mathewhe/aqua_rat huggingface dataset:
Question: I have to run a 100 meter dash.
How many steps would I need to take if with each step i cover 20 centimeters ?
(A) 20
(B) 500
(C) 50
(D) 10
(E) 45
Rationale: 100centimeters=1meter
x centimeters=100meters
(20 centimeters per step) x (nos running steps)=10000 centimeters
nos running steps= 10000 centimeters /20 centimeters
500steps
The answer is B
Answer: (B) 500
Question: Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 33~ ?
(A) 31
(B) 1
(C) 2
(D) 8
(E) 0
Rationale: n~ = (n-1)!
so 33~ = (33-1)! = 32!
when 32!/33 we have 16*2 inside 32!
hence 33 gets cancelled and we get remainder as 0
E
Answer: (E) 0
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
(A) 218
(B) 265
(C) 268
(D) 480
(E) 261
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48
= 480
Answer: D
Answer: (D) 480
Question: If the price of sugar rises from Rs.10 per kg to Rs. 12 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
(A) 17%
(B) 20%
(C) 25%
(D) 30%
(E) none
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 12 = x = 83 kg.
∴ Reduction in consumption = 17%.
Answer A
Answer: (A) 17%
Question: The average of 20 number is zero of them at the most, how many may be greater than zero ?
(A) 0
(B) 1
(C) 10
(D) 19
(E) 20
Rationale: Solution
average of 20 numbers = 0.
∴ Sum of 20 numbers = (0×20) = 0.
it is quite possible that 19 of these number may be positive and if their sum is a, then 20th number is (-a). Answer D
Answer: (D) 19
Question: The average of 35 students in a class is 16 years. The average age of 25 students is 14. What is the average age of remaining 10 students?
(A) 21 years
(B) 22 years
(C) 23 years
(D) 24 years
(E) 25 years
Rationale: Sum of the ages of 14 students
= (16 * 35) - (14 * 25) = 560 - 350 = 210
Required average = (210/10) = 21 years.
Answer:A
Answer: (A) 21 years
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 11 days
(B) 66 days
(C) 30 days
(D) 77 days
(E) 88 days
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Answer: (C) 30 days
Question: A man rides at the rate of 40km/hr. But stops 20minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 200 kilometers?
(A) 5hr
(B) 6hr 30min
(C) 8hr 10min
(D) 7hr 20min
(E) 9hr
Rationale: speed of man = 40km/hr
number of rests = (200/25)-1 = 7
time taken for the man = (200/40)+7*(20/60) = 7 hr 20 min
Answer is D
Answer: (D) 7hr 20min
Question: The letters U and S are rearranged to form the word 'US'. Find its probability.
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1/7
(E) 1/5
Rationale: Explanation :
There are total 2 letters. The probability that S gets the first position is 1/2.
The probability that S is in the second position is 1/1.
Hence, the required probability is:-
=> (1/2) x 1.
=> 1/2
Answer : C
Answer: (C) 1/2
Question: In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/2 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
(A) N/8
(B) 7N/8
(C) 11N/12
(D) 17N/24
(E) 41N/48
Rationale: The number of people who answered yes to both questions is (1/2)(1/6)N = N/12
The number of people who did not answer yes to both is 1 - N/12 = 11N/12
The answer is C.
Answer: (C) 11N/12
Question: If n is an integer, when (2n + 2)2 is divided by 4 the remainder is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: We first expand (2n + 2)2
(2n + 2)2 = 4n 2 + 8 n + 4
Factor 4 out.
= 4(n 2 + 2n + 1)
(2n + 2)2 is divisible by 4 and the remainder is equal to 0. The answer is A.
Answer: (A) 0
Question: Given 2x + y + z = 3 and 5x + 3y + z = 11, what is the value of x + y - z?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: (1) 5x + 3y + z = 11
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 5
The answer is C.
Answer: (C) 5
Question: A positive number x is multiplied by 2, and this product is then divided by 5. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  9/4
(B)  3/2
(C)  4/3
(D)  2/3
(E)  1/2
Rationale: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^2
3x^2 – 2x = 0
x(3x – 2) = 0
x = 0 or
3x – 2 = 0
3x = 2
x = 3/2
Because x is positive, x = 3/2. The answer is B.
