divelab/Sys2Bench huggingface dataset:
Question: Convert 500 miles to KM?
Options:
A)600KM
B)700KM
C)800KM
D)900KM
E)1000KM
Rationale: 800KM
500*1.6=800
Answer:C
Answer: C
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 180 m, its area is?
Options:
A)90
B)882
C)277
D)261
E)281
Rationale: 5x + 12x + 13x = 180 => x = 6
a = 30, b = 72, c = 78
S = (30 + 72 + 78)/2 = 90
Answer: A
Answer: A
Question: A is twice as good workman as B, and together they complete a work in 12 days. In how many days can the work be complete by B alone?
Options:
A)36 days
B)65 days
C)45 days
D)75 days
E)95 days
Rationale: B=3A
36 days
A
Answer: A
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number T of races we need to conduct to get the top 3 fastest horses?
Options:
A)5
B)7
C)8
D)10
E)11
Rationale: T=7 is the correct answer.
Good solution Buneul.B
Answer: B
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
Options:
A)Rs. 110.75
B)Rs. 115.75
C)Rs. 124.75
D)Rs. 125
E)Rs. 126
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: C
Question: How much time does a train 225 metres long running at 90 km/hr take to pass a pole?
Options:
A)7.9s
B)2.5s
C)7.5s
D)9s
E)7.4s
Rationale: Explanation:
90 km/hr = 90 * 5/18 = 25 m/s
Speed = distance/time; v = d/t
25 = 225/t
t = 9s
ANSWER: D
Answer: D
Question: X is an even number and( Y +2) is a positive odd number. Which of the following expressions cannot be even?
Options:
A)X^5
B)X^4
C)X^3
D)X^2
E)Y+2
Rationale: Y+2 WILL BE ODD
E
Answer: E
Question: John has exactly 31 pens, and each pen is either bule, black, or red. If he has 5 more black pens than red pens, and twice as many blue pens as black pens, how many blue pens does john has ?
Options:
A)15
B)18
C)20
D)22
E)17
Rationale: x = the number of blue pens
y = the number of black pens
z = the number of red pens
From the first sentence we have
Equation #1: x + y + z = 31
...he has 5 more black pens than red pens...
Equation #2: y = 5 + z
...twice as many blue pens as black pens...
Equation #3: x = 2y
Solve equation #1 for z: z = y - 5
Now, we can replace both x and z with y in Equation #1
2y + y + (y - 5) = 31
4y - 5 = 31
4y = 36
y = 9
There are 9 black pens. This is 5 more than the number of red pens, so z = 4. Hence the answer is. x = 18, and just for check 18 + 9 + 4 = 31.
Answer = 18,(B)
Answer: B
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)16%
B)87%
C)40%
D)17%
E)18%
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP
= Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer:C
Answer: C
Question: If x is an integer and |1-x|<2 then which of the following must be true?
Options:
A)x is not a prime number
B)x^2+x is not a prime number
C)x is positive
D)Number of distinct positive factors of x+2 is a prime number
E)x is not a multiple of an odd prime number
Rationale: 1−x|<2 = -2<(1-x)<2
= -3<-x<1
= 3>x>-1
So x can hold values of 0,1 & 2 to satisfy the condition. Now we can evaluate the choices.
A) 1 & 2 primes, so incorrect
B) 1^2+1=2 is a prime, so incorrect
C) 0 is not +ve, So incorrect
D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) & 4 has 3 factors (prime). Hence correct choice.
E) 2 is multiple of 1. So incorrect.
Hence Answer D.
Answer: D
Question: From the integer n, if n*n*n is odd, then what is true from below options?
Options:
A)n is odd and n*n is even
B)n is odd
C)n*n is even
D)n*n is odd
E)n is even
Rationale: n is odd and n*n is even
Option A
Answer: A
Question: If four students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then one row is empty. How many students have to sit a row such that each row has equal number of students and all students are seated?
Options:
A)0
B)1
C)4
D)5
E)9
Rationale: Let there be a rows.
