divelab/Sys2Bench huggingface dataset:
Question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination. How many miles did John drive?
Options:
A)235 miles.
B)245 miles.
C)225 miles.
D)265 miles.
E)275 miles.
Rationale: The total distance D traveled by John is given by
D = 45 * 2 + 3 * 45 = 225 miles.
Answer C
Answer: C
Question: If k, (k+200), (k+350), and 15*K are all multiples of A, then A could equal which of the following ?
Options:
A)20
B)A=25
C)75
D)100
E)150
Rationale: {Multiple of A} - {Multiple of A} = {Multiple of A}.
(K+200) - k = 200 = {Multiple of A}.
(K+350) - k = 350 = {Multiple of A}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Answer: B
Question: In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M?
Options:
A)278
B)2890
C)270
D)2702
E)1050
Rationale: 504/M = 384/800
(504 * 800) / 384 = M
M = 1050
Answer:E
Answer: E
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,071 bacteria each. How many bacteria are there approximately?
Options:
A)10^7
B)10^11
C)10^9
D)10^10
E)10^8
Rationale: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,071 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,071=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is E.
Answer: E
Question: The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
Options:
A)72
B)78
C)80
D)82
E)84
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 268 - (A + D) = 268 - 132 = 136.
B + B -28 = 136
B = (136 + 28)/2 = 82
ANSWER:D
Answer: D
Question: If 1+2+3+...+n=n (n+1), then
2 (1+3+5+....+99)=?
Options:
A)6000
B)5000
C)2500
D)6500
E)None of these
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 99=1+(n-1)2
=> n=50
Use value of n in (1)
then,
Sn = (50/2)(1+99) = 2500
Ans:- 2(Sn) = 5000
Hence (B) is correct
Answer : B
Answer: B
Question: 3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is:
Options:
A)2/9
B)1/9
C)8/9
D)7/9
E)6/9
Rationale: let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house
there will be 1 case when x,y,z will buy house a
another when they buy house b
and another when they buy house c
so the prob that they buy same house is 3*1/27=1/9
ANSWER:B
Answer: B
Question: Find the highest common factor of 36 and 84.
Options:
A)4 years
B)6
C)7
D)8
E)12
Rationale: 36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
Answer: Option E
Answer: E
Question: X, Y, Z working alone finish constructing a house in 4, 6 and 12 hrs. resp. X starts alone and works for 1 hr. He is then joined by Y and they work together for 1 hr. Finally Z joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
Options:
A)11.30 am
B)11.35 am.
C)11.40 am.
D)12 am
E)11.20am
Rationale: Let the total work be 12 units
Efficiency of X = 3 units/ hour
Efficiency of Y = 2 units/ hour
Efficiency of Z = 1 units/ hour
So, X completes 3 units of work by 10 am
So, X and Y completes 5 units of work by 11 am
Work left is 4 units ( 12 - 3 - 5 ) and combined efficiency of X, Y and Z is 6 units
So, time required to complete 4 units will be 4/6 => 4/6*60 = 40 minutes...
So they will require 40 minutes after 11 am to complete the remaining work...
Hence answer will be (C) 11:40 am
Answer: C
Question: Sandy bought 65 books for $1280 from one shop and 55 books for $880 from another shop. What is the average price that Sandy paid per book?
Options:
A)$12
B)$14
C)$16
D)$18
E)$20
Rationale: average price per book = (1280 + 880) / (65 + 55) = 2160 / 120 = $18
The answer is D.
Answer: D
Question: If the sum of a number and its square is 182, what is the number?
Options:
A)15
B)26
C)28
D)91
E)None of these
Rationale: Let the number = x
Then, x2 + x = 182
or, x2 + x – 182 = 0
or, x + 14x – 13x – 182 = 0
or, x(x + 14) – 13(x + 14) = 0
or, (x – 13)(x + 14) = 0
or, x = 13 (negative value is neglected)
Answer E
Answer: E
Question: The number which exceeds 16% of it by 42 is :
Options:
A)50
B)52
C)58
D)60
E)62
Rationale: Solution
Solution
Let the number be x.
x-16% of x =42
x-16/100x =42
x-4/25x=42
21/25x=42
x=(42x25/21)= 50
Answer A
Answer: A
Question: Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?
