divelab/Sys2Bench huggingface dataset:
Question: The average runs scored by a batsman in 30 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
Options:
A)24.3
B)25.3
C)26.3
D)28.3
E)34.5
Rationale: Total score of the batsman in 30 matches = 600.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 730.
Average score of the batsman = 730/30 = 24.3.
ANSWER:A
Answer: A
Question: What is the prime factors’ number of 36?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^2*3^2
prime factors’ number will be 2+2 = 4.
Hence, answer is C.
Answer: C
Question: A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
Options:
A)a) 5 inches
B)b) 6 inches
C)c) 7 inches
D)d) 8 inches
E)e) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
25=5*5
35=5*7
GCF = 5
P.S you can make squares with side of 5
Answer : A
Answer: A
Question: A courtyard is 20 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
Options:
A)16000
B)27778
C)20000
D)27999
E)17799
Rationale: Number of bricks =Courtyard area/1 brick area
=(2000×1600/20×10)=16000
Answer: A
Answer: A
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.9880. Find the share of B?
Options:
A)2880
B)3000
C)3018
D)3019
E)3012
Rationale: 60*5:36*6:75*3
100: 72: 75
72/247 * 9880 = 2880
Answer: A
Answer: A
Question: How many pieces can a square pizza be cut into by making 4 linear cuts?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: 1 cut makes two pieces
a second cut can make 4 pieces by cutting through 2 of the pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
B
Answer: B
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time W will it take to fill the tank now?
Options:
A) 50% less time
B) 50% more time
C) 75% less time
D) 75% more time
E) 100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that W=is 50 % less.A
Answer: A
Question: What approximate value should come in the place of question mark (?) in the following equation?
1325√(17) + 508.24 of 20% – 85.39 of 3⁄4 = ?
Options:
A)5500
B)5200
C)5800
D)4900
E)5900
Rationale: ? = 1325√(17) + 508.24 of 20% – 85.39 of 3⁄4
= 1325√(17) + 500 of 20% – 85 × 0.75
= 5460 + 100 – 60 = 5500
Answer A
Answer: A
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
Options:
A)18
B)76
C)48
D)27
E)12
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer:C
Answer: C
Question: A box contains five bulbs out of which 3 are defective. If three bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/12
B)1/11
C)1/10
D)1/198
E)1/126
Rationale: Out of five, two are good and three are defective. Required probability
= 3C3/5C3
= 1/10
Answer: C
Answer: C
Question: hree seventh of a number is 12 more than 40% of that number. What will be the 60% of that number?
Options:
A)238
B)129
C)126
D)197
E)112
Rationale: Explanation:
3/7 x â€“ 40/100 x = 12
x = 35 * 12
35 * 12 * 60/100 = 252/2 = 126
Answer:C
Answer: C
Question: Find the largest number of four digits which is exactly divisible by 25,18,12,15
Options:
A)9900
B)9710
C)9720
D)9730
E)9740
Rationale: Explanation:
LCM of 25-18-12-15 is 900.
After dividing 9999 by 900 we get 99 remainder.
So answer will be 9999-99 = 9900
Option A
Answer: A
Question: In expressing a length of 102.472 km as nearly as possible with the three significant digits, find the percentage error
Options:
A)0.38%
B)0.27%
C)0.027%
D)0.038%
E)None of these
Rationale: Explanation:
Error = (102.5 - 102.472) = 0.028
Required percentage =
0.028/ 102.472Ã—100=0.027
Option C
Answer: C
Question: What is the remainder when 1273 * 1275 * 1277 *1285 is divided by 12?
Options:
A) 9
B) 1
C) 11
D) 0
E) 7
Rationale: 1271*1275*1277*1285 = (1272 + 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.
Answer: A
Answer: A
Question: In what time will a train 50 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)1.25 sec
B)2.75 sec
C)3.5 sec
D)2.39 sec
E)9.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 50/40
= 1.25 sec.
Answer: A
Answer: A
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 4th position from either end of the row.
Can you find out how many girls are practicing together?
Options:
A)4
B)9
C)7
D)6
E)8
Rationale: As judith is 4th from either end of the row, it means that 3 girls are on one of her sides and 3 are present on the other.
3 + 3 + 1(judith herself) = 7.
