mathewhe/aqua_rat huggingface dataset:
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) Rs.48
(B) Rs.64
(C) Rs.44
(D) Rs.46
(E) Rs.34
Rationale: π (152 - 132)
= 176
176 * 1/4
= Rs.44
Answer: C
Answer: (C) Rs.44
Question: There are 1000 students in a school and among them 30 % of them attends chess class. 10% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
(A) 1
(B) 10
(C) 100
(D) 30
(E) 20
Rationale: 30% of 1000 gives 300. so 300 attends chess and 10% of 300 gives 30.
so 30 enrolled for swimming
Answer: D
Answer: (D) 30
Question: A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 76, how many questions did Student A answer correctly?
(A) 92
(B) 60
(C) 73
(D) 82
(E) 91
Rationale: let the number of correct responses be x
then the number of incorrect responses =100-x
according to question
x-2(100-x)=76 (subtracting twice of incorrect from correct)
3x=276
x=92
ANSWER:A
Answer: (A) 92
Question: If x + 4 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?
(A)  -2 and 10
(B)  -3 and 4
(C)  2 and 7
(D)  3 and 4
(E)  3 and 10
Rationale: Let’s isolate x in each inequality.
x + 4 > 2
x > -2
Next we simplify x – 3 < 7.
x – 3 < 7
x < 10
We know that x is greater than -2 and less than 10.
The answer is A.
Answer: (A)  -2 and 10
Question: Of 30 applicants for a job, 12 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 14
(B) 13
(C) 9
(D) 7
(E) 5
Rationale: D. 7
30 - 3 = 27
27 - 12 - 18 = -7
Then 7 are in the intersection between 4 years experience and degree.
Answer D
Answer: (D) 7
Question: X and Y invested in abusiness. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is :
(A) 35,000
(B) 40,000
(C) 50,000
(D) 60,000
(E) None
Rationale: Sol.
Suppose Y invested Rs. y. Then, 40000/y = 2/3 or y = [40000 * 3 / 2] = 60000.
Answer D
Answer: (D) 60,000
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 30 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?
(A) 57
(B) 177
(C) 178
(D) 89
(E) 378
Rationale: Lets say she sales x items so her commission will be : x * 1500*30/100 = 450x
Salary difference is: 85000 - 45000 = 40000
So commission must at least be equal to salary difference i.e. x = 40000/450 = 89 (Approx).
Hence answer is D
Answer: (D) 89
Question: If an object travels at two feet per second, how many feet does it travel in one hour?
(A) 3488
(B) 3778
(C) 7200
(D) 1800
(E) 2881
Rationale: Explanation:
If an object travels at 2 feet per second it covers 2x60 feet in one minute, and 2x60x60 feet in one hour.
Answer = 7200
Answer: C) 7200
Answer: (C) 7200
Question: The series of differences between consecutive prime numbers is represented as dp1, dp2, dp3, .... dpn .Whare dp1 is the difference between the second and the first prime number. Find the sum of series when n = 23, given that the 23rd prime number is 83 ?
(A) 81
(B) 82
(C) 83
(D) 87
(E) 86
Rationale: S1 = 1 when last prime number is 3
S2 = 3 when last prime number is 5
S3 = 5 when last prime number is 7 and so on.
So the sum of the series is 2 less than the last prime number.
So S23 = 83 - 2 = 81
ANSWER:A
Answer: (A) 81
Question: The triplicate ratio of 1:3 is?
(A) 1:27
(B) 1:8
(C) 1:3
(D) 1:1
(E) 1:2
Rationale: 1^3: 3^3 = 1:27
Answer: A
Answer: (A) 1:27
Question: 25.25/3000 is equal to:
(A) 0.008416667
(B) 0.110773333
(C) 0.12526234
(D) 0.01072333
(E) 0.12725002
Rationale: 25.25/3000 = 2525/300000
= 0.008416667
ANSWER:A
Answer: (A) 0.008416667
Question: 80 x 100 + 80 x 11 = ?