Answer: (B)  3/2
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 85, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 85 + 77*5x) = 260x+510x+385x = 1155x
total number of students = 15x
average = 1155x/15x = 77
D is the answer
Answer: (D) 77
Question: A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 9 less, he would have gained 25%. Find the cost price of the article.
(A) 150
(B) 160
(C) 170
(D) 180
(E) 360
Rationale: Let the C.P. be 100
First S.P. = 115
Second C.P. = 90
Second S.P = 125% of 90 = 112.50
Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100
But actual difference is 9.
∴ C.P. = 100⁄2.50 × 9 = 360.
Answer E
Answer: (E) 360
Question: Which of the following is equivalent to the pair of inequalities x + 8 > 10 and x - 4 <= 5 ?
(A)  2 < x < 16
(B)  2 <= x < 4
(C)  2 < x <= 9
(D)  4 < x <= 8
(E)  4 <= x <= 16
Rationale: Solution:
Let’s isolate x in both inequalities, starting with x + 8 > 10.
x + 8 > 10
x > 2
Next we isolate x in the inequality x – 4  5.
x – 4 <= 5
x <= 9
Bringing these two inequalities together we know:
2 < x <= 9
The answer is C.
Answer: (C)  2 < x <= 9
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 19
(E) None
Rationale: EXPLANATION
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Answer A
Answer: (A) 0
Question: Ratio between Rahul and Deepak is 4:3, After 10 Years Rahul age will be 26 years. What is Deepak present age
(A) 12
(B) 15
(C) 20
(D) 22
(E) 23
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 10 = 26 => x = 4
So Deepak age is = 3(4) = 12
Answer: Option A
Answer: (A) 12
Question: The number N is 5,3H7, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
(A) 4
(B) 3
(C) 5
(D) 8
(E) 2
Rationale: If the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number.
Answer: B
Answer: (B) 3
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word MANGO could be arranged to create a five-letter code?
(A) 5!
(B) 5! − (3! + 2!)
(C) 5! − (3! × 2!)
(D) 5!/(3! + 2!)
(E) 5!/(3! × 2!)
Rationale: MANGO - five letters can be arranged in 5! ways
since there is no repetition in MANGO so
5!
Ans. A) 5!
Answer: (A) 5!
Question: If x < y < 0, which of the following must be true?
(A) (-x)+ (-y) is positive integer
(B) 2x+y is a negative integer
(C) x-y is a positive integer
(D) 2xy/3x is a negative integer
(E) xy/2
Rationale: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
x-y is false since xSo, option A is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)
Answer : A
Answer: (A) (-x)+ (-y) is positive integer
Question: The average age of a class of 22 students is 10 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 30 Years
(B) 31 Years
(C) 33 Years
(D) 34 Years
(E) 49 Years
Rationale: Total age of students is 22X10 = 220 Years
Total age inclusive of teacher = 23X (10+1) = 253
So, Teacher's age is 253-220 = 33 Yrs
There is a shortcut for these type of problems
Teacher's age is 10+(23X1) = 33 Years
C
Answer: (C) 33 Years
Question: Given that a is the average (arithmetic mean) of the first seven positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
(A) 3:4
(B) 8:13
(C) 5:6
(D) 13:10
(E) 4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=24 and b=(36+42)/2=39 --> a/b=24/39=8/13.
Answer: B.
Answer: (B) 8:13
Question: If the sum of 9 consecutive integers is 90, what is the sum of the following 9 consecutive integers?
(A) 99
(B) 135
(C) 145
(D) 171
(E) 180
Rationale: 1) greatest of each will have a difference of 9 and next greatest too will have a difference of 9 and so on..
Therefore all nine terms will have a term MORE by 9..
Sum =90+(9*9)=171
2) if sum is 90, the average= median=90/9=10..The median of next 9 will be 10+9=19..
