mathewhe/aqua_rat huggingface dataset:
Question: Simplify: 500 x 500- 200 x 200
(A) 761200
(B) 761400
(C) 761800
(D) 210000
(E) None of them
Rationale: (500)^2 - (200)^2 = (500 + 200) (500 - 200) = 700 x 300 = 210000.
Answer is D.
Answer: (D) 210000
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
(A) 6 hours
(B) 10 hours
(C) 15 hours
(D) 30 hours
(E) 35 hours
Rationale: suppose first pipe filled the tank in x hour
so second in x-5 and third in x-9
1/x+1/(x-5)=1/(x-9)
by solving it we get x=15
ANSWER:C
Answer: (C) 15 hours
Question: Rahul went to a shop and bought things worth Rs. 35, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) A)19.7
(B) B)19.9
(C) C)20.9
(D) D)21.9
(E) E)29.7
Rationale: Total cost of the items he purchased = Rs.35
Given that out of this Rs.35, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (35−30/100−x)6/100 = 30/100
⇒ 6(35 −0.3 −x) = 30
⇒ (35 − 0.3 − x) = 5
⇒ x = 35 − 0.3 − 5 = 29.7
E)
Answer: (E) E)29.7
Question: Look at this series: (1/9), (1/3), 1, ____ , 9, ... What number should fill the blank?
(A) (2/3)
(B) 3
(C) 6
(D) 27
(E) 28
Rationale: Explanation: This is a multiplication series; each number is 3 times the previous number.
Answer: Option B
Answer: (B) 3
Question: A palindrome is a number that reads the same forward and backward, such as 120. How many odd, 4-digit numbers are palindromes?
(A) 40
(B) 55
(C) 50
(D) 90
(E) 2500
Rationale: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc
You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.
Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.
In how many ways can you pick two digits such that the first one is an odd digit?
The first digit can be selected in 5 ways.(1/3/5/7/9)
The second digit can be selected in 10 ways.(0/1/2/3...8/9)
Total = 5*11 = 55 ways
B
Answer: (B) 55
Question: For which of the following functions is f(r+b)=f(r)+f(b) for all positive numbers r and b?
(A) a) f(x)=x^2
(B) b) f(x)=x+1
(C) c) f(x)=root x
(D) d) f(x)=2/x
(E) e) f(x)= -3x
Rationale: f(r+b)=f(r)+f(b) Its E
Answer: (E) e) f(x)= -3x
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) 4
(B) 3
(C) 2
(D) 1
(E) 8
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: A
Answer: (A) 4
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 5 years?
(A) 14300
(B) 24883
(C) 14500
(D) 14600
(E) 15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^5 = 24883
B)
Answer: (B) 24883
Question: If a rectangular room measures 12 meters by 6 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
(A) 288,000,000
(B) 240,000
(C) 2,400,000
(D) 24,000,000
(E) 240,000,000
Rationale: A. 288,000,000
12*100*6*100*4*100 = 288,000,000
Answer: (A) 288,000,000
Question: Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 10ft how many poles do he need?
(A) 20
(B) 30
(C) 40
(D) 60
(E) 65
Rationale: If each side is 120 feet..then total perimeter is 150*4=600
poles every 10 feet hence no of poles= 600/10=60
ANSWER:D
Answer: (D) 60
Question: Look at this series: 53, 53, 43, 43, 33, 33, ... What number should come next?
(A) A)23
(B) B)14
(C) C)27
(D) D)53
(E) E)86
Rationale: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer: A
Answer: (A) A)23
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 23.5
(B) 24.5
(C) 12.5
(D) 14.5
(E) 13.6
Rationale: Explanation:
If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Answer: Option B
Answer: (B) 24.5
Question: A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 14,907,200,000 pounds, how many widgets have been unloaded?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.
When we divide 14,907,200,000 by 100,000, we get 14,907,200,000 = 149,072 * 5^5 *2^5.
149,072 is not divisible by 5, thus there are 5 widgets.
The answer is D.
Answer: (D) 5
Question: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being 1/4%, is:
(A) 113.2
(B) 114
(C) 114.75
(D) 124
(E) 124.75
Rationale: Face Value = Rs. 9000.
