mathewhe/aqua_rat huggingface dataset:
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
(A) 285
(B) 377
(C) 366
(D) 288
(E) 261
Rationale: Since the month begins with a Sunday, there will be five Sundays in the month
Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285
Answer: A) 285
Answer: (A) 285
Question: There are two numbers. If 55% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) A)5/6
(B) B)5/8
(C) C)5/11
(D) D)6/7
(E) E)7
Rationale: Let the two numbers be x and y.
55/100 * x + y = 5/4y
=> 11/20 x = 1/4 y => x/y = 5/11
C)
Answer: (C) C)5/11
Question: In how many years Rs 100 will produce the same interest at 5% as Rs. 600 produce in 4 years at 10%
(A) 44
(B) 52
(C) 50
(D) 46
(E) 48
Rationale: Explanation:
Clue:
Firstly we need to calculate the SI with prinical 600,Time 4 years and Rate 10%, it will be Rs. 240
Then we can get the Time as
Time = (100*240)/(100*5) = 48
Option E
Answer: (E) 48
Question: A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: Let x be the fraction of her take-home pay that the worker saved.
Let P be the monthly pay.
12xP = 4(1-x)P
12xP = 4P - 4xP
16xP = 4P
x = 1/4
The answer is B.
Answer: (B) 1/4
Question: How many digits are required to number a book containing 250 pages?
(A) 756
(B) 642
(C) 492
(D) 372
(E) 250
Rationale: 9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
250-(90+9)=151 pages will require 151*3=453 digits.
The total number of digits is 9+180+453=642.
The answer is B.
Answer: (B) 642
Question: In how many ways can the letters of the word ACTUAL be rearranged such that the vowels always appear together?
(A) 6!/2!
(B) 3!*3!
(C) 4!/2!
(D) (4! *3!)/2!
(E) 3!*3!/2
Rationale: In the word ABACUS , there are 3 vowels - 2 A's and U
Number of ways the letters of word ACTUAL be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: (D) (4! *3!)/2!
Question: If x and y are both prime numbers greater than 10, which of the following CANNOT be true?
I. xy is an even number.
II. x - y = 117.
III.The sum of x and y is even.
(A) A)I and II only
(B)  I only
(C)  I and III only
(D)  II and III only
(E)  I, II and III
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
Since x and y are both prime numbers greater than 10, they must both be odd. Therefore xy must be an odd number, so Statement I cannot be true. Similarly, if x and y are both odd, then x - y cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since x and y are both odd, x + y must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,the correct answer is (D).
Answer : D
Answer: (D)  II and III only
Question: There is a total of 84 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/7. What is the probability that the marble will be either red or blue?
(A) 4/7
(B) 9/14
(C) 11/14
(D) 17/28
(E) 23/28
Rationale: P(red or blue) = 1 - P(white) - P(green) = 28/28 - 7/28 - 4/28 = 17/28
The answer is D.
Answer: (D) 17/28
Question: A worker makes a toy in every 1h. If he works for 100h, then how many toys will he make ?
(A) 40
(B) 54
(C) 45
(D) 39
(E) 100
Rationale: No. of toys = 100/1 = 100
Answer : E
Answer: (E) 100
Question: A chessboard is an 8×8 array of identically sized squares. Each square has a particular designation, depending on its row and column. An L-shaped card, exactly the size of four squares on the chessboard, is laid on the chessboard as shown, covering exactly four squares. This L-shaped card can be moved around, rotated, and even picked up and turned over to give the mirror-image of an L. In how many different ways can this L-shaped card cover exactly four squares on the chessboard?
(A) 256
(B) 336
(C) 424
(D) 512
(E) 672
Rationale: Select 3 squares which are in a line together first. We will call them a block of 3 squares. Consider just the vertical arrangement for now (for horizontal, we will multiply everything by 2 at the end).
Consider a block of 3 squares lying vertically on the left edge (the first column of the chess board). You can place another square on the right to make an L at either extreme of the block. So for each such block, you can make an L in 2 ways. There will be 12 such blocks (6 on either edge).
You get 12*2 Ls.