(A) 7500
(B) 8880
(C) 6200
(D) 5200
(E) None of them
Rationale: =80 x (100+11) (by distributive law)
=80 x 111
=8880
Answer is B
Answer: (B) 8880
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 190 games will be played during the tournament. What is the number of participants?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Let n be the number of participants.
The number of games is nC2 = n*(n-1) / 2 = 190
n*(n-1) = 380 = 20*19 (trial and error)
The answer is D.
Answer: (D) 20
Question: If a certain toy store's revenue in November was 2/3 of its revenue in December and its revenue in January was 1/3 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
(A)  1/4
(B)  1/2
(C)  2/3
(D)  2
(E)  3
Rationale: Let Dec rev =100
Then Nov rev is 2/3 (100) => 67
Therefore Jan rev = 1/3(Nov rev) = 1/3(67) => 23
Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (67+23)/2
x = 100/45 => 2.22=3
Ans) E
Answer: (E)  3
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
(A) 20
(B) 24
(C) 27
(D) 30
(E) 35
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: (C) 27
Question: How many multiples of 100 are there between 100 and 1000 (both are inclusive)?
(A) 2
(B) 8
(C) 4
(D) 5
(E) 10
Rationale: the answer is (1000-100)/100+1=10
Answer is E
Answer: (E) 10
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 40 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 67.5
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 40 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
40 = 180/4t
t = 67.5
B-C = 67.5mph
Answer E
Answer: (E) 67.5
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L does pass the origin.
2.Line L must passes through the first quadrant.
3.The slope of L is negative
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
aAnswer C
Answer: (C) III only
Question: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 90,000 different outfits, then for how many garments does Dave have exactly five choices?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 90,000 = 9*10,000 = 9*5^4*2^4
Dave has exactly 5 choices for four garments.
The answer is E.
Answer: (E) 4
Question: Which of the following fractions is at least twice Smaller than 13/50?
(A) 2/5
(B) 11/34
(C) 9/20
(D) 8/21
(E) 43/99
Rationale: Answer C
13/50=0.26
9/20=0.45 which is 0.07 smaller than two times of 0.26
Answer: (C) 9/20
Question: Bhatia, Ashtikar and Singh begin to play with Rs 70 each. At the end the ratio of the amounts left
with Ashtikar and Singh is 1 : 2 and of those with Singh and Bhatia is 4 : 1. What is Singh's gain
(in Rs)?
(A) 40
(B) 45
(C) 48
(D) 50
(E) 53
Rationale: We have b+a+s = 210
and s = 2a, s = 4b and a = 2b
solving these EQs we got
that singh have Rs.120 in the end
Bhatia have 30
and Astikar have 60.
so singh's profit is 120 - 70 = 50
ANSWER:D
Answer: (D) 50
Question: If a number between 10 and 20 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
(A) 2/11
(B) 1041
(C) 14/41
(D) 27/41
(E) 11/41
Rationale: If tens digi is 2 ---> ones digit : 0
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 20-10+1=11.
So the probability is 2/11.
The answer is (A).
Answer: (A) 2/11
Question: If k is an integer and 2 < k < 8, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (6-2) < k < (6+2)
4 < k < 8
Thus k = 5, 6, 7
Since 2 < k < 8, then k can be 5, 6, or 7.
The answer is D.
Answer: (D) 3
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
(A) 32
(B) 24
(C) 12
(D) 7
(E) 45
Rationale: Answer: Option B
Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
Answer: (B) 24
Question: If circles x and y have the same area and circle x has a circumference of 20π, half of the radius of circle y is:
(A) 16
(B) 5
(C) 4
(D) 2
(E) 1
Rationale: x bé radius of circle x
ý bé radius of circle y
given:
pi*x^2 = pi*ý^2
also,
2*pi*x = 20*pi
x =10
thus ý = 10
y/2 = 5
Ans: B
Answer: (B) 5
Question: If the radius of a circle is decreased 60%, what happens to the area?
(A) 10% decrease
(B) 20% decrease
(C) 36% decrease
(D) 84% decrease
(E) 50% decrease
Rationale: Area of Square = Pi* radius^2
New Radius = 0.4 * old radius
so new area = (0.4)^2 old area => 0.16 of old area =>16% old area
Ans : D
Answer: (D) 84% decrease
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 36 hours respectively. The ratio of their speeds is?