Options:
A)19 11/17%
B)15 11/17%
C)18 11/17%
D)17 11/17%
E)10 11/17%
Rationale: 850 --- 150
150 --- ? =>
=150/850 *100
=17 11/17%
Answer: D
Answer: D
Question: At the beginning of 2011, Albert invests $15,000 at 10% simple annual interest, $6,000 at 7% simple annual interest, and $x at 8% simple annual interest. If, by the end of 2011, Albert receives interest totaling 9% of the sum of his three investments, then the ratio of $x to the sum of his two other investments is
Options:
A)1 : 3
B)1 : 4
C)1 : 6
D)1 : 7
E)1 : 8
Rationale: Total interest earned = (10/100)*15000 + (7/100)*6000 + (8/100)*x = (192,000+8x)/100
Also, Total interest earned = (9/100)*(15000 + 6000 + x) = (9/100)*(21000 + x)
i.e. (9/100)*(21000 + x) = (192,000+8x)/100
i.e. 189,000 + 9x = 192,000+8x
i.e. x = 3000
Required ratio = x / (15000 +6000) = 3000 / 21000 = 1/7
Answer: option D
Answer: D
Question: A single pipe of diameter x has to be replaced by six pipes of diameters 10 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is:
Options:
A)13 cm
B)18 cm
C)24.5 cm
D)24 cm
E)25 cm
Rationale: Volume of water flowing through 1 pipe of dia x = Volume discharged by 6 pipes of dia 6 cms
As speed is same, area of cross sections should be same.
Area of bigger pipe of dia x = Total area of 6 smaller pipes
pi*R^2 = 6 * pi* 5^2
R = 12.25 cm
Dia = 24.5 cm
ANSWER:C
Answer: C
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places)?
Options:
A)178.26
B)178.29
C)178.2
D)178.23
E)178.21
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm
= 180 cm - 1.71 cm = 178.29 cm.
Answer:B
Answer: B
Question: The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?
Options:
A)1.
B)2.
C)3.
D)4.
E)5.
Rationale: X divided by 10 gives reminder of 2. X can be 2/12/22....
X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....
If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2
Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2
Hence the answer must be 2 (B)
Answer: B
Question: First code word is defined to be a sequence of 5 different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J,
Second code word is defined to be a sequence of 5 different letters chosen from the 11 letters A, B, C, D, E, F, G, H, I,J and K.
What is the ratio of the number of code words that can be formed from First Code to the Second Code.
Options:
A)1 to 1
B)5 to 11
C)6 to 11
D)11 to 6
E)11 to 5
Rationale: First Code word can be formed from permutation of 10 letters to form 5 letters word = 10P5 = 10!/5!
Second Code word can be formed from permutation of 11 letters to form 5 letters word = 11P5 = 11!/6!
Ratio of the number of code words that can be formed from First Code to the Second Code
= (10!/5!) / (11!/6!)
= 10*9*8*7*6 / 11*10*9*8*7
= 6/11
Answer: C
Answer: C
Question: A standard Veggiematik machine can chop 30 carrots in 5 minutes. How many carrots can 4 standard Veggiematik machines chop in 4 minutes?
Options:
A)88
B)90
C)96
D)121
E)137
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 30 Carrots - 5 minutes,
1 standard Veggiematik machine - 6 Carrots - 1 minute,
Now
4 standard Veggiematik machine - ? Carrots - 4 minutes,
Hence = 6X4X4 =96 Carrots
Answer C
Answer: C
Question: If shares of two persons in profits are Rs.300 and Rs.600 then ratio of their capitals is
Options:
A)3:4
B)2:3
C)4:3
D)1:3
E)1:2
Rationale: total profit =1000
ratio=300/600
=1:2
ANSWER:E
Answer: E
Question: In how many ways the letters of the word COMPUTER be arranged?
Options:
A)40320
B)42334
C)45000
D)34200
E)76581
Rationale: Total ways of arranging the letters = 8! = 40320 ways.
A)
Answer: A
Question: Set S consists of integers {2,3,4,5}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 5?
Options:
A)5/6
B)1/2
C)2/3
D)1/4
E)2/7
Rationale: Number of ways you can choose 2 from 4 = 4C2 = 6
E = event of getting the 2 numbers is more than 5 = (2,4),(2,5),(3,4)(3,5),(4,5) = 5
probability = 5/6
Answer is A
Answer: A
Question: The product of first twelve positive integers is divisible by all of the the following EXCEPT?