Now consider the blocks of 3 squares lying vertically in columns 2 to 7. You can make an L by placing a square on left or right at either end. So for each block of 3 squares, you can make 4 Ls. There are 6 such blocks in each of the 6 columns
You get 6*6*4 Ls.
Total you get 12*2 + 6*6*4 = 168 Ls.
Now you just multiply it by 2 to account for the Ls lying horizontally too. Since it is a square, the number of Ls found vertically will be the same as the number of Ls found horizontally.
Total = 168*2 = 336
Answer (B)
Answer: (B) 336
Question: A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is
(A) 1:10
(B) 1:12
(C) 1:15
(D) 1:20
(E) 1:25
Rationale: Milk = m liters;
Water = w liters;
Cost of m+w liters = 6.4m;
Selling price of m+w liters = 8(m+w).
Given that 6.4m*1.375 = 8(m+w) --> w/m=1/10.
Answer: A.
Answer: (A) 1:10
Question: A train speeds past a pole in 15 sec and a platform 150 m long in 25 sec, its length is?
(A) 238
(B) 150
(C) 988
(D) 177
(E) 225
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 150)/25 = x/15 => x = 225 m.
Answer: E
Answer: (E) 225
Question: The number 94 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?
(A) 2
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-2, +/-3 and +/-9, so the difference could be 7, 11 or 12. Since only one of them is among the choices, then it must be the correct answer.
Answer: C
Answer: (C) 7
Question: The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 9!?
(A) 3(5!)
(B) 4(5!)
(C) 6(5!)
(D) 5(5!)
(E) 7(5!)
Rationale: GCF is the product of common factors of the numbers involved.
GCF = 5!
a = 9! = 9*8*7*6*5!
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 5 (5!) and 9! will have GCF as 5!
Ans D
Answer: (D) 5(5!)
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 72 seconds. What is the length of each train (in meters)?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 72 seconds, the relative difference in distance traveled is 72 * 25/9 = 200 meters
This distance is twice the length of each train.
The length of each train is 200/2 = 100 meters
The answer is D.
Answer: (D) 100
Question: A certain article of clothing was discounted during a special sale to 2/3 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
(A) 50%
(B) 22.22%
(C) 25%
(D) 16.66%
(E) 12.5%
Rationale: Say the original retail price of the item was $200.
The price after the first sale = 2/3 * $200 = $400/3.
The price after the second sale = 1/2 * $200 = $100.
The percent change from the first sale to the second = (400/3 - 100) / 150 = 1/3 = 22.22%.
Answer: B.
Answer: (B) 22.22%
Question: In a lottery, there are 10 prizes and 20 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/10
(B) 2/5
(C) 1/3
(D) 5/7
(E) None
Rationale: Solution
P(getting a prize)	= 10 / (10+20)
‹=› 10 / 30
‹=› 1/ 3.
Answer C
Answer: (C) 1/3
Question: In a 500 m race, Ravi beats Ramesh by 5 seconds or 100 m. They decide to run another race and this time Ravi gives Ramesh a head tart of 200 m. If Ravi’s speed is twice his previous speed and Ramesh’s speed is one and half times his previous speed, how far from the starting point should the winning post be so that they finish at the same time?
(A) 500 m
(B) 1000 m
(C) 1500 m
(D) 2000 m
(E) 2500 m
Rationale: Ravi beats ramesh by 5 sec or 100 mtr....means ramesh cover 100mtr in 5 sec....by this we can get ramesh speed in 20m/sec
20.............in 1 sec
500........in 500/20=25 sec(Ramesh's time)
so ravi take 20 sec to cover 500 mtr......by this we can get that ravis speed is 25m/sec
now assume x be the distance from staring line where we need to put the winning post.
According to question ravi’s speed will be 25*2=50m/sec & ramesh’s speed will be 20*1.5=30 m/sec
now assume x be the distance from staring line where we need to put the winning post.
they will take same time to reach the wining post.
As ravi gives Ramesh a 200 m ahead start so he has to accede x meter and Ramesh has to accede (x-200) meter
Hence we may write,
x/50=(x-200)/30
x=500 meter
ANSWER:A
Answer: (A) 500 m
Question: What is the Compound Interest on Rs.9500 at 6% p.a. compounded half-yearly for 1 1/2 years.