(A) 6:5
(B) 6:3
(C) 4:4
(D) 4:8
(E) 4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √36 : √9
= 6:3
Answer: B
Answer: (B) 6:3
Question: Let n be divided by 5,and the remainder obtained is 4. What will be the remainder when 5 divided by 2n?
(A) 2
(B) 4
(C) 1
(D) 3
(E) 5
Rationale: n=5*x+4
so, 2*(n)/5=(10*x+8)/5
10*x divided by 5
when 8 divided by 5 then remainder is 3.
ANSWER:D
Answer: (D) 3
Question: The difference between a number and its two-fifth is 510. What is 15% of that number?
(A) 152.01
(B) 85
(C) 76
(D) 168.2
(E) 127.5
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
15% of 850 = 127.5.
Answer:E
Answer: (E) 127.5
Question: If S is the sum of reciprocals of a list of consecutive integers from 15 to 24, inclusive, S is approximately equal to
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
Rationale: We need to find the approximate value of 1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24. Now, the sum of these 10 terms will be very close to 10 times 1/20, which is 0.05*10=0.5.
Answer: E.
Answer: (E) 0.5
Question: An article is bought for Rs.800 and sold for Rs.600, find the loss percent?
(A) 18 2/3%
(B) 16 7/3%
(C) 16 2/8%
(D) 25%
(E) 76 2/3%
Rationale: 800 ---- 200
100 ---- ? => 25%
Answer:D
Answer: (D) 25%
Question: At what rate percent on simple interest will a sum of money double itself in 50 years?
(A) 3 1/3%
(B) 3 1/9%
(C) 3 9/3%
(D) 2%
(E) 3 6/3%
Rationale: P = (P*50*R)/100
R = 2%
Answer: D
Answer: (D) 2%
Question: In a zoo, the ratio of the number of cheetahs to the number 4 then what is the increase in the number of pandas?
(A)  2
(B)  12
(C)  5
(D)  10
(E)  15
Rationale: One short cut to solve the problem is
c:p = 1:3
c increased to 5
=> 1:3 = 5:x
=> x = 15
=>p increased by 12
B is the answer
Answer: (B)  12
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 35 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
(A) 65%
(B) 70%
(C) 75%
(D) 89%
(E) 95%
Rationale: find the product of the two increases: (1.4) * (1.35) which is 1.89 and a 89% increase.
D
Answer: (D) 89%
Question: In a 1200 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
(A) 100 sec.
(B) 50 sec
(C) 60 sec
(D) Data not sufficient
(E) None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1200/5 = 240 sec.
Time taken by Baley to complete the race is D = 1200/4 = 300 sec.
Hence, D-B = 60 sec
ANSWER:C
Answer: (C) 60 sec
Question: 9823 + x = 13200, then x is ?
(A) 3327
(B) 3237
(C) 3337
(D) 3377
(E) None of these
Rationale: Answer
x = 13200 - 9823 = 3377
Option: D
Answer: (D) 3377
Question: If 8 women can color 400 m long cloth in 5 days, then 10 women can color 500 m long cloth in?
(A) 6 days
(B) 4 days
(C) 5 days
(D) 15 days
(E) 10 days
Rationale: The length of cloth painted by one woman in one day = 400/ 8× 5 = 10 m
No. of days required to paint 500 m cloth by 10 women = 500/ 10 × 10 = 5 days
Answer : C
Answer: (C) 5 days
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 70% marks is
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
Rationale: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 1 subject where he secured more that 70 %.
The answer is 1.
C
Answer: (C) 1
Question: If 10 % of an electricity bill is deducted, 45 is still to be paid. How much was the bill?
