divelab/Sys2Bench huggingface dataset:
Question: P is a set containing 8 different positive odd numbers. Q is a set containing 7 different numbers, all of which are members of P. Which of the following statements CANNOT be true?
Options:
A)The range of Q is even.
B)The mean of P is even.
C)The mean of Q is even.
D)The range of P is equal to the range of Q.
E)The median of Q is equal to the mean of Q.
Rationale: Given: P is a set containing 8 different positive odd numbers
Easily inferred: Q is a set containing 7 differentoddnumbers
(A) The range of Q is even. - Always even, since it is a difference of two odd numbers
(B) The mean of P is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of Q is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of P is equal to the range of Q.
(E) The median of Q is equal to the mean of Q
Option C.
Answer: C
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)54
B)62
C)48
D)62
E)62
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer:C
Answer: C
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards F will he need to gain this Sunday if he wants to keep his season average above 100 yards?
Options:
A)101
B)116
C)130
D)F=131
E)F=141
Rationale: Sorry the answer F=131 is D.
Answer: D
Question: What percent of a day in 6 hours?
Options:
A)10%
B)15%
C)20%
D)25%
E)50%
Rationale: Required percentage = 6/24 * 100 = 100/4 = 25%
Answer is D
Answer: D
Question: The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 84, and the average of the female students’ grades was 92, how many female students took the test?
Options:
A)8
B)9
C)10
D)21
E)24
Rationale: Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 84 Thus M = 672 ---------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(672+92f)/(8+f) = 90
solving this we get f = 24
Ans: E
Answer: E
Question: A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 5 a.m.?
Options:
A)23 Minutes
B)24 Minutes
C)25 Minutes
D)27 Minutes
E)None of these
Rationale: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-4:00 a.m =13*2=26 total=27
ANSWER:D
Answer: D
Question: The price of a T.V. set worth Rs. 10000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)9000
B)26699
C)96000
D)19000
E)26711
Rationale: Money paid in cash = Rs. 1000
Balance payment = (10000 - 1000) = Rs. 9000
Answer: A
Answer: A
Question: If n is the product of three consecutive integers, and n is divisible by 11, which of the following is not necessarily a divisor of n ?
Options:
A)990
B)1210
C)1716
D)0
E)2
Rationale: IF ONE NO. IS 11 THEN OTHER CONSEQUTIVE NO. ARE 9*10*11=990 ,10*11*12 =1210 , 11*12*13 =1716
N IS NOT DIVISOR ANY ABOVE NO =0
D
Answer: D
Question: The cost price of 5 oranges equal to the selling price of 8 oranges. Calculate the % profit or loss.
Options:
A)38.5%
B)37.5%
C)73.5%
D)32.5%
E)31.5%
Rationale: Let the cost price of 1 orange is Rs 1
Cost of 8 orange = Rs 8
Selling price of 8 orange = 5
Gain/loss = 8 - 5 = 3
%=3/8âˆ—100= 37.5
Answer: B
Answer: B
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a three. You pick a card from a full playing-card deck, and success would be picking a ace with heart card.
If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
Options:
A)61/312
B)13/624
C)325/624
D)181/312
E)163/625
Rationale: Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting three in a roll of dice = 1/6
Event(3): Probability of getting ace with heart in a pack of card = 1/52
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*5/6*51/52 +1/2*1/6*51/52 +1/2*5/6*1/52
=255/624 + 102/624 +5/624
=362/624
= 181/312
Answer :D
Answer: D
Question: In a certain game, you pick a card from a standard deck of 52 cards. If the card is a clever, you win. If the card is not a clever, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a clever, and the point is to measure how many draws did it take before the person picked a clever and won. What is the probability that there will be at least four draws involved in a win, i.e. someone picking her clever on the fourth draw or later?