And sum would be 19*9=171
ANSWER:D
Answer: (D) 171
Question: Question:	A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $180. The cost for 1 bat and 6 balls is $190, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $195 for the purchase?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: IMO it should be C that is C
reason:
formed an equation... bat = b ball = c
2b+4c=180
1b+6c=190
solving both we get b that is bat = 40 and c that is ball = 25
new equation 195 to be divided in equal
3b+3c=195
3*40 + 3*25 = 195
120+75= 195
Answer: (C) 3
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 18 households had a both a car and a bike and 44 had a car, how many had bike only?
(A) 30
(B) 35
(C) 20
(D) 18
(E) 10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-18+11 --> {Bike}=53 --> # those who have bike only is {Bike}-{Both}=53-18=35.
Answer: B.
Answer: (B) 35
Question: In what time will Rs.4200 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 8 1/3
(B) 8 1/6
(C) 8
(D) 8 1/2
(E) 8 1/5
Rationale: (4200*3*R)/100 = (5000*5*4)/100
R = 8
Answer: C
Answer: (C) 8
Question: A thief steels a car at 2.30p.m. and drives it at 60kmph. The theft is discovered at 3p.m. and the owner sets off in another car at 75 kmph. When will he overtake the thief?
(A) 5p.m.
(B) 6p.m.
(C) 4p.m.
(D) 7p.m.
(E) 3p.m.
Rationale: Suppose the thief overtakes x hours after 2.30p.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1/2 hours)
60x = 75(x-1/2)
15x = 75/2
x = 5/2 hrs
Thief is overtaken at 5p.m.
Answer is A
Answer: (A) 5p.m.
Question: (1/36)+(1/37)+……+(1/66)+(1/67) is including in which of the following ranges?
(A) 2
(B) 1
(C) 1~ 2
(D) 3
(E) 1/2~1
Rationale: Number of terms in the given series = 32.
The lowest term is 1/67 , the largest being 1/36.
Thus, the sum of the given series will be more than
1/67 + 1/67.....1/67 (32 times)
---> 32*(1/67) = 32/67
less than 1/36 + 1/36...... 1/33 (32 times)
---> 32*(1/36) = 32/36 = 1 (approx)
E
Answer: (E) 1/2~1
Question: B completes a work in 3 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
(A) 2.31 days
(B) 4.31 days
(C) 5.31 days
(D) 6.31 days
(E) 7.31 days
Rationale: 1/3 + 1/10 = 13/30
30/13 = 2.31 days
ANSWER:A
Answer: (A) 2.31 days
Question: The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
(A) 2197
(B) 1267
(C) 1750
(D) 2267
(E) 1262
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 1750
Answer:C
Answer: (C) 1750
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
(A) 100
(B) 360
(C) 120
(D) 240
(E) 60
Rationale: Explanation:
The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
ANSWER IS E
Answer: (E) 60
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 25
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
A
Answer: (A) 16
Question: If the function Q is defined by the formula Q = 5e/(4x(z^2)), by what factor will Q be multiplied if e is quadrupled, x is doubled, and z is tripled?
(A) 1/9
(B) 2/9
(C) 4/9
(D) 3/9
(E) 2/27
Rationale: We just need to find the factor thats all,
e -> quadrupled -> 4e
x-> doubled -> 2x
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
e is in numerator, and x*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B
Answer: (B) 2/9
Question: The greatest common factor of two numbers is 6!. Which of the following can be the second number, if one of the numbers is 8!?
(A) 3(5!)
(B) 4(5!)
(C) 5(5!)
(D) 6(6!)
(E) 7(5!)
Rationale: GCF is the product of common factors of the numbers involved.
GCF = 6!
a = 8! = 8*7*6!
b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)
Looking at the answers only 6 (6!) and 8! will have GCF as 6!
Ans D
Answer: (D) 6(6!)
Question: if the ratio of simple interest on certain sum with same rate is 4:3.what is the ratio of time.
(A) 3:5
(B) 6:5
(C) 5:4
(D) 4:3
(E) 2:3
Rationale: let ratio constant be x.
4x/3x=(p*r*t1/100)/(p*r*t2/100)
t1/t2=4:3.
answer D
Answer: (D) 4:3
Question: The average of the first five prime numbers greater than 20 is:
(A) 32.2
(B) 32.22
(C) 31.22
(D) 32.27
(E) 32.28
Rationale: Explanation:
Required prime numbers are 23, 29, 31, 37, 4.
