divelab/Sys2Bench huggingface dataset:
Question: Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high.
Options:
A)878 cm^2
B)858 cm^2
C)838 cm^2
D)868 cm^2
E)None of them
Rationale: Volume = (16 x 14 x 7) m^3 = 1568 m^3.
Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] cm^2 = (2 x 434) cm^2 = 868 cm^2.
Answer is D
Answer: D
Question: If x is a positive integer with fewer than 3 digits, what is the probability W that x*(x + 1) is a multiple of either 4 or 5?
Options:
A)4/99
B)2/25
C)8/99
D)49/100
E)86/99
Rationale: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.
We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability W that x(x+1) is a multiple of either 4 or 5.
When will this happen? If either x OR (x+1) is a multiple of 4 or 5.
Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.
Out of the numbers from 1 to 20:
4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20
So, 14 out of the first 20 numbers match our criteria. Since:
probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (E) is the only answer greater than 1/2, we go with (E).
Answer: E
Question: Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
Options:
A) 20%
B) 42%
C) 44%
D) 66%
E) 84%
Rationale: You are correct. People who cover local politics are a subset of people who cover politics.
25% of reporters who cover politics do not cover local politics so 75% DO cover local politics.
Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters
Reporters covering politics/All Reporters = 25/75 = 1/3
Reporters not covering politics/All Reporters = 2/3 = 66%=D
Answer: D
Question: What least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Sol. On dividing 2000 by 17, we get 11 as remainder.
Required number to be subtracted = 11.
Option A
Answer: A
Question: The least number which should be added to 1920 so that the sum is exactly divisible by 5,6,4 and 3 is :
Options:
A)3
B)13
C)23
D)33
E)28
Rationale: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 1920 by 60, the remainder is 32.
∴ Number to be added = (60-32) = 28. Answer E
Answer: E
Question: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 40mph, what was his average speed over the three hour portion of his ride?
Options:
A)14 mph
B)40 mph
C)70/3 mph
D)80/3 mph
E)34 mph
Rationale: Average speed for first two hours, S1 = 40 mph
Distance travelled in these two hours, D1 = 80 miles
Average speed for the entire 5 hour ride, S = 40 mph
Total Distance traveller in the entire 5 hour ride, D = 40 x 5 = 200 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 200 - 80 = 120
Average speed for the latter 3 hour period S2 = D2/3 = 120/3=40
Hence, the correct answer is B
Answer: B
Question: Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
Options:
A)5040
B)2520
C)360
D)120
E)42
Rationale: 6! = 720
720/2=360 half the time carmelo is in front, vice versa
Answer:
(C) 360
Answer: C
Question: 60 % of 2 is equal to
Options:
A)1.2
B)0.4
C)0.6
D)0.7
E)0.9
Rationale: 60 % of 2 = (60 / 100) * 2 = 1.2
Answer: Option A
Answer: A
Question: Find the cost price of an item if by selling at Rs.320, a profit of 6% is made?
Options:
A)Rs.300
B)Rs.200
C)Rs.500
D)Rs.100
E)Rs.310
Rationale: SP = 320
CP = (SP)*[100/(100+P)]
= 320 * [100/(100+6)]
= Rs.300
Answer: A
Answer: A
Question: The speed at which a man can row a boat in still water is 6 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 80 meters?
Options:
A)28
B)32
C)36
D)40
E)44
Rationale: The speed of the boat downstream = 6 + 3 = 9 km/hr
9 km/hr * 5/18 = 2.5 m/s
The time taken to cover 80 meters = 80/2.5 = 32 seconds.
The answer is B.
Answer: B
Question: A shopkeeper sold an article at $100 with 15% profit. Then find its cost price?
Options:
A)$120
B)$100
C)$91
D)$87
E)$69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/115 = $87(approximately)
Answer is D
Answer: D
Question: Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome, if he will buy no more than 3 packages of the generic golf tees?
Options:
A)16
B)10
C)8
D)22
E)2
Rationale: At least 20 golf tees for each member of his foursome = total of at least 4*20 = 80 tees.
3 packages of the generic golf tees, that are packaged by the dozen = 3*12 = 36 tees.
So, Bill must by at least 44 Aero tees. They come by the pair, hence he must by at least 44/2 = 22 packages of Aero flight tees.
Answer: D
Answer: D
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
Options:
A)2 years
B)8 years
C)3 years
D)4 years
E)1 years
Rationale: 28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer:D
Answer: D
Question: There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
Options:
A)3
B)6
C)9
D)15
E)21
Rationale: List down possibilities: From only 1 box all the way to all 6
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.
Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
Option E
Answer: E
Question: In a kilo meter race, if A gives B a 40 m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40 m. Find the time taken by B to run 5,000 m?