Then 4a + 6 = 6(a-1) [equating the number of students]
=> a= 6
and total number of students = 30
Therefore 5 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (D)
Answer: D
Question: At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $10.50 per hour, how much less than a manager does a chef earn each hour?
Options:
A)$1.40
B)$2.40
C)$3.40
D)$4.40
E)$4.30
Rationale: Manager wages per hour = $10.50
Dishwasher wages per hour = half of manager's wages. = 1/2($10.50) ==> $5.25
Chef wages per hour = 20% greater than Dishwasher wages
--> 20% of $5.25 = (20*($5.25)) /100
--> ($95)/100
--> $0.95
Therefore,
Chef wages per hour = $5.25 + $0.95 ==> $6.20
Difference of wages between manager and chef = $10.50 - $6.20 ==> $4.30
ANSWER:E
Answer: E
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 32mph. If he wants to travel 80 miles in 4 hours using bike and walking at their constant rates, how much distance would he require to walk?
Options:
A)20
B)30
C)48
D)60
E)72
Rationale: Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 32
Time traveled in bike = t2
d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 32*t2 = 80
t1 + 4*t2 = 10 ----- (1)
Given: t1 + t2 =4 ----- (2)
(1) - (2) -->3 t2 = 6 , t2=2 and t1 = 8 - 2 = 6
Walking distance = s1*t1 = 8*6 = 48
Answer: C
Answer: C
Question: The slant height of a cone is 14 cm and radius of the base is 12cm, find the curved surface of the cone.
Options:
A)150
B)170
C)48
D)528
E)600
Rationale: π * 12*14 =528
Answer:D
Answer: D
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)1/114
B)2/117
C)1/216
D)2/111
E)3/111
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 8:30 a.m. and drives north on the same highway at an average speed of 75 km per hour. Mr. Dinkle will
Options:
A)overtake Mr. Smitherly at 9:30 a.m.
B)overtake Mr. Smitherly at 10:30 a.m.
C)overtake Mr. Smitherly at 11:00 a.m.
D)be 30 miles behind at 8:35 a.m.
E)never overtake Mr. Smitherly
Rationale: After thirty minutes, Mr. Smitherly is ahead by 25 km.
Mr. Dinkle gains on Mr. Smitherly 25 km each hour.
1 hour after 8:30 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is A.
Answer: A
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 15 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 15 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 15-3 = 12. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer E
Answer: E
Question: What's 8 x 600?
Options:
A)4,800
B)4,600
C)4,400
D)5,400
E)6,800
Rationale: A. 4,800
Answer: A
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of hydrogen are there in 171 grams of water?
Options:
A)11
B)13
C)15
D)17
E)19
Rationale: (2/18)*171 = 19 grams
The answer is E.
Answer: E
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 pens per minute. At this rate, how many pens could 10 such machines produce in 4 minutes?
Options:
A)1500
B)1545.6
C)1640.33
D)1800
E)None of these
Rationale: Explanation :
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
machines 6:10|
|::270:x
time 1:4 |
=> 6 * 1 * x = 10 * 4 * 270
=> x = (10 * 4 *270)/6
=> x = 1800
Answer : D
Answer: D
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 588 sq m, then what is the breadth of the rectangular plot?
Options:
A)16
B)17
C)18
D)19
E)14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 588
3b2 = 588
b2 = 196
b = 14 m.
Answer: Option E
Answer: E
Question: If (5^9)(9^5)=3(15^x), what is the value of x?
Options:
A) 7
B) 9
C) 11
D) 13
E) 15
Rationale: (5^9)(9^5)=3(15^x)
=> 5^9 * 3^10 = 3 * 3^x * 5^x
=> 5^9 * 3^10 = 3^(x+1) * 5^x
Value of x = 9
Answer B
Answer: B
Question: At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 5 tickets?
Options:
A)20%
B)33.3%
C)40%
D)60%
E)66.6%
Rationale: let the price of a ticket be Rs.100, so 3 tickets cost 300 & 5 tickets cost 500
5 tickets purchased at price of 3 tickets ie., for 300, so amount saved s Rs.200,
% of 5 tickets = (200 /500)*100 =40 %
ANSWER:C
Answer: C
Question: what is the value of (2)^-6 ?
