mathewhe/aqua_rat huggingface dataset:
Question: If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer?
I. w + t + 2
II. w^2 + 2wt + t^2
III. w^2 + t^2
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III
Rationale: w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even.
Check all options:
I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Answer: (A) None
Question: There are w members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of w?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 22
Rationale: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, w = m + 1(Michael) = 12
option B
Answer: (B) 12
Question: In a class ratio of boys and girls is 16:25. If number of total student is 82. Find the number of girls?
(A) 36
(B) 40
(C) 50
(D) 38
(E) 45
Rationale: Let number of girls and boys is 25x and 16x
16x+25x = 82
41x = 82
x = 2
Number of girls = 25*2 = 50
Answer : C
Answer: (C) 50
Question: A can do a piece of work in 10 days and B alone can do it in 20 days. How much time will both take to finish the work ?
(A) A)5.333
(B) B)6
(C) C)6.666
(D) D)8.333
(E) E)9
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 10 x 20 / (10 + 20)
= 200 / 30
= 6.666 days
Answer: C
Answer: (C) C)6.666
Question: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 35 percent ryegrass, what percent of the weight of this mixture is X ?
(A)  10%
(B)  33.33 %
(C)  40%
(D)  50%
(E)  66.66 %
Rationale: ---------------->Ryegrass
X-------------->	40%
Y-------------->	25%
M(mixture)---->35%
0.4X + (M-X)0.25 = 0.35M
0.15X = 0.10M
X = 0.6666M
X = 66.66% of M
E
Answer: (E)  66.66 %
Question: The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 20, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)
(A) 36
(B) 47
(C) 58
(D) 65
(E) 91
Rationale: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.
Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.
As given that N = P + 10, then N=2*N/2.54+20 --> N=~91.
Answer: E.
Answer: (E) 91
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 180 students answered yes only for subject M, how many of the students did not answer yes for either subject?
(A) 100
(B) 220
(C) 300
(D) 400
(E) 500
Rationale: Since 180 students answered yes only for subject M, then the remaining 320 students who answered yes for subject M, also answered yes for subject R. So, 320 students answered yes for both subjects.
If 320 students answered yes for both subjects, then 400-320=80 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
80 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+80+300)=220 students did not answer yes for either subject.
Answer: B.
Answer: (B) 220
Question: when i was married 10 years ago,my wife was the 6th member in the family.today,my father died,and a baby was born to me.the average age in my family today is what it was when i was married.how old was my father when he died?
(A) 50yrs
(B) 60yrs
(C) 70yrs
(D) 80yrs
(E) indeterminate
Rationale: 10 years ago the family members there were 6 members with age= I+Father+Wife+3 others
Now 6 members with age= (I+10)+(Wife +10)+ (3 others+3*10) + (baby=0).
I+Father+Wife+3 others=(I+10)+(Wife +10)+ (3 others+3*10) + (baby=0)
Father =50+0 = 50 = Father's age 10 year ago
So now father's age=50 +10=60.
ANSWER:B
Answer: (B) 60yrs
Question: A can do a piece of work in 7 days and B can do it in 6 days how long will they both work together to complete the work?
(A) 6/11
(B) 8/13
(C) 3/13
(D) 9/11
(E) 10/13
Rationale: Explanation:
A’s one day work = 1/5
B’s one day work = 1/6
(A+B)’s one day work = 1/7 + 1/6 = 13/42 => time = 42/13 = 3 3/13 days
Answer: Option C
Answer: (C) 3/13
Question: At a certain university, 65% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
(A) 25
(B) 37.5
(C) 50
(D) 62.5
(E) 75
Rationale: total women = 65%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 25%
but question wants to know the percent of men that are tenured
25%/40% = 62.5%
D
Answer: (D) 62.5
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:8
(B) 6:2
(C) 6:5
(D) 6:4
(E) 6:2
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer: C
Answer: (C) 6:5
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.145. How much was lent at 5%?