Options:
A)210
B)88
C)75
D)60
E)34
Rationale: The product of the first twelve positive integers, 12!12! contains only the primes less than 12 (2, 3, 5, 7, 11), which means that the product won't be divisible by any number containing higher prime number.
Now, you can notice that 34=2*17 --> 12! is not divisible by 17 (prime >11), thus 12! is not divisible by 2*17=34 too.
Answer: E.
Answer: E
Question: Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian?
Options:
A)23 m
B)23 2/9 m
C)27m
D)27 7/9m
E)29 7/9m
Rationale: relative speed=20kmph=50/9m/sec
length of the train=50/9*5=250/9=27 7/9m
ANSWER:D
Answer: D
Question: Set S is the prime integers between 0 and 40. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
Options:
A)15/56
B)3/8
C)15/28
D)5/8
E)3/4
Rationale: Total number of combinations=12C3=220................(1)
Total number of combinations including 2 and two other numbers=11C2=55......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(220-55)=165
So, probability=165/220=3/4
E
Answer: E
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
Options:
A)20/67
B)20/63
C)20/28
D)20/29
E)20/21
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄
= (10 * 4)/126
= 20/63
Answer: B
Answer: B
Question: What is the total number of integers between 10 and 50 that are divisible by 2?
Options:
A)18
B)19
C)22
D)25
E)10
Rationale: 12, 14, 16, ..., 46,48
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (48 - 12) / (2) + 1 = 36/2 + 1 = 18 + 1 = 19
Answer is B
Answer: B
Question: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 80 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
Options:
A)53
B)66
C)60
D)85
E)80
Rationale: Yes, ensure that you understand the relation thoroughly!
Cost per liter = K * Fraction of Spirit
80 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 40 cents. Fraction of spirit is 1/2.
40 = K * (1/2)
K = 80
Cost per liter = 80 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 80 * (1/3) * 3 = 80 cents
E. 80 cents
Answer: E
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $21 more than Eliot in his account. How much money does Eliot have in his account right now?
Options:
A)$110
B)$120
C)$180
D)$220
E)$210
Rationale: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 21 + 1.2E ==> 11A =210 +12E -------(2)
Substituting (1) in (2):
13E = 210+12E ==>E = 210
E
Answer: E
Question: Three maths classes: X, Y and Z take an algebra test. The average score of class X is 83. The average score of class Y is 76. The average score of class Z is 85. The average score of class X and Y is 79 and average score of class Y and Z is 81. What is the average score of classes X, Y, Z?
Options:
A)81.5
B)80.5
C)83
D)78
E)87
Rationale: Let the number of students in classes X, Y and Z be A, B and C respectively.
Then, total score of X= 83A, total score of Y = 76B, total score of Z = 85C.
Also given that,
(83A + 76B) / (A + B) = 79
=>4A = 3B.
(76B + 85C)/(B + C) = 81
=>4C = 5B,
=>B = 4A/3 and C = 5A/3
Therefore, average score of X, Y, Z = ( 83A + 76B + 85C ) / (A + B + C) = 978/12 = 81.5.
ANSWER:A
Answer: A
Question: Find the cost price of an item if by selling at Rs.890, a profit of 15% is made?
Options:
A)Rs.256
B)Rs.756
C)Rs.656
D)Rs.956
E)Rs.356
Rationale: SP = 890
CP = (SP)*[100/(100+P)]
= 890 * [100/(100+15)]
= Rs.756
Answer: B
Answer: B
Question: Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Options:
A)2:3
B)6:7
C)4:3
D)9:16
E)10:2
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = âˆšb : âˆša = âˆš16 : âˆš9 = 4 : 3.
ANSWER C
Answer: C
Question: An amount of money is to be divided between R, S and T in the ratio of 3:6:12. If the difference between the shares of R and S is Rs.1800, what will be the difference between S and T's share?
Options:
A)1266
B)3000
C)2866
D)3600
E)2678
Rationale: 6-3 =3.... > 1800
12-6 = 6 => 1800/3*6 = 3600
Answer: D
Answer: D
Question: How many positive integers less than 240 are multiple of 4 but NOT multiples of 6?
Options:
A)40
B)31
C)42
D)53
E)64
Rationale: From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. Answer choice A is correct here.