Options:
A)1/62
B)1/64
C)1/65
D)1/66
E)1/67
Rationale: 2^-6= 1/(2)^6= 1/64
ANSWER:B
Answer: B
Question: Arun is travelling on his cycle and has calculated to reach point A at 2 pm if he travels at
10 kmph. He will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?
Options:
A)8 kmph
B)12 kmph
C)10 kmph
D)14 kmph
E)15 kmph
Rationale: Let distance be x km
travelling at 10 kmph reach at 2 pm
travelling at 15 kmph reach at 12 noon
=>time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs
x/10 - x/15 = 2
3x-2x*30
x=60
time needed if travelled at 10kmph = 60/10 = 6 hrs=>reach at 1 pm => (6-1) = 5 hrs
req speed = 60/5 = 12 kmph
ANSWER B
Answer: B
Question: Two trains of length 100 m and 200 m are 70 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)2 sec
B)32/3 sec
C)20/7 sec
D)32/3 sec
E)53/2 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 70/35 = 2 sec.
Answer:a
Answer: A
Question: rahul played weel in this season.his current batting averagge is 52.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
Options:
A)8
B)12
C)9
D)6
E)5
Rationale: 52x+78=54(x+1)
=>2x=24
=>x=12
ANSWER:B
Answer: B
Question: How many 7-letter words can be formed using the letters of the English alphabet that contain 3 different vowels and 4 different consonants?
Options:
A)5!*5c2 *21c2
B)4!*5c2 *21c2
C)4!*5c3 *21c2
D)6!*5c3 *21c2
E)7!*5c3 *21c4
Rationale: combination for 3 vowels out of 5 = 5c3 ways
combination for 4 consonants of 21 = 21c4 ways
Additionally the arrangement can be = 7!
total arrangements =7!*5c3 *21c4
E
Answer: E
Question: A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
Options:
A)63
B)336
C)567
D)3024
E)5040
Rationale: All the cordinates are integer hence,
possible AT values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Answer: D
Question: In the equation g = 36.12f, f and g are integers. If g/f leaves a remainder of r, which of the following must divide into r?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: 1) It says it is a equation, so g=36.12f should be 36.12 * f..
2) It says f is an integer, again it means 36.12 * f..
Otherwise f would be just a digit and it would be mentioned..
Although not clearly mentioned that 36.12f is actually 36.12 * f, BUT entire info points towards that..
and that is why I have taken g/f = 36.12
Answer: B
Question: How many positive integers between 100 and 500 are there such that they are multiples of 19?
Options:
A)10
B)15
C)21
D)18
E)19
Rationale: Multiples of 19 = 114,133,152,-----,494
Number of multiples of 19 => 494-114/19+1= 21
Answer is C
Answer: C
Question: How many of the factors of 120 are divisible by 2?
Options:
A)4
B)8
C)10
D)12
E)16
Rationale: 120 = 2^3*3*5
The total number of factors is (1+3)(1+1)(1+1) = 16
The odd factors are 1, 3, 5, and 15.
The number of even factors is 16-4 = 12
The answer is D.
Answer: D
Question: The length of each side of an equilateral triangle having an area of 4âˆš3 cm2 is?
Options:
A)4/3 cm
B)3/4 cm
C)3 cm
D)4 cm
E)5 cm
Rationale: Explanation:
âˆš3/4a2=4âˆš3->a=4
ANSWER IS D
Answer: D
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
Options:
A)15/7
B)4/17
C)7/18
D)19/6
E)7/15
Rationale: Let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Option E
Answer: E
Question: A bag contains 24 purple jellybeans, 16 green jellybeans, and 10 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
Options:
A)15%
B)20%
C)25%
D)32%
E)35%
Rationale: Probability of green beans = 16 / (24 + 16 + 10) = 16/50 = 32%
Answer is D
Answer: D
Question: A sum amounts to Rs.3087 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
Options:
A)s.4000
B)s.5000
C)s.4500
D)s.4800
E)s.2800
Rationale: CI=3087,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
3087=P[21/20]^2
3087[20/21]^2
2800
ANSWER:E
Answer: E
Question: A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is :
Options:
A)8 cm
B)6 cm
C)4 cm
D)3 cm
E)None
Rationale: Sol.