Options:
A) 1/2
B)27/64
C) 11/16
D) 13/16
E) 15/16
Rationale: Probability of picking a clever on any draw = 1/4
Probability of NOT picking a heart on the first draw AND on the second draw And 3rd draw = [1-(1/4)] X [1-(1/4)] X [1-(1/4)]= 3/4 X 3/4 X 3/4 = 27/64
Answer : B
Answer: B
Question: Kareem is three times as old as his son. After ten years, the sum of their ages will be 76 years. Find their present ages.
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Sol. Let the present age of Kareem’s son be x years.
Then, Kareem’s age = 3x years
After 10 years, Kareem’s age = 3x + 10 years
and Kareem’s son’s age = x + 10 years
∴ (3x + 10) + (x + 10) = 76
=> 4x = 56 => x = 14
∴ Kareem’s present age = 3x = 3 × 14 = 42 years
Kareem’s son’s age = x = 14 years.
Answer B
Answer: B
Question: Anand starts from a point P towards point Q, where PQ = 70 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
Options:
A)(45/7) kmph
B)(60/7) kmph
C)(40/7) kmph
D)(20/3) kmph
E)(65/7) kmph
Rationale: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (70-x) km
Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph
So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km
And between their first meeting point and second, they both together covered a distance of 2(90-x) km.
2x+3x=2(70-x)
5x=140-2x
7x=140
x=140/7 km
Anand's speed=x/3=140/(3*7)=20/3 kmph
Ans:D
Answer: D
Question: A particular parking garage is increasing its rates by 40 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
Options:
A)20%
B)25%
C)29%
D)33%
E)40%
Rationale: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.4P = x*P
N*x = x/1.4 which is about 0.71x, thus a 29% reduction.
The answer is C.
Answer: C
Question: Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 29 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
Options:
A)14.5 minutes
B)29 minutes
C)35 minutes
D)58 minutes
E)87 minutes
Rationale: Danny's time is 29 minutes. The time to reach halfway is 14.5 minutes.
Steve's time is 58 minutes. The time to reach halfway is 29 minutes.
The time difference is 29 - 14.5 = 14.5 minutes
The answer is A.
Answer: A
Question: At what time between 4 and 5 o’clock the hands are in opposite direction?
Options:
A)3 2/11 minutes past 4 o’clock
B)3 5/11 minutes past 4 o’clock
C)10 10/11 minutes past 4 o’clock
D)10 2/11 minutes past 4 o’clock
E)54 6/11 mintues past 4'0 clock
Rationale: To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
50 min. spaces are gained in 60/55 x 50 min. or 54 6/11 min. Required time = 54 6/11 min. past 4 o’clock
ANSWER:E
Answer: E
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 48 kmph, find the speed of the stream?
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)16 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 48/3 = 16 kmph
ANSWER:E
Answer: E
Question: Each of the 9 squares shown is to contain one number
chosen from 1, 2, 3, 4, 5, 6, 7, 8, and 9. No number is to
be repeated. Suppose the sum of the 5 squares aligned
vertically on the right is 32 and that the sum of the 5
squares aligned horizontally on the bottom is 20. What
number goes in the shared corner square?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: If x is the number in the corner square, then the sum of all the numbers in the squares is equal
to the sum of the numbers in the five squares aligned vertically plus the sum of the numbers in the
five squares aligned horizontally minus x. Hence,
1 + 2 + · · · + 9 = 32 + 20 − x.
The sum on the left is 45, so x = 52 − 45 = 7.
correct answer E
Answer: E
Question: In how many ways can the letters D, I, T , K , T be arranged so that the two I's are not next to each other?
Options:
A)36
B)48
C)72
D)96
E)128
Rationale: 1 D
1 I
1 G
2 T
Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60
Consider 2 Is as 1 entity and thus the number of arrangements for (TT)DGI = 4! = 24
Total allowed cases = 60-24 =36
A is the correct answer.