Average will be (23 + 29 + 31 + 37 + 41)/5 = 32.20
Answer: A
Answer: (A) 32.2
Question: 4623.186 is rounded off to the nearest thousand, hundred, ten and one. Let the results be represented with the alphabets r,s,t,u respectively. which of the statements below is accurate?
(A) t<s<u<r
(B) u<t<s<r
(C) s<r<u<t
(D) s<u<t<r
(E) s<t<u<r
Rationale: 4623.186..
Nearest thousand 5000..r
Nearest hundred 4600..s
Nearest ten 4620..t
Nearest one 4623..u
s<t<u<r
The correct option is E
Answer: (E) s<t<u<r
Question: Four numbers are in the ratio 2:3:4:5 add up to give a sum of 1344. Find the biggest number.
(A) 480
(B) 239
(C) 270
(D) 282
(E) 112
Rationale: ANSWER : A
Answer: (A) 480
Question: A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 10 percent. The area of the new garden
(A) has increased by 20 percent
(B) has increased by 12 percent
(C) has increased by 8 percent
(D) is exactly the same as the old area
(E) cannot be expressed in percentage terms without actual numbers
Rationale: Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.9W*1.2L = (0.9)(1.2)L*W = 1.08*L*W
The answer is C.
Answer: (C) has increased by 8 percent
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) None
Rationale: Solution
part filled by (A+B+C) in 1 hour	= (1/5 + 1/6 + 1/30)
‹=› 1/3.
All the three pipes together will fill the tank in 3 hours.
Answer C
Answer: (C) 3
Question: On a trip, a cyclist averaged 9 miles per hour for the first 18 miles and 10 miles per hour for the remaining 12 miles. If the cyclist returned immediately via the same route and took a total of 7.2 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
(A) 6.9
(B) 7.2
(C) 7.5
(D) 7.8
(E) 8.1
Rationale: The time to go 30 miles was 18/9+12/10=2+1.2=3.2 hours.
The average speed for the return trip was 30 miles/4 hours= 7.5 mph.
The answer is C.
Answer: (C) 7.5
Question: The cricket team of 11members is 28yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 28
Rationale: Let the average age of the whole team be x years.
11x - (28 + 31) = 9 (x - 1)
=> 11x - 9x = 50
=> 2x = 50
=> x = 25.
So, average age of the team is 25 years.
D
Answer: (D) 25
Question: If the sides of a triangle are 30 cm, 28 cm and 12 cm, what is its area?
(A) 120 cm2
(B) 112 cm2
(C) 776 cm2
(D) 666 cm2
(E) 168 cm2
Rationale: The triangle with sides 30 cm, 28 cm and 12 cm is right angled, where the hypotenuse is 30 cm.
Area of the triangle = 1/2 * 28 * 12 = 168 cm2
Answer: E
Answer: (E) 168 cm2
Question: A group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 30 speak English well, while 40 of them do not speak English. If 86% of students do not speak French, how many students were surveyed?
(A) 500
(B) 450
(C) 250
(D) 350
(E) 525
Rationale: Number of students who speak French are 30 + 40 = 70
Of total students, the percentage of students who do not speak French was 86% --> percentage of who do is 14%
70-------14%
x ------- 100%
x = 70*100/14 = 500 = number of all students
Answer is A
Answer: (A) 500
Question: The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is:
(A) 101
(B) 107
(C) 111
(D) 112
(E) 113
Rationale: Let the numbers be 37a and 37b.
Then, 37a * 37 b = 4107 => ab = 3
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 * 1, 37 * 3) i.e., (1, 111).
Greater number = 111.
ANSWER:C
Answer: (C) 111
Question: When positive integer x is divided by 6, the remainder is 1. Which of the following must be true?
I. x is a prime number
II. x is odd
III. x is divisible by 7
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: X=6q+1
Examine II) put q=0,1,2,3....... we have x=1,7,13,...25 so x must be odd
Examine III) 14/6 has reminder 2 & 49/7 has reminder 1 so not always true
Examine I) X= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Answer: (B) II only
Question: Rs.8000 become Rs.8988.80 in a certain interval of time at the rate of 6% per annum of C.I. Find the time?