Let the height of the cone be h cm. Then,
1/3 ∏ * 6 * 6 * h = 4/3 ∏ * 3 * 3* 3 ⇒
h = [36 * 3 / 36] = 3 cm.
Answer D
Answer: D
Question: If x and y are positive integers, and 3 is not a factor of y, then y may be which of the following?
Options:
A)(x−1)·x·(x+1)
B)(x−3)·(x−1)·(x+1)
C)(x−2)·x·(x+2)
D)(x−1)·x·(x+2)
E)(x−3)·(x+1)·(x+2)
Rationale: Plugged in values :
let x=5
A. (x−1)·x·(x+1) --> divisible by 3
B. (x−3)·(x−1)·(x+1) --> divisible by 3
C. (x−2)·x·(x+2) --> divisible by 3
D. (x−1)·x·(x+2) --> not divisible. Hence the answer.
Answer: D
Question: If y = x^2 + px + q, y is minimum when x is:
Options:
A)p /q
B)-p/q
C)-p/2
D)-q/2
E)q/p
Rationale: We're given the equation Y = X^2 + pX + q.
IF.. we use a simple Classic Quadratic....
p = 2
q = 1
Y = X^2 + 2X + 1
We can then go about finding the answer that yields the MINIMUM result when X = ...
Answer A: p/q = 2/1 = 2 --> 4+4+1 = +9
Answer B: -p/q = -2/1 = -2 --> 4-4+1 = +1
Answer C: -p/2 = -2/2 = -1 --> 1-2+1 = 0
Answer D: -q/2 = -1/2 -->(1/4)-1+1 = +1/4
Answer E: q/p = 1/2 --> (1/4)+1+1 = +2 1/4
From these results, we can see the minimum result:
C
Answer: C
Question: (7.5×7.5+3.75+2.5×2.5) is equal to
Options:
A)30
B)60
C)80
D)100
E)90
Rationale: Solution
Given expression=	(7.5x7.5+2×7.5×2.5+2.5×2.5)²
= (a²+2ab+b²)
=(a+b)²
= (7.5+2.5)²
= 10²
= 100.
Answer D
Answer: D
Question: After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
Options:
A)8
B)0
C)9
D)72
E)4
Rationale: Ans: Tricky one but simple. How do you put exactly 1 letter in the wrong envelope? we need minimum two. So answer is 0.
Answer:B
Answer: B
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 300 envelopes
Options:
A)6 minutes
B)5 minutes
C)7 minutes
D)3 minutes
E)4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 300 envelopes they will take 300/60 mins. i.e., 5 mins.
ANSWER:B
Answer: B
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
Options:
A)17/28
B)17/25
C)17/26
D)17/76
E)17/22
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer: B
Answer: B
Question: In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 7a then which of the following is c equal to?
Options:
A)a/12
B)a/8
C)6a
D)10a
E)12a
Rationale: The sum of the roots is = -b/a = -7a/a = -7. Let the other root be x. Thus, x-2 = -7
x = -5. Again, the product of the roots is -2*-5 = 10. Thus, c/a = 10. c = 10a.
D.
Answer: D
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
Options:
A)30
B)35
C)37
D)41
E)43
Rationale: Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years.
Answer: Option B
Answer: B
Question: You have three pills with you which you are required to take one after every thirty minutes.
How long can the pills run for you?
Options:
A)1 hour
B)2 hour
C)3 hour
D)4 hour
E)None
Rationale: Solution:
The pills can run for an hour.
Explanation:
If you had ninety minutes in mind, then you are wrong. You took the first pill at the zero minute. Then you took the second pill after 30 minutes and the third pill after 30 + 30 i.e. 60 minutes or an hour
Answer A
Answer: A
Question: Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?