Answer: A
Question: The bankers gain of a certain sum due 2 years hence at 10% per annum is Rs 24 .The percent worth is
Options:
A)387
B)238
C)278
D)600
E)281
Rationale: Explanation:
T.D = (B.G * 100) / (Rate * Time)
(24*100) / (10 * 2)
= 120.
P.W = (100 *T.D) / (Rate * Time)
= (100 * 120) /(10 * 2)
= 600
Answer: D) 600
Answer: D
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)736
B)988
C)999
D)729
E)737
Rationale: Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
Answer: Option C
Answer: C
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
Options:
A)10 cm
B)15 cm
C)20 cm
D)18 cm
E)24 cm
Rationale: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 75 => 5x - 25 = 75 => x = 20.
Length of the rectangle = 20 cm.
Answer: Option C
Answer: C
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)729
B)720
C)718
D)750
E)782
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2
=750
Answer:D
Answer: D
Question: A man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being 12%The rate of interest obtained is
Options:
A)13.09%
B)15.5%
C)14%
D)14.25%
E)14.95%
Rationale: Explanation :
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.5 = Rs.55
Number of shares = 40
Dividend = 12 %
Dividend per share = 60×12×100=Rs.7 1/5
Total dividend = (40 × 7 1/5)
ie, He got a dividend of (40 × 7 1/5) for an investment of Rs.(40 × 55)
Interest obtained = 40×7 1/5×100/40×55=13.09%
Answer : Option A
Answer: A
Question: Which of the following is equal to the average (arithmetic mean) of (x+1)^2 and (x-1)^2?
Options:
A)x^2
B)x^2+1
C)x^2 +4
D)x^2+2x
E)x^2+4x
Rationale: Avg = [(x+1)^2 + (x-1)^2] / 2
Expanding and simplifying, (x^2 + 2x + 1 + x^2 -2x + 1 ) / 2 = x^2 + 1
Answer B.
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
Options:
A)177 m
B)189 m
C)120 m
D)178 m
E)200 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 10
=200 m.
Answer: E
Answer: E
Question: The ratio of the present ages of Giri and Hari is 5 : 8. 12 years hence, the ratio of their ages will be 11 : 14. Find the difference in their present ages?
Options:
A)5 years
B)6 years
C)3 years
D)9 years
E)2 years
Rationale: Let the present ages of Giri and Hari be 5x and 8x years respectively.
(5x + 12) / (8x + 12) = 11/14
70x + 168 = 88x + 132 => x= 2
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
= 8x - 5x = 3x = 6 years.
Answer:B
Answer: B
Question: Three candidates contested an election and received 3644 votes, 7636 votes, and 12720 votes respectively. What percentage of the total votes did the winning candidate receive?
Options:
A)53%
B)55%
C)57%
D)59%
E)61%
Rationale: The total number of votes polled = (3644 + 7636 + 12720) = 24000
The winner's percentage = 12720/24000 * 100 = 53%
The answer is A.
Answer: A
Question: What will be the fraction of 10%
Options:
A)1/4
B)1/5
C)1/10
D)1/8
E)None of above
Rationale: Explanation:
It will 10*1/100 = 1/10
Answer: Option C
Answer: C
Question: The length of a rectangle is increased by 40% while its width is halved. What is the % change in area?
Options:
A)25%
B)30%
C)50%
D)65%
E)70%
Rationale: The original area is L*W
The new area is 1.4L*0.5W = 0.7*L*W = L*W - 0.3*L*W
The area decreased by 30%.
The answer is B.
Answer: B
Question: 3x^2 + 10x - 8 =
Options:
A)(3x-4)(x-1)
B)(3x-4)(x+2)
C)(3x-4)(x-2)
D)(3x-2)(x+4)
E)none of above
Rationale: 3x^2 - 10x - 8
= 3x^2 + 12x - 2x - 8
= 3x (x + 4) - 2 (x+4)
= (3x-2) (x+4)
Option D
Answer: D
Question: Let x < 0, 0 < y < 1, z > 1. Which of the following may be false?