(A) 6 years
(B) 8 years
(C) 9 years
(D) 3 years
(E) 2 years
Rationale: 8988.80 = 8000(53/50)N
(53/50)^2 = (53/50)^N
N = 2
At the end of two years what will be the comp.Answer: E
Answer: (E) 2 years
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 45. By how much do the two digits differ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: we are given that if the integer N has its digits reversed the resulting integer differs from the original by 45. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 45 we can say:
10B + A – (10A + B) = 45
10B + A – 10A – B = 45
9B – 9A = 45
B – A = 5
Since B is the tens digit and A is the units digit, we can say that the digits differ by 5.
The answer is C.
Answer: (C) 5
Question: Veena ranks 73rd from the top in a class of 198. What is her rank from the bottom if 22 students have failed the examination?
(A) 88
(B) 104
(C) 110
(D) 90
(E) 93
Rationale: total student=198
failed=22
paasd student=198-22=176
from bottom her rank is=176-73+1=104
ANSWER:B
Answer: (B) 104
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138+2x131= 400.
(a + b + c) = square root of 400 = 20
answer :A
Answer: (A) 20
Question: Which of the following has 60^80 as a factor?
(A) 15^60
(B) 30^40
(C) 120^80
(D) 60^60
(E) 90^80
Rationale: Here 60^80 = 30^80 * 20^80 Only Option C has both .
Smash C
Answer: (C) 120^80
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word TIE could be arranged to create a three-letter code?
(A) 3!
(B) 3! − (3! + 2!)
(C) 3! − (2!)
(D) 3!/(3! + 2!)
(E) 3!/(3! × 2!)
Rationale: TIE - three letters can be arranged in 3! ways
since 'there is no repetition'
3!
Ans. A) 3!
Answer: (A) 3!
Question: ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 150 students answered yes only for subject M, how many of the students did not answer yes for either subject?
(A) 100
(B) 250
(C) 300
(D) 400
(E) 500
Rationale: Since 150 students answered yes only for subject M, then the remaining 350 students who answered yes for subject M, also answered yes for subject R. So, 350 students answered yes for both subjects.
If 350 students answered yes for both subjects, then 400-350=50 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
50 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+50+300)=250 students did not answer yes for either subject.
Answer: B.
Answer: (B) 250
Question: In 1982 and 1983, Company B’s operating expenses were $10.0 million and $12.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
(A) 3%
(B) 16 2/3%
(C) 25%
(D) 21 3/7%
(E) 60%
Rationale: Profit in 1982 = 15.6 - 10 = 5.6 million $
Profit in 1983 = 18.8 - 12 = 6.8 million $
Percentage increase in profit = (6.8-5.6)/5.6 * 100 %
= 21 3/7%
Answer D
Answer: (D) 21 3/7%
Question: A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
(A) 71.11
(B) 71.12
(C) 71.1
(D) 71.17
(E) 71.13
Rationale: Car travels first 160 km at 64 km/hr
Time taken to travel first 160 km = distancespeed=16064
Car travels next160 km at 80 km/hr
Time taken to travel next 160 km = distancespeed=16080Total distance traveled = 160+160=2×160Total time taken = 16064+16080Average speed = Total distance traveledTotal time taken=2×16016064+16080=2164+180=2×64×8080+64=2×64×80144=2×8×8018=6409=71.11 km/hr
Answer:A
Answer: (A) 71.11
Question: Two terms are in 3 : 4, if 10 is added to each of the terms, they will be 4 : 5. Find second term?
(A) 10
(B) 30
(C) 20
(D) 40
(E) 35
Rationale: Solution:
Let the two numbers be 3x and 4x. Then, (3x+10)/(4x+10) = 4/5.
=> 15x+50 = 16x+40 => x = 10.
.'. Second term = 4*10 =40.
ANSWER IS D
Answer: (D) 40
Question: How many different ways can you select a pilot and a co pilot if you have 70 people to choose from?
(A) 199
(B) 200
(C) 398
(D) 4950
(E) 4830
Rationale: 1) PERMUTATION:-
since it is selection, we have to find permutation..
70P2= 70!/(70-2)!=4830
ANS:E
Answer: (E) 4830