Options:
A)5
B)3
C)7
D)2
E)4
Rationale: E
Answer: E
Question: When Sally went to the candy store, she bought 25 licorice sticks. As she was walking home, she ate 1 licorice stick for each block that she walked. She walked 5 blocks. How many licorice sticks did she have left when she arrived at home?
Options:
A)30
B)25
C)20
D)19
E)21
Rationale: To determine the number of licorice sticks that she ate, you have to multiply the number of blocks that she walked by the number that she ate per block (5*1=5)To determine the number of licorice sticks remaining when she arrived home, you have to subtract the number of licorice sticks that she ate from the total that she bought. (25-5=20)
The correct answer is C
Answer: C
Question: Kiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?
Options:
A)1500
B)5500
C)3500
D)6500
E)2500
Rationale: Let the no of fifty rupee notes be x
Then, no of 100 rupee notes =(85-x)
50x+100(85-x)=5000
x+2(85-x)=100
x=70
so, required amount=Rs.(50*70)= Rs.3500
Answer is C
Answer: C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire?
Options:
A)2
B)1
C)4
D)3
E)5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 48,000 m : C is the circumference
C = 2 meters
correct answer A
Answer: A
Question: A committee of 6 is chosen from 7 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
Options:
A)455
B)700
C)1404
D)2620
E)3510
Rationale: The only cases possible are :
1. 2 men and 4 women : 7C2 * 5C4 = 105
2. 3 men and 3 women: 7C3*5C3 = 350
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 105+350 = 455. Thus A is the correct answer.
Answer: A
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Options:
A)33
B)77
C)26
D)12
E)99
Rationale: Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps	4	:	3 :: 8 : x
Days	1	:	2
4 x 1 x x = 3 x 2 x 8
x =	(3 x 2 x 8)
(4)
x = 12.
Answer:D
Answer: D
Question: Aarti can do a piece of work in 3 days. In how many days will she complete 10 time of work of same type?
Options:
A)6 days
B)18 days
C)21 days
D)30 days
E)13 days
Rationale: We have the important relation, More work, More time (days)
A piece of work can be done in 3 days.
10 times of work of same type can be done in 3 x 10
= 30 days
Answer D
Answer: D
Question: The least number which should be added to 2400 so that the sum is exactly divisible by 5,6,4 and 3 is :
Options:
A)3
B)13
C)20
D)33
E)43
Rationale: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 2400 by 60, the remainder is 40.
∴ Number to be added = (60-40) = 20. Answer C
Answer: C
Question: In a series of six consecutive odd numbers, the third number is 31. What is the fifth number?
Options:
A)35
B)33
C)45
D)31
E)29
Rationale: Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 3) = 31
=> x = 28
The fifth number = x + 7 = 28 + 7 = 35.
Answer: A
Answer: A
Question: Sixteen machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2* 16 = 24
So we need 24-16 = 8 more machines.
Answer : E
Answer: E
Question: Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
Options:
A)887pages
B)656 pages
C)435 pages
D)451 pages
E)232pages
Rationale: Pages read in the first book in one week which is 7 days with 25 pages everyday.
25 *7 = 175 pages
Pages read in the second book in 12 days with 23 pages everyday.
23 *12 = 276 pages
Total number of pages read
175 + 276 = 451 pages
correct answer D
Answer: D
Question: If 0.5 of a number is equal to 0.09 of another number, the ratio of the numbers i
Options:
A)2 : 3
B)3 : 4
C)3 : 20
D)3 : 7
E)9 : 50
Rationale: Sol.
0.5A = 0.09 B â‡” A / B = 0.09 / 0.50 = 9/50
âˆ´ A : B = 9 : 50.
Answer E
Answer: E
Question: Marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 10%. What percent of the projected revenue was the actual revenue ?
Options:
A)53%
B)58%
C)62.5%
D)64%
E)75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 90;
Projected revenue = 120.
Actual/Projected*100=90/120*100 = 75%.
Answer: E.
Answer: E