Hence, 7 girls are practicing the dance together.
correct answer is C)7
Answer: C
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
Options:
A)228
B)224
C)288
D)266
E)121
Rationale: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: B
Answer: B
Question: For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
Options:
A)5/27
B)2/9
C)1/3
D)4/9
E)2/3
Rationale: Probability of not burning out during the first 6 months 1-1/3=2/3
Probability of not burning out during the next 6 months 2/3/2=1/3, hence probability of burning out 1-1/3=2/3.
Probability of burning out during the period from 6 months to 1 year = Probability of not burning out in first 6 months * Probability of burning out in next 6 months = 2/3 * 2/3 =4/9
Answer: D.
Answer: D
Question: A thief steels a car at 6a.m. and drives it at 40kmph. The theft is discovered at 7a.m. and the owner sets off in another car at 60 kmph. When will he overtake the thief?
Options:
A)9a.m.
B)9.30a.m.
C)10a.m.
D)11.45a.m.
E)10.15a.m.
Rationale: Suppose the thief overtakes x hours after 6a.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)
40x = 60(x-1)
20x = 60
x = 3 hrs
Thief is overtaken at 9 a.m.
Answer is A
Answer: A
Question: Two trains 110 meters and 180 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.2
B)7.85
C)6.85
D)5.85
E)6.15
Rationale: T = (110+ 180)/ (80 + 65) * 18/5
T = 7.20
ANSWER:A
Answer: A
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
Options:
A)123
B)145
C)166
D)170
E)180
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: C
Question: 50 men took a dip in water tank 40 m long and 20 m broad on a religious day. If the average displacements of water by a man is 4 m3, then the rise in the water level in the tank will be
Options:
A)20 cm
B)25 cm
C)35 cm
D)50 cm
E)None
Rationale: Solution
Total number of water displaced	= (4 ×50)m3
‹=› 200m3
Rise in water level	= (200 / 40×20)m
= 0.25 m
‹=› 25 cm
Answer B
Answer: B
Question: A shopkeeper sold an article for 1000 after giving 20% discount on the labelled price and made 25% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
Options:
A)25%
B)56.25%
C)23%
D)28%
E)None of these
Rationale: Cost price = 1000×100/125= 800
S.P. at no discount = 1000×100/80 = 1250
∴ % profit = 450×100/800 = 56.25 %
Answer B
Answer: B
Question: David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
Options:
A)75
B)27.6
C)66.6
D)16.5
E)11
Rationale: Explanation:
Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6.
Answer:C
Answer: C
Question: Of the 19,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
Options:
A) 14.3%
B) 16.67%
C) 33%
D) 28.6%
E) 49.67%
Rationale: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.
If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.
What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 33%.
Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.
The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?
The correct answer is 2nd place.
Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.C
Answer: C
Question: Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be
Options:
A)9,000
B)12,000
C)11,000
D)10,000
E)None of these
Rationale: Sum invested by A, B and C is
5 × 12 : 7 × 12 : 6 × 6 + 3 × 6
or, 60 : 84 : 54 or, 10 : 14 : 9
\Share of C = 9⁄33 × 33,000 = 9,000
Answer A
Answer: A
Question: If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
Options:
A)45
B)56
C)64
D)78
E)90
Rationale: A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
D
Answer: D
Question: The ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be?
Options:
A)1 : 9
B)1 : 3
C)1 : 2
D)1 : 1
E)3 : 3
Rationale: Suppose age of Laxmi is x years.
The difference of their ages
\inline \therefore Ratio of their ages after 3 years = =
= 12 : 36 = 1 : 3
Answer:B
Answer: B
Question: If the product of two numbers is 82500 and their H.C.F. is 55, find their L.C.M.
Options:
A)2574
B)2500
C)1500
D)1574
E)None of these
Rationale: Explanation:
HCF * LCM = 82500, because we know
Product of two numbers = Product of HCF and LCM
LCM = 82500/55 = 1500
Option C
Answer: C
Question: 4, 5, 7, 11, 19, (...)
Options:
A)22
B)35
C)27
D)32
E)30
Rationale: 4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer is B.
Answer: B
Question: If k > 0, x + k = y, and y + 4k = z, what is the ratio between z - x and y - x ?
Options:
A)2 to 1
B)3 to 2
C)3 to 1
D)4 to 1
E)5 to 1
Rationale: y-x = k
z-y = 4k
Let's add the two equations together:
z-x = 5k
The ratio of z-x to y-x is 5:1.
The answer is E.