(A) 2333
(B) 2777
(C) 2688
(D) 500
(E) 2871
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 145
X = 500
Answer: D
Answer: (D) 500
Question: Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10% of its volume is occupied by concrete ?
(A) 6000
(B) 5400
(C) 3800
(D) 4700
(E) 2500
Rationale: Explanation:
Let 'B' be the nuber of bricks.
=> 10 x 4/100 x 5 x 90/100 = 25/100 x 15/100 x 8/100 x B
=> 10 x 20 x 90 = 15 x 2 x B
=> B = 6000
ANSWER IS A
Answer: (A) 6000
Question: A number is said to be prime saturated if the product of all the different positive prime factors of g is less than the square root of g. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: g=96 = 3 * 32 = 3 * 2^5
Answer is D.
Answer: (D) 96
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 13 family members in a row for the picture?
(A) 14!
(B) 12×11!
(C) 11×12!
(D) 13!/2!
(E) 13!
Rationale: The number of ways to arrange 13 people is 13!
We need to subtract the arrangement when these two people are together.
Let's think of these two people as a single unit so there are 12 units.
The number of ways to arrange 12 units is 12!
We need to multiply this by 2 since these two people could switch places.
The total number of valid arrangements is 13! - 2*12! = 12!*(13-2) = 11x12!
The answer is C.
Answer: (C) 11×12!
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score A of team B?
(A) 1)8
(B) 2)10
(C) 3)20
(D) 4)40
(E) 5)80
Rationale: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Answer: (A) 1)8
Question: a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. a = b = 3c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
(A) 112
(B) 213
(C) 331
(D) 511
(E) 745
Rationale: Ratio of a:b:c= 3:3:1
Two possible greatest single digit values for a are 9 and 6
if a is 9, then x= 993
if a is 6, then x= 662
difference= 993-662= 331
C is the answer
Answer: (C) 331
Question: . A car covers a distance of 810 km in 5 hours. Find its speed?
(A) 104
(B) 55
(C) 162
(D) 174
(E) 2761
Rationale: 810/5 = 162 kmph
Answer: C
Answer: (C) 162
Question: Set E consists of all the prime numbers between 10 and 25. What is the range of set E?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 23
Rationale: Answer of set E is 12=A
Answer: (A) 12
Question: If 7<x<9<y<15, then what is the greatest possible positive integer difference of x and y?
(A) 7
(B) 4
(C) 5
(D) 6
(E) 3
Rationale: Let x=7.1 and y=14.1
Greatest possible difference=14.1-7.1=7
Answer A
Answer: (A) 7
Question: The average age of 32 students in a group is 10 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
(A) 45
(B) 43
(C) 51
(D) 53
(E) 57
Rationale: age of the teacher=(33*11-32*10)
=43 years.
ANSWER:B
Answer: (B) 43
Question: Three candidates contested in an election and received 2136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
(A) 45%
(B) 49%
(C) 57%
(D) 54%
(E) 62%
Rationale: Total number of votes polled = 2136+7636+11628 = 21400
Required percentage = 11628*100/21400 = 54%
Answer is D
Answer: (D) 54%
Question: If xy+4z = x(y+z), which of the following must be true?
(A) 1. x=0 and z=0
(B) 2. x=1 and y=1
(C) 3. y=1 and z=0
(D) 4. x=1 or y=0
(E) 5. x=4 or z=0
Rationale: xy+4z=x(y+z)
xy+4z=xy+xz
4z=xz
it means x=4 or z=0
Answer E
Answer: (E) 5. x=4 or z=0
Question: If 5x = 6y and xy ≠ 0, what is the ratio of 1/3*x to 1/5*y ?