Options:
A)(x^2– z^2) has to be positive.
B)yz can be less than one.
C)xy can never be zero.
D)(y^2– z^2) is always negative.
E)None
Rationale: Explanation :
Let's take any random value satisfying the given condition i.e x < 0, 0 < y < 1, z > 1.
Take x = -1, and z = 2
x2 - z2 -> (-1)2 - (2)2 = -3 .
Take y= 0.1,
then , yz -> (1/10)*2 = 1 /5 i.e less than 1.
According to the given condition, x and y both are non zero, so there product can't be zero.
Since, value of z will always be greater than 2 and y will always be less than 1, So, y2 - z2 will always result into a negative value.
Hence, only first option is false.
Answer : A
Answer: A
Question: A man can row 9 1/3 kmph in still water and finds that it takes him thrice as uch time to row up than as to row down the same distance in the river. The speed of the current is:
Options:
A)3 1/2 km/hr
B)2 1/3 km/hr
C)4 1/2 km/hr
D)4 2/3 km/hr
E)None
Rationale: Sol.
Let speed upstream be x kmph. Then, speed downstream = 3x kmph.
Speed in still water = 1/2(3x + x) kmph = 2x kmph.
∴ 2x = 28/3 ⇒ x = 14/3
So, Speed upstream = 14/3 km/hr; Speed downstream = 14/hr.
Hence, speed of the current = 1/2 [14 - 14/3] km/hr = 14/3 km/hr = 4 2/3 km/hr.
Answer D
Answer: D
Question: If selling price is doubled, the profit triples. Find the profit percent:
Options:
A)170
B)320
C)100
D)280
E)200
Rationale: C
100%
Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Answer: C
Question: The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Options:
A)8
B)4
C)12
D)16
E)7
Rationale: Explanation:
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
Answer B
Answer: B
Question: What is the units digit of (5!*4! + 6!*5!)/3?
Options:
A)4
B)3
C)2
D)0
E)1
Rationale: (5!*4! + 6!*5!)/3
=5!(4! + 6!)/3
=120 ( 24 + 720)/3
=(120 * 744)/3
= 120 * 248
Units digit of the above product will be equal to 0
Answer D
Answer: D
Question: If the sum and difference of two numbers are 10 and 8 respectively, then the difference of their square is:
Options:
A)12
B)28
C)160
D)180
E)80
Rationale: Let the numbers be x and y.
Then, x + y = 10 and x - y = 8
x2 - y2 = (x + y)(x - y) = 10 * 8 = 80.
ANSWER:E
Answer: E
Question: Monika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its Selling Price. Find her gain percent.
Options:
A)10
B)20
C)25
D)15
E)18
Rationale: Let the Selling Price be $X. then Cost Price = $9x/10, Receipt=108% of $x= $27x/25 Gain=$(27x/25*9x/10)=$(108x-90x/100)=$18x/100
Gain%=(18x/100*10/9x*100)%=20%
Answer B) 20.
Answer: B
Question: In how many ways letters of the word CORPORATION be arranged?
Options:
A)125879
B)3326400
C)369
D)1698
E)8723
Rationale: CORPORATION has 11 letters, out of which O repeated 3 times, R repeated 2 times. Hence total ways = 11! / (3!*2!) = 3326400 ways
B
Answer: B
Question: 279936, 46656, 7776, 1296, 216, ?
Options:
A)60
B)46
C)36
D)66
E)76
Rationale: Explanation :
Go on dividing by 6 to the next number
Answer : Option C
Answer: C
Question: 12.1212+17.0005 - 9.1102 = ?
Options:
A)20.0015
B)20.0105
C)20.0115
D)20.1015
E)None
Rationale: Solution
Given expression
=(12.1212+17.0005)-9.1102
= (29.1217 - 9.1102)
=20.0115.