Answer: A
Question: The total age of A and B is 15 years more than the total age of B and C. C is how many year younger than A
Options:
A)A)11
B)B)12
C)C)13
D)D)14
E)E)15
Rationale: Explanation:
Given that A+B = 15 + B + C
=> A – C = 15 + B – B = 15
=> C is younger than A by 15 years
Answer: Option E
Answer: E
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds Y that it is an ace?
Options:
A)1/52
B)1/26
C)1/13
D)1/4
E)5/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability Y that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: C
Question: Let d > c > r > a. If c is twice as far from a as it is from d, and r is twice as far from c as it is from a, then (d - r)/(d - a) = ?
Options:
A)2/9
B)1/3
C)2/3
D)7/9
E)3/2
Rationale: Draw a number line and label with x and y. You would have:
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d -r and d -a
d - r= x +2y = 7/2 y
d - a = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D
Answer: D
Question: If a, g, and c are consecutive even integers and a < g < c, all of the following must be divisible by 4 EXCEPT
Options:
A)a + c
B)g + c
C)ac
D)(bc)/2
E)(abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - g + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: B
Question: A bag contains 3red, 2blue and 3green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)2/21
B)3/41
C)3/28
D)3/31
E)5/32
Rationale: P(Both are red),
=3C2/8C2=6C213C2
=3/28
C
Answer: C
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 51 kmph, find the speed of the stream?
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)17 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 = 51/3 = 17 kmph
ANSWER:E
Answer: E
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
Options:
A)1/7
B)2/8
C)3/9
D)4/5
E)113/7
Rationale: Explanation:
(x â€“ 5)/15 + x/20 = 1
x = 11 3/7 days
Answer:E
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
Options:
A)287
B)699
C)677
D)168
E)100
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 6 = 100 m
Answer: E
Answer: E
Question: box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/129
B)1/124
C)1/128
D)1/139
E)1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer: E
Answer: E
Question: Mean of 3 numbers is 10 more than the least of the numbers and 15 less than greatest of the 3. If the median of 3 numbers is 5, Find the sum of the 3 numbers?
Options:
A)33
B)30
C)28
D)27
E)01
Rationale: Ans: Median is when the given numbers are arranged in ascending order, the middle one. Let the numbers are x, 5, y where x is the least and y is greatest.
Given that x+5+y3=x+10x+5+y3=x+10
and x+5+y3=y−15x+5+y3=y−15
Solving we get x = 0 and y = 25.
So sum of the numbers = 0 + 5 + 25 = 30
Answer:B
Answer: B
Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number V is
Options:
A)74
B)V=75
C)V=175
D)V=680
E)690
Rationale: I solved this question by plugging in numbers from the answer choices.
A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.
B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer isB
Answer: B
Question: Insert the missing number
2, ..., 8, 16, 32, 64, 128, 256
Options:
A)6
B)5
C)4
D)3
E)8
Rationale: series is 2* Previous Number.
ANSWER:C
Answer: C
Question: According to a survey, at least 75% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
Options:
A)15%
B)20%
C)25%
D)0%
E)30%
Rationale: It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 75 - (100-75) = 50%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 50 - (100-80) =30%
E
Answer: E
Question: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 13 cm?
Options:
A)216cm2
B)238cm2
C)240cm2
D)247cm2
E)250cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (13)
= 247 cm2
Answer:D
Answer: D
Question: Average between two sets of numbers is closer to the set withmore no's?
Options:
A)80
B)90
C)110
D)120
E)130
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: B
Question: How long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak, but due to the leak it will take one additional hour to be filled?
Options:
A)12 hours
B)111 hours
C)15 hours
D)14 hours
E)11 hours
Rationale: Part filled without leak in 1 hour = 1/3
Part filled with leak in 1 hour = 1/4
Work done by leak in 1 hour
=1/3âˆ’1/4=12 hours
Answer:A
Answer: A
Question: 3 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
Options:
A)12
B)15
C)18
D)36
E)24
Rationale: The list should be WMWMW. Hence, from women 3! And men 3!, we get (3!)(3!)=36. Therefore, the correct answer is D.
Answer: D
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)13, 3
B)12, 6
C)15, 3
D)14, 4
E)None of these
Rationale: Explanation:
Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: Option D
Answer: D
Question: Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
Options:
A)22
B)77
C)28
D)18
E)19
Rationale: 93 + 123 + 153 = a3 => a
= 18
Answer: D
Answer: D