Dividend = 10.5%.
Annual Income = Rs. 756.
Brokerage per Rs. 100 = Rs. 0.25.
Dividend is always paid on the face value of a share.
Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.
= 9000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.
= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 125.
= Market Value of Rs. 100 stock = Rs. 125 - Re. 0.25.
= Market Value of Rs. 100 stock = Rs. 124.75.
answer : E
Answer: (E) 124.75
Question: A drought decreased the amount of water stored in State J reservoirs from 200 billion gallons to 150 billion gallons. If the drought decreased the amount of water in the reservoirs to 30 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the rain?
(A)  340
(B)  304
(C)  352
(D)  300
(E)  350
Rationale: After the reservoir is filled to 150 gallons the amount of water is at 30% - which means that 70% of the reservoir is empty. To figure out what that 70% is : 150 gallons /30 percent = x gallons /70 percent , therefore, x = 350 gallons , answer choices A,B,E,D are below 350 . We know that the reservoir must be short more than 350 gallons, therefore, the only possible choice is C.
Answer: (C)  352
Question: In a simultaneous throw of two dice, what is the probability of getting a total of 7?
(A) 1/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 4/5
Rationale: We know that in simultaneous throw of two dice, n(S) = 6 x 6 = 36.
Let E = event of getting a total of 7 ={(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
P(E) = n(E)/n(S) = 6/36 = 1/6.
Answer A.
Answer: (A) 1/6
Question: Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
(A) (a) 80
(B) (b) 55
(C) (c) 82
(D) (d) 83
(E) (e) 84
Rationale: T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples.
So, final number of sets is 11*5=55
Answer : B
Answer: (B) (b) 55
Question: 12 members were present at a board meeting. Each member shake hands with all of the other members before and after the meeting .How many hand shakes were there?
(A) 237
(B) 268
(C) 132
(D) 827
(E) 261
Rationale: Explanation:
In order to have a hand shake there must be two members. Therefore to select 2 out of 12 we have 12C2.
This happens twice that is before and after the meeting
Answer = 12C2 ×2 = 132
Answer: C
Answer: (C) 132
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, 20 speak English well, while 60 of them do not speak English. If 60% of students do not speak French, how many students were surveyed?
(A) 250
(B) 225
(C) 175
(D) 195
(E) 200
Rationale: Number of students who speak French are 60 + 20 = 80
Of total students, the percentage of students who do not speak French was 60% --> percentage of who do is 40%
80-------40%
x ------- 100%
x = 80*100/40 = 200 = number of all students
Answer is E
Answer: (E) 200
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 176 m
(B) 178 m
(C) 120 m
(D) 187 m
(E) 144 m
Rationale: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Answer: (C) 120 m
Question: How many ways are there to arrange the letters in the word Settees ?
(A) 210
(B) 1260
(C) 3780
(D) 7560
(E) 11340
Rationale: 7 total words, 3E, 2S, 2T
= 9! / 3! 2! 2! = 210. Answer A
Answer: (A) 210
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment T that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
(A) a. 3/5
(B) b.2/3
(C) c.7/10
(D) d.3/4
(E) e.4/5
Rationale: X(10) --- Net(0) --- T(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Answer: (A) a. 3/5
Question: A retailer bought a machine at a wholesale price of $126 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?
(A) 81
(B) 100
(C) 120
(D) 135
(E) 168
Rationale: My solution: Wholesale Price= 126
Retail Price, be = x
He provides 10 % discount on Retail price= x-10 x/100
This Retail price = 20 % profit on Wholesale price
x-10 x/100 = 126+ 1/5(126)
x=168;
ANSWER:E
Answer: (E) 168
Question: A train met with an accident 40km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?
(A) 40 km/hr
(B) 55 km/hr
(C) 65 km/hr
(D) 70 km/hr
(E) 48 km/hr
Rationale: let the original speed be 6x. A/q, traveling 40 km at 5/6th of original speed costs him 12 minutes etc
40/5x =40/6x +12/40 -> x =10 , 4x= 40.
