 1 = 17
Answer C
Answer: C
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Options:
A)39
B)35
C)42
D)40.5
E)41.5
Rationale: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+87
then average run after 17th inning=(16x+87)/17
(16x+87)/17=x+3;
x=36;
average after 17th inning =36+3=39
ANSWER:A
Answer: A
Question: Set S consists of integers {8, 11, 12, 14, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 25%. What is the value of integer n?
Options:
A)28
B)32
C)36
D)40
E)44
Rationale: The average of the numbers in set S is 12.
If we increase the mean by 25%, the new mean is 15.
Thus, on average, 5 numbers increase by 5.
Therefore n = 15+25 = 40
The answer is D.
Answer: D
Question: There are 6 people and 6 chairs. In how many different ways people can occupy the chairs?
Options:
A)360
B)500
C)420
D)720
E)840
Rationale: number of ways =6! = 720
Answer is D
Answer: D
Question: The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area?
Options:
A)228
B)148
C)992
D)772
E)222
Rationale: 2(4*5 + 5*6 + 4*6) = 148
Answer: B
Answer: B
Question: Find the sum of first 32 natural numbers
Options:
A)470
B)468
C)465
D)463
E)528
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)/2
=32(32+1)/2=32(33)/2=528
Answer: Option E
Answer: E