Answer: E
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
Options:
A)384
B)287
C)279
D)267
E)229
Rationale: Average mark scored by all the three boys =
[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer: A
Answer: A
Question: Car A runs at the speed of 52km/hr & reaches its destination in 10hr. Car B runs at the speed of 46 km/h & reaches its destination in 8h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)62:25
B)66:52
C)68:15
D)65:41
E)23:59
Rationale: Sol. Distance travelled by Car A = 52 × 10 = 520 km
Distance travelled by Car B = 46 × 8 = 368 km
Ratio = 520/368 = 65:41
D
Answer: D
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
Options:
A)4/5
B)7/8
C)9/8
D)1/3
E)6/5
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: D
Answer: D
Question: In a garden, 26 trees are planted at equal distances along a yard 300 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
Options:
A)10
B)8
C)12
D)14
E)16
Rationale: 26 trees have 25 gaps between them.
Length of each gap = 300/25 = 12
i.e., distance between two consecutive trees = 12
Answer is C.
Answer: C
Question: a man and a woman, walking together start out by both taking a step with the left foot. in order to keep together, the man whose stride is longer, takes two steps while the woman takes three. how many steps will the woman have taken they are both about to step out on the right foot for the first time together?
Options:
A)10
B)20
C)30
D)40
E)never
Rationale: it never happens
so answer is never
ANSWER:E
Answer: E
Question: It costs $2 for the first 15 minutes to use the bumper cars at a fair ground. After the first 15 minutes it costs $6 per hour. If a certain customer uses the bumper cars for 3 hours and 25 minutes, how much will it cost him?
Options:
A)$22
B)$3
C)$15
D)$21
E)$30
Rationale: 3 hrs 25 min = 205 min
First 15 min ------> $2
Time left is 190 min...
Now, 60 min costs $ 6
1 min costs $ 6/60
190 min costs $ 6/60*190 => $ 19
So, Total cost will be $19 + $2 => $ 21
The answer will be (D) $21
Answer: D
Question: Bella is taking a trip in her car from New York (point A) Chicago, Illinois (point B). She is traveling at an average speed of 50 miles per hour, If the total distance from point A to point B is 790 miles, in approximately how long will Bella reach her destination?
Options:
A)10 hours
B)12.50 hours
C)15.80 hours
D)25 hours
E)1 day
Rationale: Answer is (C). If she is traveling at a speed of 50 miles per hour and her trip is a total of 790 miles, 790 miles divided by 50 miles per hours would equal 15.80 hours, just shy of 16 hours.
Answer: C
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is?
Options:
A)4 months
B)6 months
C)8 months
D)9 months
E)1 months
Rationale: S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time =(100 x 80/1600 x 15)year
=1/3	year = 4 months.
Answer:A
Answer: A
Question: A 12 lt solution is 33 1/3% acid. How much water must be added to get the solution having 20 % acid.
Options:
A)8
B)9
C)10
D)7
E)5
Rationale: A 12 lt solution is 33 1/3% acid.
means 4 ltr acid and 8 ltr water.
If x is final solution, then
4 ltr = x* 20/100
x=20 ltr
so water to be added = 20-12= 8 ltr
ANSWER:A
Answer: A
Question: A man can row at 5 kmph in still water. If the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options:
A)2.4 km
B)2.9 km
C)3.4 km
D)4.4 km
E)1.6 km
Rationale: Explanation:
Speed in still water = 5 kmph
Speed of the current = 3 kmph
Speed downstream = (5+3) = 8 kmph
Speed upstream = (5-3) = 2 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/8+x/2=1
â‡’x+4x=8
â‡’5x=8
â‡’x=1.6 km
Answer: Option E
Answer: E
Question: If x > 7, which of the following is equal to (x^2 + 2x + 1)/(x^2 - 1) ?
Options:
A)(x + 4)/(4(x - 4))
B)(x - 4)/(x + 4)
C)(x - 2)/(x + 4)
D)(x + 1)/(x - 1)
E)(x - 8)/(x - 4)
Rationale: (x^2 + 2x + 1)/(x^2 - 1)
= (x + 1)(x + 1) / (x + 1)(x - 1)
=(x + 1)/(x - 1)
D. (x + 1)/(x - 1)
Answer: D
Question: At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 20% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
Options:
A)4/25
B)8/23
C)2/5
D)8/14
E)2/3
Rationale: let there be 100 books in all
Historic fiction books = 40% of total = 40
Other books = 60
New historic fiction = 40% of 40 = 16
Other new books = 20% of 60 = 12
total new books = 28
fraction = 16/28 = 8/14
Ans: D
Answer: D
Question: What is the decimal equivalent of (1/4)^2?