(A) 810.91
(B) 840.91
(C) 880.91
(D) 887.91
(E) 980.91
Rationale: Compound interest : A = P(1 + r/n)nt
A = 10,380.91
C.I. >> 10,380.91 - 9500 >> Rs. 880.91
Answer:C
Answer: (C) 880.91
Question: Five farmers have 7,9,11,13 & 14 apple trees respectively in their orchards.last year each of them discovered that every tree in their own orchard bore exactly d same no of apples.further,if d 3rd farmer gives one apple to the 1st,& the 5th gives 3 to each of the 2nd & d 4th,they would all exactly have the same no of apples, what were d yields per tree in the orchards of d 3rd & 4th farmers?
(A) 8,9
(B) 10,11
(C) 11,12
(D) 11,9
(E) 11,8
Rationale: Let a, b, c, d & e be the number of apples bored last year in each farmer's tree.
Given that 7a + 1 = 9b + 3 = 11c - 1 = 13d + 3 = 14e - 6
But the question is to find the number of apples bored per tree in 3rd nd 4th orchard.It is enough to consider 11c - 1 = 13d + 3..
Therefore 11 c - 1 = 13 d + 3
By trial and error method, we get the value for c and d as 11 and 9.
5th nd 4th
14e - 6 = 13d + 3
14e - 13d = 9
here if u put e=d=1, result ll be 1, e=d=2 difference ll be 2, .... e=d=9 ,result ll be 9
so e=9 , d=9
So 5ht tree ll give 14 * 9 = 126 no. of apples
4th tree ll give 13 * 9 = 117 no. of apples
for 5th nd 2nd
14 * 9 -6 = 9 * b + 3
120=9b + 3
b = 13
So 2nd tree ll give 9 * 13 = 117
A= 119 , per tree = 17
B= 117 , per tree = 13
C= 121, per tree = 11
D= 117, per tree = 9
E = 126 , per tree = 9
3'rd farmer have 11 apples per tree and
4'th farmer have 9 apples per tree.
ANSWER:D
Answer: (D) 11,9
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
(A) 17/27
(B) 17/25
(C) 17/76
(D) 17/20
(E) 17/23
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20
= 17/20
Answer: D
Answer: (D) 17/20
Question: Find the probability that a non leap year selected at random will have 53 Sundays
(A) 6/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 1/7
Rationale: There are 365 days in a leap year: 52 weeks and 1 more days. So, 52 Sundays and 1 days.
This 1 days can be {Mon, Tue, Wed, Thu, Fri, Sat,Sun} (7 cases). In order to have 53 Sundays we should have Sun case.
The probability of that is 1/7.
Answer: E.
Answer: (E) 1/7
Question: Of the 200 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 45 percent of the employees prefer City Y and 55 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
(A)  65
(B)  100
(C)  115
(D)  130
(E)  135
Rationale: 110 prefer X (Group 1);
90 prefer Y (Group 2).
City Y needs 150 people: letall 90 who prefer Y (entire Group 2) be relocated there, the rest 60 will be those who prefer X from Group 1;
City X needs 40 people: 110-60=40 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 90+40=130.
Answer: D.
Answer: (D)  130
Question: Johnny has 4 classes. He averaged a mark of 83 in those classes. If Johnny takes night school and scores an 88 in the course, what will his new average be?
(A) 83
(B) 84
(C) 85
(D) 85.5
(E) 86
Rationale: (sum of the 4 marks)/4 = 83
sum of the 4 marks = 332
new sum = 332 + 88 = 420
new average = 420/5 = 84
ans: B
Answer: (B) 84
Question: A student chose a number, multiplied it by 7, then subtracted 150 from the result and got 130. What was the number he chose?
(A) 40
(B) 42
(C) 44
(D) 46
(E) 48
Rationale: Let x be the number he chose, then
7⋅x−150=130
7x=280
x=40
correct answer A
Answer: (A) 40
Question: The surface area of a cube is 1734 sq. cm. Find its volume
(A) 2334 cubic.cm
(B) 3356 cubic.cm
(C) 4913 cubic.cm
(D) 3478 cubic.cm
(E) None of these
Rationale: Explanation:
Let the edge of the cube bea. Then,
6a2 = 1734
=> a = 17 cm.