(A)  25/6
(B)  36/25
(C)  2
(D)  5/6
(E)  25/36
Rationale: 5x = 6y => x/y = 6/5
1/3*x to 1/5*y = x/y * 5/3 = (6/5)*(5/3)=2
Ans: C
Answer: (C)  2
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 7 min
(B) 8 min
(C) 9 min
(D) 10 min
(E) 11 min
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/54)x60 = 10 min
answer : D
Answer: (D) 10 min
Question: In an examination the number of successful students was 4 times the numbr of unsuccessful students If there were 35 less students nd the numbr of unsuccessful students were 9 more,then the ratio of their numbr would have been 2:1 . Find the total numbr of students
(A) 155
(B) 145
(C) 135
(D) 125
(E) 112
Rationale: successful students 4x,unsuccessful student x.total 5x
now,total students become 5x-35 & unsuccessful students x+9 then successful students 4x-44
ratio 4x-44 / x+9=2 / 1
x=31 then total student 5x=155
ANSWER:A
Answer: (A) 155
Question: A box contains 20 green balls, 15 red balls and 25 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?
(A) 6/7
(B) 5/11
(C) 3/8
(D) 1/13
(E) 7/12
Rationale: Total number of balls = 20+15+25 = 60
n(s)=60
E1 = event of drawing a red ball = 15/60 = 1/4
E2 = event of drawing a green ball = 20/60 = 1/3
P(E1)+P(E2) = (1/4)+(1/3) = 7/12
Answer is E
Answer: (E) 7/12
Question: 5 OUT OF 1000 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
(A) 11/50
(B) 2/9
(C) 1/2
(D) 2/45
(E) NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(5/1000*100)%=1/2%
CORRECT OPTIONS: C
Answer: (C) 1/2
Question: For any number d, d* is defined as the greatest positive even integer less than or equal to d. What is the value of 5.2 – 5.2*?
(A) 0.2
(B) 1.2
(C) 1.8
(D) 2.2
(E) 4.0
Rationale: Since d* is defined as the greatest positive even integer less than or equal to d, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: (B) 1.2
Question: On a clock, how many times a day do the minute and hour hand overlap?
(A) 10
(B) 11
(C) 20
(D) 22
(E) 24
Rationale: 22 times: 12:00:00, 1:05:27, 2:10:55, 3:16:22, 4:21:49, 5:27:16, 6:32:44, 7:38:11, 8:43:38, 9:49:05, 10:54:33. Each twice a day.
Answer: (D) 22
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 22
(B) 40
(C) 38
(D) 21
(E) 11
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
Answer: B
Answer: (B) 40
Question: If the cost of A metres of wire is C rupees, then what is the cost of E metres of wire at the same rate?
(A) Rs. (EC/A)
(B) Rs. (EC)
(C) Rs. (C/A)
(D) Rs. (E/A)
(E) Rs. (AC/E)
Rationale: cost of A metres of wire = Rs.C
cost of 1 metre of wire = Rs.(C/A)
cost of E metre of wire = Rs.(E×C/A)=Rs. (EC/A)
ANSWER:A
Answer: (A) Rs. (EC/A)
Question: Which one of the following is not a prime number?
(A) 31
(B) 61
(C) 71
(D) 91
(E) None of these
Rationale: Explanation:
91 is divisible by 7. So, it is not a prime number.
ANSWER IS D
Answer: (D) 91
Question: Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 121, then which of the following can be a value of 2y + 3g?
(A) 81
(B) 130
(C) 141
(D) 142
(E) 160
Rationale: 800score Official Solution:
First note that g can either be 11 or -11. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 11 and then g = -11. If g = 11, then x = 2. If g = -11, then x = -12/5. Since all of our solutions are whole numbers, we can dismiss -12/5. We use g = 11 and x = 2 to determine the value of y: y = 2(11) + 4 = 24. Finally, we substitute the values for y and g into the last expression to determine its value : 2(24) + 3(11) = 48 + 33 = 81;the correct answer is (A).
Answer: (A) 81
Question: If Jan 1, 2006 was a Monday, What was the day of the week Jan 1, 2010?