Options:
A)150 s
B)450 s
C)750 s
D)825 s
E)925 s
Rationale: When B is given a 40 m start then B runs 960m in T secs and A runs 1000m in T-19 secs.
When B is given a 30 second start then B runs 1000m in t secs and A runs 960m in t - 30 secs.
Assume that the speed of A (Va) and B (Vb) is constant in both situations.
Then Vb = 960 ÷ T = 1000 ÷ t, and Va = 1000 ÷ (T - 19) = 960 ÷ (t - 30)
So 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.
Substituting for t in 960t = 1000T
gives : -960T + 282240 = 1000T
1960T = 282240
T = 144
B 's speed is 960 / T = 960 / 144 = 6.67 metres per second.
Assuming the same constant speed to run 5000 metres then the time taken is
5000 / 6.67 = 750 seconds
ANSWER:C
Answer: C
Question: Which of the following CANNOT be a value of 5/(x–5)?
Options:
A)-1
B)-1/2
C)0
D)2
E)5
Rationale: The question doesn't ask for the value of x here, but for the possible results of the equation.
If 5/(x-5) = 0, then the numerator must be 0. But since the numerator is 5, the fraction can not be equal to 0.
The answer is C.
Answer: C
Question: The average weight of 4 person's increases by 3 kg when a new person comes in place of one of them weighing 70 kg. What might be the weight of the new person?
Options:
A)75 kg
B)82 kg
C)86 kg
D)Data inadequate
E)None of these
Rationale: Total weight increased = (4 x 3) kg = 12 kg.
Weight of new person = (70 + 12) kg = 82 kg.
Answer: Option B
Answer: B
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)11
B)26
C)21
D)89
E)62
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Answer: D
Question: When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
Options:
A)4.5
B)5
C)5.6
D)7
E)7.2
Rationale: if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A
Answer: A
Question: What is the tens digit of 6^21?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3.
The tens digit of 6^3=216 is 1.
The tens digit of 6^4=...96 is 9.
The tens digit of 6^5=...76 is 7.
The tens digit of 6^6=...56 is 5.
The tens digit of 6^7=...36 is 3 again.
etc...
21 has the form 5n+1, so the tens digit of 6^21 is 5.
The answer is C.
Answer: C
Question: Trapezoid ABCD has AB parallel to CD, with \ADC = 90o. Given that AD = 5, BC = 13
and DC = 18, compute the area of the trapezoid.
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: The trapezoid can be divided into a right triangle with legs of length 5 and 12, and
a rectangle with side lengths 5 and 6. This gives an area of 60 .
correct answer D
Answer: D
Question: The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
Options:
A)221
B)240
C)388
D)288
E)113
Rationale: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x - 2) = 84
Second least number of the other set = 2(84) - 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
Answer: B
Answer: B
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 90 players took part in that tournament.
How many matches were played?
Options:
A)99 matches.
B)89 matches.
C)77 matches.
D)66 matches.
E)55 matches.
Rationale: Solution:
89 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 89 matches were played.
Answer B
Answer: B
Question: If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 30 minutes?
Options:
A)165km
B)170km
C)176.4km
D)180km
E)190km
Rationale: 14 m/s = 14 * 18/5 kmph
3 hours 30 minutes = 3 1/2 hours = 7/2 hours
Distance = speed * time = 14 * 18/5 * 7/2 km = 176.4 km.
Answer:C
Answer: C
Question: If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
A)2m −1
B)4m
C)6m
D)7m
E)6m/5
Rationale: 20m - n = p
Add n to both sides:
20m = n + p
Add m to both sides:
21m = n + p + m
Now, divide both sides by 3
7m = (n + p + m)/3 = the average of n, p, and m
D
Answer: D
Question: 3 men or 6 women can do a piece of work in 21 days. In how many days will 12 men and 8 women do the same work?
Options:
A)63/16 days
B)15/4 days
C)18/4 days
D)11/4 days
E)35/4 days
Rationale: 3M = 6W ---- 21 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 21 32 -----?
6 * 21 = 32 * x => x = 63/16 days
Answer:A
Answer: A
Question: An outlet pipe can empty 1/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
Options:
A)4/9
B)4/3
C)2/9
D)4/8
E)4/1
Rationale: 1/3 ---- 12
? ----- 8 ==> 2/9
Answer: C
Answer: C
Question: Which one the following fractions has the Highest value?
Options:
A)A)120/847
B)B)120/849
C)C)120/874
D)D)120/877
E)E)240/1700
Rationale: 240/1700 = 120/850.
Now, all options have the same numerator 123.
If numerator is same, the fraction with the Highest value will be the one with the Lowest denominator.
Answer (A).
Answer: A
Question: How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
Options:
A)20.0 kgs
B)12.5
C)16.0 kgs
D)200.0 kgs
E)None of these
Rationale: Explanation :
Given, there is 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.