Volume = a3 = 173 = 4193 cm3
Answer: C
Answer: (C) 4913 cubic.cm
Question: A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 150 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
(A) 280
(B) 210
(C) 300
(D) 310
(E) 320
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/350 + 400/150 = 80/21
=> avg speed = (800*21)/80 = 210(approx)
ans is B
Answer: (B) 210
Question: The average of 11 numbers is 10.6. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
(A) 71.5
(B) 11.5
(C) 81.5
(D) 14.8
(E) 21.5
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.6 x 11] = 14.8.
Answer: D
Answer: (D) 14.8
Question: A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount?
(A)  $7.20
(B)  $8.00
(C)  $8.10
(D)  $8.27
(E)  $9.00
Rationale: sale price = (original price - 10% decrease) - 10% decrease
price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10
The answer is C.
Answer: (C)  $8.10
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ?
(A) -280
(B) 300
(C) -350
(D) -380
(E) None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 680 - 80 = 250
And x = -350.
Answer C
Answer: (C) -350
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70 percent
(C) 100%
(D) 120%
(E) None
Rationale: Solution
Let C.P. = Rs. 100.	Then, Profit = Rs.320,
S.P. = 420.
Let C.P. = Rs. 125% of Rs. 100	= Rs.125.
New S.P. = Rs.420.
Profit = Rs. (420 - 125)	= Rs.295.
∴ Required percentage	= (295 / 420 x 100)%
= 1475 / 21%
= 70%.
Answer B
Answer: (B) 70 percent
Question: 6+3+2 = 242116
8+9+1 = 727216
5+7+4 = 505644
2+7+5 =?
(A) 224210
(B) 224220
(C) 224230
(D) 224240
(E) 224250
Rationale: 6+3+2 = 242116 = 6*(3+2-1) 3*(6+2-1) 2*(6+3-1)=6*4 3*7 2*8= 242116
8+9+1 = 727216
5+7+4 = 505644 = (5*10) (7*8) (4*11)
2+7+5 = 2*(7+5-1) 7*(2+5-1) 5*(2+7-1) = 224240
ANSWER:D
Answer: (D) 224240
Question: The ratio 25:50 expressed as percent equals to
(A) 50 %
(B) 85 %
(C) 25 %
(D) 75 %
(E) None of above
Rationale: Explanation:
Actually it means 25 is what percent of 50, which can be calculated as,
(25/50)*100 = 25 * 2 = 50
Answer: Option A
Answer: (A) 50 %
Question: Find the C.I. on a sum of Rs.10000 for 6 months at 25% per annum, interest being compounded quarterly?
(A) 10290
(B) 5290
(C) 1289
(D) 1290
(E) 2290
Rationale: C.I.= 2000(21/20)^2-1800
= 1289
Answer: C
Answer: (C) 1289
Question: If pqr < 0 and qr > 0, which of the following must be positive?
(A)  xy
(B)  xz
(C)  (p^2)qr
(D)  p(q^2)r
(E)  xy(z^2)
Rationale: Given that qr is positive and pqr is negative, you can say that p MUST be negative. As for q and r either they are both positive or both negative.
Option (C) has p^2 which is positive and qr which is positive. So (C) must be positive.
Answer: (C)  (p^2)qr
Question: 56 +57+58+59=230. How many such 4 consecutive numbers are there less than 500 when added gives a sum which is divisible by 10?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: since 1+2+3+4=10 & 6+7+8+9=30
any combination with these no be will give u desirable result...
so total no in 100 will be 20 & that's why in in 500,it will be 20x5=100.
ANSWER:A
Answer: (A) 100
Question: Consider a quarter of a circle of radius 36. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
(A) 16*(sqr2 -1)
(B) 8*(sqr3 -1)
(C) 4*(sqr7 - 1)
(D) 36* (sqr2 -1)
(E) None of these
Rationale: I got 36/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is D
Answer: (D) 36* (sqr2 -1)
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
(A) 3!*8!*4!*4! ways
(B) 8!*4!*4! ways
(C) 3!4! ways
(D) 3!*5! ways
(E) 3!*6! ways
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
ANSWER A
Answer: (A) 3!*8!*4!*4! ways
Question: A woman named Ragavi started a business investing Rs. 7,000. Roja joined him after six months with an amount of Rs. 7,000 and Sachin joined them with Rs. 7,000 after another six months. The amount of profit earned should be distributed in what ratio among Ragavi, Roja and Sachin respectively, 3 years after A woman started the business ?