(A) 50
(B) 60
(C) 55
(D) 70
(E) None of these
Rationale: Let the bill be x. Then
90% of x = 45
⇒ x = 45×100/90 = 50
Answer A
Answer: (A) 50
Question: A three-person committee must be chosen from a group of 8 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
(A) A)70
(B) B)696
(C) C)630
(D) D)1,260
(E) E)1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 10 students and 8 professors - Number of ways to select 3 people from 10 student (i.e. without including any professor)
= 18C3 - 10C3 = 816 - 120 = 696
ANSWER:B
Answer: (B) B)696
Question: Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
(A) $160
(B) $1,600
(C) $2,200
(D) $4,400
(E) $5,840
Rationale: 11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B)
Answer: (B) $1,600
Question: If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
(A) 3
(B) 1
(C) 2
(D) 5
(E) 4
Rationale: Given number = 97215x6
(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.
x = 3
ANSWER A
Answer: (A) 3
Question: Working together, Tim and Tom can type 12 pages in one hour. If they would be able to type 15 pages in one hour if Tom increases his typing speed by 30%, what is the ratio of Tom's normal typing speed to that of Tim?
(A) 1/5
(B) 5/1
(C) 4/1
(D) 1/4
(E) 1/3
Rationale: Lets say Tim types x pages an hour and Tom types y pages an hour.
We know that x+y=12
Tom increase speed by 30% means he will type 1.3 y pages an hour.
So we get x+1.3 y=15
We need to know the ratio of Tom's speed to Tim's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.3 y=3 so y=10 ... so x=2
(y/x)=10/2 =5/1
Answer is (B)
Answer: (B) 5/1
Question: If |t|=−t, which of the following must be true?
(A) x≥0
(B) t≤0
(C) x2>x
(D) x3<0
(E) 2x<x
Rationale: |t| =-t means absolute value of t is equal to negative of t. Since absolute value cannot be negative hence negative of t should result in a non negative number. It means t is a non positive number i.e. t<0. Answer is B
Answer: (B) t≤0
Question: 60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $200 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
(A) 12
(B) 18
(C) 32
(D) 40
(E) 44
Rationale: Lets take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $200 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 18 (44-12) must be those with four screens or more
B is the answer
Answer: (B) 18
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is
(A) 277
(B) 668
(C) 119
(D) 177
(E) 121
Rationale: Number of words which can be formed
= 5! - 1 = 120 - 1 = 119.
Answer: C
Answer: (C) 119
Question: Four of the following five parts lettered a, b, c, d and e are exactly equal. Which of the following is not equal to the other four?
(A) 24(2) – 12(2) + 112 ÷ 14
(B) 17 × 12 + 59 × 4
(C) 15 × 28 + 20
(D) 27 × 16 + 56 ÷ 8
(E) 185 × 6 ÷ 2 – 23 × 5
Rationale: Other parts are equal to 440.
Answer D
Answer: (D) 27 × 16 + 56 ÷ 8
Question: The radius of the two circular fields is in the ratio 5: 4 the area of the first field is what percent greater than the area of the second?
(A) 22%
(B) 32%
(C) 34%
(D) 64%
(E) 36%
Rationale: r = 5 Ï€r2 =25
r = 4Ï€r2 = 16
25 Ï€ â€“ 9Ï€
100 ---- ? => 36%.Answer:D
Answer: (D) 64%
Question: A can run 192 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
(A) 38 metre
(B) 28 metre
(C) 24 metre
(D) 15 metre
(E) 28 metre
Rationale: Clearly, A beats B by 4 seconds
Now find out how much B will run in these 4 seconds
Speed of B = Distance/Time taken by B=192/32=6 m/s
Distance covered by B in 4 seconds = Speed Ã— time =6Ã—4=24 metre
i.e., A beat B by 24 metre
Answer is C
Answer: (C) 24 metre
Question: At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 10 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?
(A) 20%
(B) 50%
(C) 55%
(D) 75%
(E) 80%
Rationale: R + W + P = 120
S + L = 120
1/3 * 120 = 40
Short-Stemmed White = 20
Short-Stemmed Pink = 10
=> Short-Stemmed Red =10
10/P =10/R
=> R = P
So Total Long Stemmed = 80
And Long Stemmed Red + Long Stemmed Pink = 80
So Long Stemmed Red/Long Stemmed = ?