C.P of 1 kg of rice of 1st kind = Rs. 42.
C.P of 1 kg of rice of 2nd kind = Rs. 24.
Mean price = Rs. 40
By the rule of alligation, we have:
C.P. of 1kg of C.P. of 1kg of
rice of 1st rice of 2nd
kind (Rs. 42/kg) kind (Rs. 24/kg)
\ /
Mean Price
(Rs. 32/kg)
/ \
40 - 24 : 42 - 32
(8) (10)
Let the amount of Basmati rice being mixed be x kgs.
=>8/10=x/25.
=>x=20.
Hence, amount is 20.0 kgs.
Answer : A
Answer: A
Question: The difference between the place values of 9 and 4 in the number 529435 is
Options:
A)8500
B)8900
C)8600
D)6970
E)None
Rationale: Sol.= (Place value of 9) – (place Value of 4)= (9000 - 400)= 8600 Answer C
Answer: C
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 38 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Options:
A)405
B)420
C)440
D)447
E)490
Rationale: Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 38t
t=14
Distance traveled by car X from the time car Y began traveling until both cars stopped is
35 x 14
= 490 miles
Answer:- E
Answer: E
Question: A and B started a business with their capitals Rs. 24,000 and 48,000 respectively. Annual profit will be distributed between them in the ratio
Options:
A)1:4
B)2:3
C)1:2
D)1:5
E)2:5
Rationale: 24,000:48,000
Ans. 1:2
ANSWER:C
Answer: C
Question: An article when sold for 200 fetches 25 per cent profit. What would be the percentage profit/loss if 6 such articles are sold for 1,056?
Options:
A)10 per cent loss
B)10 per cent profit
C)5 per cent loss
D)5 per cent profit
E)None of these
Rationale: CP = 200⁄125 × 100 = 160
∴ CP of 6 articles = 6 × 160 = 960
∴ profit = 1056 – 960 = 96
Percentage profit = 96⁄960 × 100 = 10%
Answer B
Answer: B
Question: There are 4 girls and 4 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
Options:
A)A)1/8!
B)B)6!5!/8!
C)C)2*4!4!/8!
D)D)2∗6!6!/12!
E)E)6!7!/12!
Rationale: If girls are alternate, then only no 2 girls can be together.
So among 8 places, girls can be seated in 4 alternate places in 4! ways.
And boys can be seated in the remaining 4 places in 4! ways.
Therefore total number of ways = 4! * 4!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*4! * 4!
Also total number of ways to fill 8 places = 8!
Hence probability =2∗4!4!/8!
Answer:C
Answer: C
Question: In a village they organize 4 programs for an festival. The festival occurs in 2 days. In how many ways that the 4 programs can be divided for 2 days festival?
Options:
A)12
B)10
C)6
D)4
E)2
Rationale: Here 4 programs organize for 2 day festival. So, 4C2 ways to solve this problem.
4C2=4!/2!*2!
4C2=4*3*2!/2!*2*1=6
There are 6 ways to divided the programs.
Answer:option C
Answer: C
Question: Which of the following inequalities is equivalent to –2 < x < 4 ?
Options:
A) | x – 2 | < 4
B) | x – 1 | < 3
C) | x + 1 | < 3
D) | x + 2 | < 4
E) None of the above
Rationale: First remove the mod
then set the expression to 0
then get a value of X
then add and subtract the value from the given number on the RHS
Lets try with an example (B) --------------> | x – 1 | < 3
First remove the mod -------------------> x-1
then set the expression to 0--------------> x-1=0
then get a value of x---------------------> x=1
then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2
the range become -2 to 4 correct answer
Now try its with an incorrect option (C) | ----------> |x + 1 | < 3
First remove the mod --------------------------> x+1
then set the expression to 0----------------------> x+1=0
then get a value of x------------------------------> x=-1
then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4
the range become -4 to 2 Incorrect
THE CORRECT ANSWER IS B
Answer: B
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 2500?
Options:
A)7
B)9
C)11
D)13
E)15
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 < 2500, then the greatest possible length of integer z is 11.
The answer is C.
Answer: C
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 69 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
Options:
A)2000
B)2100
C)2200
D)2300
E)2400
Rationale: 1 percent for 3 years= 69
1 percent for 1 year = 23
=> 100 percent = 2300
ANSWER:D
Answer: D
Question: It takes Avery 2 hours to build a brick wall while Tom can do it in 5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Options:
A)25 minutes.
B)30 minutes.
C)40 minutes.