(A) 7:6:10
(B) 12:15:16
(C) 42:45:56
(D) 42:45:55
(E) 6:5:4
Rationale: Explanation :
Akash : Roja : Sachin = (7000 x 36) : (7000 x 30) : (7000 x 24)
= 36:30:24 => 6:5:4
Answer :E
Answer: (E) 6:5:4
Question: Dan's age after 16 years will be 4 times his age 8 years ago. What is the present age of Dan?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: Let Dan's present age be x.
x+16 = 4(x-8)
3x = 48
x = 16
The answer is B.
Answer: (B) 16
Question: A train covers a distance of 18 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 120m
(B) 180m
(C) 240m
(D) 220m
(E) 280m
Rationale: Speed = (18/10 * 60) km/hr = (108 * 5/18) m/sec = 30 m/sec.
Length of the train = 30 * 6 = 180 m.
ANSWER:B
Answer: (B) 180m
Question: Use distributive property to solve the problem below:
Maria bought 10 notebooks and 5 pens costing 3 dollars each.How much did Maria pay?
(A) 30 dollars
(B) 40 dollars
(C) 45 dollars
(D) 60 dollars
(E) 70 dollars
Rationale: Solution
3 × (10 + 5) = 3 × 10 + 3 × 5 = 30 + 15 = 45 dollars
Answer C
Answer: (C) 45 dollars
Question: The present ages of three persons in proportions 4 : 7 : 5. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 20, 35, 25
(D) 16, 28, 34
(E) 16, 28, 33
Rationale: Let their present ages be 4x, 7x and 5x years respectively.
Then, (4x - 8) + (7x - 8) + (5x - 8) = 56
16x = 5.
Their present ages are 4x = 20 years, 7x = 35 years and 5x = 25 years respectively.
Answer:C
Answer: (C) 20, 35, 25
Question: Jackson has $313,192 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,192 = 19 and 18 is divisible by 9.
Hence we need to subtract 1 to this number for it to be divisible by 9
Correct Option: A
Answer: (A) $1
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat(in still water) and the stream is
(A) 1:2
(B) 1:3
(C) 2:1
(D) 3:1
(E) None
Rationale: Sol.
Let man’s rate upstream be x kmph. Then, his rate downstream = 2x kmph.
∴ (Speed in still water) : (Speed of stream)
= [2x + x / 2] : [2x - x / 2]
3x / 2 : x / 2 = 3:1.
Answer D
Answer: (D) 3:1
Question: How many words can be formed by using all letters of word ALIVE.
(A) 120
(B) 236
(C) 128
(D) 261
(E) 191
Rationale: Explanation:
The word ALIVE contains 5 different letters
Therefore,
Required number of words = 5p5 = 5!
= (5*4*3*2*1) = 120
ANSWER:A
Answer: (A) 120
Question: one person Tharak speed with the current is 10 km/hr and the speed of the current is 4 km/hr. Tharak's speed against the current is:
(A) 0 km/hr
(B) 1 km/hr
(C) 2 km/hr
(D) 3 km/hr
(E) 4 km/hr
Rationale: Man's speed with the current = 10 km/hr
=> speed of the man + speed of the current = 10 km/hr
speed of the current is 4 km/hr
Hence, speed of the man = 10-4 = 6 km/hr
man's speed against the current = speed of the man - speed of the current
= 6-4 = 2 km/hr
ANSWER:C
Answer: (C) 2 km/hr
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
(A) 8%
(B) 2%
(C) 3%
(D) 4%
(E) 6%
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100
=0.04 * 100
= 4%
Answer:D
Answer: (D) 4%
Question: The smallest number when increased by " 1 " is exactly divisible by 6,18,36,48, 60 is:
(A) 724
(B) 721
(C) 720
(D) 719
(E) 700
Rationale: LCM = 720
720 - 1 = 719
ANSWER:D
Answer: (D) 719