Answer C
Answer: C
Question: Find the wrong number below mentioned series
13,60,100,500,850
Options:
A)13
B)60
C)100
D)500
E)850
Rationale: 13 is the only prime number or odd number in the series.
ANSWER:A
Answer: A
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
Options:
A)4/7
B)5/3
C)4/5
D)5/8
E)7/18
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
ANS: E
Answer: E
Question: How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 9 (X)
2343 12 (/)
3474 18 (X)
4131 9 (X)
5286 21 (/)
5340 12 (/)
6336 18 (X)
7347 21 (/)
8115 15 (/)
9276 24 (/)
Required number of numbers = 6.
Answer: B
Answer: B
Question: If x≠0 and x=√4xy−4y^2, then, in terms of y, x =
Options:
A)2y
B)y
C)y/2
D)-(4y^2)/(1-2y)
E)-2y
Rationale: Well it means :
Squaring we get:
x^2 =4y(x-y)
Assume X^2=m >>>>>>>>>>>1
Than ,m=4y(m^1/2-y)
on solving:m-4y(m)^1/2+4y^2=0 >> quadratic in y s solve for y.
Y comes out to be =(m^1/2)/2
Hence,put m =x^2 from 1.
So x=2y
ANSWER:A
Answer: A
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)22
B)24
C)44
D)48
E)50
Rationale: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer: Option C
Answer: C
Question: Find the 2nd greatest number of five digits which is exactly divisible by 12, 15 and 18?
Options:
A)A)13050
B)B)12960
C)C)14090
D)D)16200
E)E)12080
Rationale: The largest five digit numbers are
16200,14090,13050,12960,12080,
16200 is divisible by 12, 15 and 18 ------(1st largest no)
14090 is not divisible by 12
13050 is not divisible by 12
12960 is divisible by 18, 12 and 15 -------(2nd largest)
12080 is not divisible by 12
ANSWER:B
Answer: B
Question: If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true?
I.	L exactly passes through 2 quadrants
II.	The slope of L is negative
III.	The slope of L is positive
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: Let (m,n) = (2,3)
(-m,-n) = (-2,-3)
Slope = (3+3)/(2+2) = 6/4 = 3/2
So II may not be true
Let (m,n) = (2,-3) then (-m,-n) = (-2,3)
So slope = (3 +3)/(-2-2) = -3/2
so III may not be true
So such a line would be -> (y - 3) = 3/2(x - 2)
=> 2y - 6 = 3x - 6
=> 2y - 3x = 0, hence no x or y intercept, so it passes through origin.
I is true.
Answer - A
Answer: A
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many P cubes are painted on only 2 faces?
Options:
A)12
B)8
C)6
D)10
E)16
Rationale: 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. P=4 + 4 + 4 = 12. Answer A
Answer: A
Question: The average runs of a cricket player of 10 innings was 20. How many runs must he make in his next innings so as to increase his average of runs by 4?
Options:
A)12
B)42
C)64
D)76
E)84
Rationale: Explanation:
Average after 11 innings = 24
Required number of runs = (24 * 11) – (20 * 10)
= 264 – 200 = 64
ANSWER C
Answer: C
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent E of the lights that are on are supposed to be off?
Options:
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%
Rationale: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 E= 10%.D
Answer: D
Question: If 315,214 football shoes need to be placed in boxes and each box can contain at most 2 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:
Options:
A)1football shoes
B)0 football shoes
C)4 football shoes
D)7 football shoes
E)9 football shoes
Rationale: The number of football shoes that can be placed in boxes of 2 football shoes is the last number that is divisible by 2 that occurs before 315,214.
In order to divide the sum in 2 parts, the last number must be divisible by 2
Divisibility rule of 2: The last digit must be divisible by 2
last digit of 315,214 is 4 and 4 is divisible by 2.
Hence, there is no unfilled box.
Correct Option: B
Answer: B