(A) Friday
(B) Thursday
(C) Tuesday
(D) Saturday
(E) None of these
Rationale: Explanation :
Given that Jan 1 2006 was a Monday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Monday + 5 odd days) = Saturday.. Answer : Option D
Answer: (D) Saturday
Question: The present ratio of students to teachers at a certain school is 50 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
(A) 3
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: We are given that the ratio of students to teacher is 50 to 1. We can rewrite this using variable multipliers.
students : teachers = 50x : x
We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:
Students/Teachers  25/1 = (30x + 50)/(x + 5)
If we cross multiply we have:
25(x + 5) = 50x + 50
25x + 125 = 50x + 50
3 = x
Since x is the present number of teachers, currently there are 3 teachers.
Answer A.
Answer: (A) 3
Question: A man can hit the target once in two. If he fires four shots in succession, what is the probability that he will hit the target?
(A) 1
(B) 1/16
(C) 81/16
(D) 15/16
(E) 185/256
Rationale: In four shots he can hit once,twice,thrice,all hit
the probability of hitting the target is p(1hit out of 4)+P(2hit out of 4)+p(3hit out of 4)+p(All hit)
it is total probability-probability of not hitting the target
=>1-(1/2*1/2*1/2*1/2)
=>15/16
ANSWER:D
Answer: (D) 15/16
Question: A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, two-third were left handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of lefthanded players who were not at practice?
(A) 1/3
(B) 2/3
(C) 5/7
(D) 7/5
(E) 3/2
Rationale: Say the total number of players is 18, 9 right-handed and 9 left-handed.
On a certain day, two-thirds of the players were absent from practice --> 12 absent and 6 present.
Of the players at practice that day, one-third were left-handed --> 6*2/3=4 were left-handed and 2 right-handed.
The number of right-handed players who were not at practice that day is 9-2=7.
The number of left-handed players who were not at practice that days is 9-4=5.
The ratio = 7/5.
Answer: D
Answer: (D) 7/5
Question: If x is chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, then what is the probability that xy will be even?
(A) 5/6
(B) 2/6
(C) 2/3
(D) 1/2
(E) 1/4
Rationale: S = {(1,5), (1,6), (1,7), (2,5), (2,6), (2,7), (3,5), (3,6), (3,7), (4,5), (4,6), (4,7)}
Total element n(S) = 12
xy will be even when even x or y or both will be even.
Events of xy being even is E.
E = {(1,6), (2,5), (2,6), (2,7), (3,6), (4,5), (4,6), (4,7)}
n(E) = 8
P(E) = n(E)/n(S)
= 8/12
= 2/3
ANSWER:C
Answer: (C) 2/3
Question: If 5% more is gained by selling an book for $ 350 than by selling it for $ 340, the cost of the book is:
(A) 500
(B) 400
(C) 200
(D) 300
(E) 100
Rationale: C
200
Let C.P. be $ x.
Then, 5% of x = 350 - 340 = 10
x/20 = 10 => x = 200
Answer: (C) 200
Question: One of the number is odd, Which one ?
(A) 4377
(B) 3954
(C) 9862
(D) 9862
(E) 9862
Rationale: E
9862
Sum of digits of all other numbers is 21 , but sum of digits of 9862 is 25
Answer: (E) 9862
Question: If 0 < x ≤ 4, then which one of the following is the maximum value of (x – 1)^2 + x ?
(A) 13
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 4 is when x=4 --> (x – 1)^2 + x = 13
Answer A
Answer: (A) 13
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 2429
(C) 2428
(D) 2421
(E) 2408
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Answer: (A) 2400
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) 3929
(B) 3998
(C) 3128
(D) 3900
(E) 3920
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Answer: (D) 3900
Question: If 1/a^3 + a^3 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?