Options:
A)0.0016
B)0.0625
C)0.16
D)0.25
E)0.5
Rationale: 1/4= 25/100 => (25/100)^2=625/10000 = 0.0625
ANSWER:B
Answer: B
Question: 2x + y = 18
|y| <= 18
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
Options:
A)11
B)13
C)15
D)17
E)19
Rationale: Hi - The questions says |y| <=18 so the values of y will range from 0 to 18.So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18. So 19 (E) is the answer. remember sign doesn't matter for y as y will always be positive.E
Answer: E
Question: Find the simple interest on $1000 for 3 years at 10% per annum?
Options:
A)$250
B)$300
C)$500
D)$600
E)$1000
Rationale: SI = PTR/100
= 1000*3*10/100 = $300
Answer is B
Answer: B
Question: For how many values of W, is |||W - 5| -10| -5| = 2?
(Those ls are mods)
Options:
A) 0
B) 2
C) 4
D) 8
E) More than 8
Rationale: I think its 8
|||W-5|-10|-5| =2
let |W-5| = a which makes above
||a-10|-5| =2
let |a-10| = b which makes
|b-5| = 2
now for the above b can take 3, 7
for every b =3 a can have 13, 7
and for b = 7 a can have 17 and 3
so 'a' has four solutions 13, 7, 17 and 3
for a = 13; W has 18 or -8 thus has 2 for every combination hence 4x2 = 8
answer D
Answer: D
Question: what is the remainder of (3682*3684*3686) divided by 19?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 3686%19 = 0
so ans = 0
ANSWER:A
Answer: A
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 20% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?
Options:
A)A)(1/2)m
B)B)(1/3)m
C)C)(1/4)m
D)D)(1/5)m
E)E)(1/11)m
Rationale: let angela work for 10hrs and get 1100 rs. (m =1100)
According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs.
so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11
answer E
Answer: E
Question: An artist sells paintings through an on-line store, which take a commission of 11% of the price set by the distributor. The distributor obtains the painting from an artist at the price of $20 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 11% profit on the cost of the item?
Options:
A)28.11
B)27.99
C)36.44
D)44.12
E)14.99
Rationale: Painter price = $20;The distributor wants to maintain a 11% profit on the cost of the item, thus he must get $20*1.11 = $22.20 after the store takes a commission of 11% of the final price --> (final price)*0.79 = $22.20 --> (final price) = $28.11. Answer: A.
Answer: A
Question: If a coin is tossed twice, what is the probability that one of the flips was heads and one of the flips was tails?
Options:
A)1/2
B)1/8
C)1/4
D)1/6
E)3/4
Rationale: The possible cases are =>{Head,Head} {Head,Tail} {Tail,Head} {Tail,Tail}
Possible Cases=4
Favourable cases = 2
P(E) = 2/4 = 1/2
Answer: A
Answer: A
Question: The average age of a board of 8 functional directors in a company is the same as it was 3 years ago, a younger man having been substituted for one of the directors. How much younger was the new man than the director whose place he took.
Options:
A)24 years
B)26 years
C)28 years
D)27 years
E)None of the above
Rationale: Let the new man was younger than the director = x years and 3 years ago, the sum of ages of board of directors
= S – 8 × 3 = S – 24
Then, 3 years ago, average age of board of directors
= S−24/8
Now, S−24/8=S−x/8
⇒ x = 24 years
Shortcut Method : If the new young director would have been not substituted, then total age would have increased at present by 8 × 3 = 24 years.
Therefore, the new man is 24 years younger keeping the average at present same as 3 years ago.
Answer A
Answer: A
Question: What is the remainder when 121212.......(300) digits is divided by 99.
Options:
A)18
B)36
C)72
D)0
E)1
Rationale: 12/99=12
1212/99=24
121212/99=36
.
.
.
121212...(300)/99=(12*300)%99=36
if they say 300 digits then (12*150)%99=18
ANSWER:A
Answer: A
Question: 31, 29, 24, 22, 17, ?
Options:
A)15
B)23
C)13
D)25
E)28
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : A.
Answer: A