Total White = 20 (As no Long stemmed white)
=> R + R + 20 = 120
=> 2R = 100 and R = 50
Long Stemmed R = 50 - 10 = 40
So Long Stemmed Red/R = 40/80 = 50%
Answer - B
Answer: (B) 50%
Question: A shop sells 1 chocolate at the rate Rupee 1 each . You can exchange three warppers for one chocolate.
If you have Rs. 15, what is the maximum number of chocolates you can get?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Rs.15 = 15 chocolates
15 wrappers = 5 Chocolates
5 wrappers = 1 chocolate(u have 2 wrappers with you..)
count this wrapper with already existing wrappers = 15+5+1+1 = 22 chocolates..
ANSWER:B
Answer: (B) 22
Question: A discount of 20 percent on an order of goods followed by a discount of 40 percent amounts to
(A) the same as one 45 percent discount
(B) the same as one 40 percent discount
(C) the same as one 36 percent discount
(D) the same as one 52 percent discount
(E) the same as one 25 percent discount
Rationale: 0.8*0.6*x=0.48x from initial value, meaning 0.52 or 52% discount
D
Answer: (D) the same as one 52 percent discount
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, exclusive ?
(A) 5
(B) 1
(C) None of the above
(D) 3
(E) 4
Rationale: Given that n* denotes the product of all the integers from 1 to n, exclusive so, 7* + 3 = 7! + 3 and 7* + 6 = 7! + 6.
Now, notice that we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 3 and 7! +6, inclusive. Which means that there are no primes in this range.
Answer: C
Answer: (C) None of the above
Question: Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed
(A) 486
(B) 366
(C) 299
(D) 278
(E) 1888
Rationale: Explanation:
Volume of new cube = =
Edge of new cube = = 9cm
Surface area of the new cube = ( 6 x 9 x 9) = 486
Answer: A) 486
Answer: (A) 486
Question: Seats for Mathematics,PhysicsandfBilogy in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
(A) 2:3:4
(B) 6:7:8
(C) 6:8:9
(D) 5:8:9
(E) 2:4:6
Rationale: Let the no.of seats Maths, physics and Biology be 5x, 7x and 8x
No.of increased seats are (140%5x), (150%7x) and (175%8x)
Required ration = (150%7x)= 7x:21x/2:2x = 2:3:4
ANSWER : A 2:3:4
Answer: (A) 2:3:4
Question: In 10 years,A will be 1.5 times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
(A) 17 Years
(B) 29 Years
(C) 39 Years
(D) 49 Years
(E) 59 Years
Rationale: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
âˆ´ (x + 9)+ 10 = 1.5 (x - 10) â‡” x + 19 = 1.5x- 15 â‡” 0.5x = 34. x=17Answer A
Answer: (A) 17 Years
Question: The number of stamps that Kaye and Alberto had were in the ration of 6:4 respectively. After Kaye gave Alberto 5 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 8:6. As a result of the gift, Kaye had how many more stamps than Alberto ?
(A) 22
(B) 25
(C) 15
(D) 35
(E) 30
Rationale: K1 = 6x
A1 = 4x
K2 = 6x - 5
A2 = 4x + 5
K2/A2 = 8/6
(6x-5)/(4x+5) = 8/6
6*(6x-5) = 8*(4x+5)
36x - 30 = 32x + 40
4x = 70
x = 17.5
K2 = 6*17.5 -5 = 100
A2 = 4*17.5 + 5 =75
K2 - A2 = 100-75=25
Answer : B
Answer: (B) 25
Question: The area of a square is added to one of its sides, and the perimeter is then subtracted from this total, the result is 4. What is the length of one side?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: The equation is; side + Area - Perimeter = s + A - P = s + s^2 - 4s = s(1 + s - 4).
By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.
Answer: B
Answer: (B) 4
Question: The ratio of the present age of Sandy to that of Molly is 9:2. Eight years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?
(A) 18
(B) 21
(C) 24
(D) 27
(E) 30
Rationale: Let the present age of Sandy be 9x years and that of Molly be 2x years.
(9x + 8) / (2x + 8) = 5 / 2
8x = 24
x = 3
Six years ago, Sandy's age was 9(3) - 6 = 21
The answer is B.
Answer: (B) 21