(A) 28
(B) 22
(C) 20
(D) 16
(E) 12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=20
So the answer should be C
Answer: (C) 20
Question: The curved surface area of a cylindrical pillar is 264 sq.m and its volume is 924 cub.m. Find the ratio of its diameter to its height
(A) 7:9
(B) 7:3
(C) 7:7
(D) 7:6
(E) 7:1
Rationale: Explanation:
{\color{Black} \frac{\prod r^{2}h}{2\prod rh}=\frac{924}{264}}
{\color{Black} \Rightarrow r=\frac{924}{264}\times 2=7m}
{\color{Black}And\; \; 2\prod rh =264 \Rightarrow h=(264\times \frac{7}{22}\times \frac{1}{2}\times \frac{1}{7})=6m}
{\color{Black}\therefore } Required Rato ={\color{Black}\frac{2r}{h} } ={\color{Black}\frac{14}{6}=7:3 }
Answer: B) 7 : 3
Answer: (B) 7:3
Question: In how many ways can 5 GIRLS and 3 BOYS be seated on 8 chairs so that no two BOYS are together?
(A) A)5760
(B) B)14400
(C) C)480
(D) D)56
(E) E)40320
Rationale: Consider the following arrangement:
*G*G*G*G*G
Now, if BOYS occupy the places of 6 stars no BOYS will be together.
# of ways 3 BOYS can occupy the places of these 6 stars is C36=20;
# of ways 3 BOYS can be arranged on these places is 3!=6
# of ways 5 GIRLS can be arranged is 5!=120
So total # of ways to arrange 3 BOYS and 5 GIRLS so that no BOY are together is 20∗6∗120=14,400
ANS:B
Answer: (B) B)14400
Question: S is a set of 45 consecutive multiples of 5. If the smallest number in S is 55, then the greatest number in S is
(A) 198
(B) 275
(C) 299
(D) 402
(E) 205
Rationale: last term =first term +(total no. of terms-1)consecutive difference
S is a set of 45 consecutive multiples of 5. If the smallest number in S is 55, then the greatest number in S is
first term = 55 ; total terms =45 ; difference = 5
55+(44)5 = 275
Ans B
Answer: (B) 275
Question: A salesman commission is 10% on all sales upto $5000 and 5% on all sales exceeding this. He remits $15000 to his parent company after deducting his commission. Find the total sales?
(A) 15456
(B) 14758
(C) 15789
(D) 13250
(E) 12450
Rationale: Let his total sales be x
Total sales - commission = $15000
x - [(10% of 5000)+5% of (x-5000)] = 15000
95x/100 = 15000
x = 15789 approximately
Answer is C
Answer: (C) 15789
Question: The product of all the prime numbers less than 24 is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: OA: B
Answer: (B) 10^8
Question: If the cost price of 12 pens is equal to the selling price of 11 pens, the gain percent is:
(A) 80%
(B) 90%
(C) 9%
(D) 40%
(E) 10%
Rationale: Explanation:
Let C.P. of each pen be Re. 1.
Then, C.P. of 11 pens = Rs. 11; S.P. of 11 pens = Rs. 12.
Gain % = 1/11 * 100 = 9%
Answer:C
Answer: (C) 9%
Question: One boy can eat 100 chocolates in half a minute, and another can eat half as many in twice the length of time. How many chocolates can both boys eat in 15 seconds?
(A) 61.5 chocolates
(B) 63.5 chocolates
(C) 62.5 chocolates
(D) 64.5 chocolates
(E) 65.5 chocolates
Rationale: 1st boy eats 100 chocos / 30 sec
so he can eat 50 in 15 sec
2nd boy can eat one-half of 100 in twice of 30 sec
so he can eat 50 in 60 sec
or that is 12.5 in 15 sec
so, together they can eat
50 + 12.5 or
62.5 chocolates in 15 seconds.
ANSWER:C
Answer: (C) 62.5 chocolates
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
(A) 12 kmph
(B) 18 kmph
(C) 19 kmph
(D) 15 kmph
(E) 11 kmph
Rationale: Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5
=12 kmph.
Answer:A
Answer: (A) 12 kmph
Question: If 28^2*17^3*12^2 = x, what is the units digit of x ?
(A) 2
(B) 8
(C) 6
(D) 7
(E) 9
Rationale: 28^2*17^3*12^2 = x
Units digit of x will be
8^2 * 7^3 * 2^2
=2* 3 * 4
=8
Therefore , units digit of x = 8
Answer B
Answer: (B) 8