D)1 hour and 30 minutes
E)1 hour and 20 minutes
Rationale: Avery's efficiency is 100/2 = 50%
Tom's = 100/5= 20%
they worked together for 1 hour and finished 70% of the job
remaining = 30 %
Tom will complete 20% in 60 minutes , and
10% in 60*10/20 minutes = 30 minutes
Time taken by Tom to finish the remaining on his own = 60+30 = 90 minutes
ANSWER:D
Answer: D
Question: E=√[2√63 + 2/(8+3√7)] =
Options:
A)8 + 3√7
B)4 + 3√7
C)8
D)4
E)√7
Rationale: In these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7)
sqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}]
E=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4
Answer is 4.D
Answer: D
Question: T is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can T be?
Options:
A)300,000
B)349,999
C)350,000
D)399,999
E)400,000
Rationale: T 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
Answer: B
Question: A box of paper clips contains 100 clips. If an office uses paper clips at the rate of 15 per 100 pieces of outgoing mail, how many boxes will be required for the 4000 pieces of outgoing mail?
Options:
A)4 boxes
B)5 boxes
C)6 boxes
D)7 boxes
E)8 boxes
Rationale: 15clips --- 100 pieces
x clips --- 4000 pieces
x = 4000/100 * 15 = 600 clips
1 box -- 100 clips
y box -- 600 clips
y = 600/100 = 6 boxes
ANSWER:C
Answer: C
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 3 is
Options:
A)3
B)189
C)221
D)227
E)230
Rationale: In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be B.
Answer: B
Question: A camera lens filter kit containing 5 filters sells for $52.50. If the filters are purchased individually, 2 of them are priced at $6.45 each, 2 at $11.05 each, 1 at $15.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
Options:
A)3.76%
B)4.76%
C)5.76%
D)6.76%
E)7.76%
Rationale: Cost of kit = $52.50
If filters are purchased individually - $6.45*2 + $11.05*2 + $15.50 = $50.50
Amount saved = $52.50 - $50.50 = $2.50
Required %age = ($2.50/$52.50)*100 = 4.76%
So, the correct answer is B.
Answer: B
Question: In an objective competitive exam, a correct answer score 4 marks and on a wrong answer 2 marks are negatively added. A student scores 420 marks from 150 question. How many answers were correct ?
Options:
A)150
B)155
C)140
D)120
E)165
Rationale: let x be the correct answer and y be the wrong answer
so the total number of questions is (x + y) = 150.....(1)
=> 4x - 2y = 420.....(2)
By solving (1) & (2), we get
=> 6x = 720
hence x = 120
Therefore, number of correct answers are 120.
Answer D
Answer: D
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 8 questions. If each question has 4 answer choices, and Kim answers every question, in how many different ways can she complete the test?
Options:
A)a 4^8
B)b 400
C)c 5^8
D)d 8^5
E)e 40^40
Rationale: different ways to solve each question is 4.
So, 4*4*4*4.. 8 times ----> 4^8
Answer will be A
Answer: A
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/2
B)5/2
C)5/3
D)5/6
E)5/8
Rationale: P(at least one graduate)
= 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Answer: D
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Options:
A)33
B)88
C)20
D)72
E)27
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
Answer: C
Answer: C
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 16000, then find his savings?
Options:
A)6769
B)3200
C)3201
D)2319
E)7591
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 16000 => x = 3200
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3200.
Answer:B
Answer: B
Question: The average age of 15 students of a class is 16 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is?
Options:
A)11 years
B)17 years
C)26 years
D)14 years
E)12 years
Rationale: Age of the 15th student
=[15 * 16 - (14 * 5 + 16 * 9)]
= (240 - 214)
= 26 years.
Answer:C
Answer: C
Question: A 6-liter solution is 25% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
Options:
A)2.1
B)2.4
C)2.7
D)3.0
E)3.3
Rationale: Let x be the amount of pure alcohol required.
0.25(6) + x = 0.5(x+6)
0.5x = 3 - 1.5
x = 3 liters
The answer is D.
Answer: D
Question: How many integers are divisible by 3 between 10! and 10! + 20 inclusive?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 0! is divisible by 3 - The way I look Factorials is that any number included will also be divisible by the product. 10,9,8,7,6,5,4,3,2,1 are all divisors of 10!
There are 6 numbers between 10! and 10!+20 that are divisible by 3.
Hence B: 7
Answer: B
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
Options:
A)297
B)278
C)287
D)140
E)272
Rationale: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
Answer: D
Answer: D
Question: A can do double work of B.so,A take 15 days less than B in doing a work.then both together in how much days will finish that work?
Options:
A)10
B)12
C)15
D)8
E)16
Rationale: let alone finish a work in x days.,then B will take 2x days
2x-x=15,x=15.
so,A alone finish this work in 15 days and B alone finish this work in 30 days
work of A in 1 days=1/15,work of B in 1 days=1/30
(A+B) work in 1 days=1/10
so, together they finish the work in 10 days
answer A
Answer: A