Ans A
Answer: (A) 40 km/hr
Question: At a certain conference, 74% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  82.22%
(E)  82.0%
Rationale: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
74% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=74% where X is the number of people who registerd 2 weeks in advance and paid full fee. (ANSWER D)
Answer: (D)  82.22%
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 52 sec
(B) 50 sec
(C) 51 sec
(D) 55 sec
(E) 58 sec
Rationale: B
50 sec
The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: (B) 50 sec
Question: The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let the two-digit number be 10a + b
a = b + 2 --- (1)
10a + b = 7(a + b) => a = 2b
Substituting a =
2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.
ANSWER:B
Answer: (B) 2
Question: The fourth proportional to 12, 14 and 18 is?
(A) 21
(B) 66
(C) 88
(D) 99
(E) 26
Rationale: (14*18)/12 = 21
Answer: A
Answer: (A) 21
Question: If x + y = 0 and x =/ 0,then what is the value of
x2007/y2007?
(A) -2007
(B) -1
(C) 0
(D) 1
(E) 2007
Rationale: x = −y=/0,so x/y=-1
correct answer B
Answer: (B) -1
Question: Which of the following describes all values of x for which 25-x^2 ≥ 0 ?
(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -5 ≤ x ≤ 5
Rationale: 25-x^2 >= 0 ---> x^2-25<=0
--> (x+5)(x-5)<=0
Above equation true for
i) x+5<=0 and x-5>=0 ---> x<= -5 and x>=5 ---> this is not possible ---Strike out this solution
ii) x+5>=0 and x-5<=0 ---> x>=-5 and x<=5 --> -5<=x<=5
Answer E
Answer: (E) -5 ≤ x ≤ 5
Question: In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that both pen will be defective?
(A) 1/6
(B) 2/9
(C) 6/11
(D) 9/16
(E) 3/4
Rationale: Method- 1
There are 9 fine pieces of pen and 3 defective in a lot of 12 pens
i.e. Probability of first pen being defective = (1/3)
i.e. Probability of Second pen being defective = (1/2)
Probability of Both pen being defective = (1/2)*(1/3) = 1/6
Answer: option A
Answer: (A) 1/6
Question: An investor bought a 1-year $5,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
(A) $408
(B) $816
(C) $1224
(D) $800
(E) $400
Rationale: 1.04*1.04*5000 = $5408
The answer is A.
Answer: (A) $408
Question: The average of first three prime numbers greater than 20 is?
(A) 10
(B) 20
(C) 30
(D) 27.7
(E) 50
Rationale: 23 + 29 + 31 = 83/3 = 27.7
ANSWER:D
Answer: (D) 27.7
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 300
(B) 250
(C) 230
(D) 250
(E) 260
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: Option B
Answer: (B) 250
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2999
(C) 2666
(D) 2888
(E) 2123
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58
= Rs.3944.
Answer: A
Answer: (A) 3944
Question: The contents of a certain box consist of 40 apples and 30 oranges. How many oranges must be added to the box so that exactly 40% of the pieces of fruit in the box will be apples?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 30
Rationale: apple = (apple + orange + x)*0.4
40 = (30 + 40 + x)*0.4
x = 30
Answer: E
Answer: (E) 30
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 150
(B) 180
(C) 190
(D) 200
(E) 250
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
ANSWER B
Answer: (B) 180
Question: Which of the following has fractions in ascending order?
(A) 2⁄5, 3⁄5, 1⁄3, 4⁄7, 5⁄6, 6⁄7
(B) 1⁄3, 2⁄5, 3⁄5, 5⁄6, 4⁄7, 6⁄7
(C) 1⁄3, 2⁄5, 3⁄5, 4⁄7, 5⁄6, 6⁄7
(D) 1⁄3, 2⁄5, 4⁄7, 3⁄5, 5⁄6, 6⁄7
(E) None of these
Rationale: 1⁄3 = 0.33; 2⁄5 = 0.4; 4⁄7 = 0.57; 3⁄5 = 0.6; 5⁄6 = 0.83 and 6⁄7 = 0.85
Answer D
Answer: (D) 1⁄3, 2⁄5, 4⁄7, 3⁄5, 5⁄6, 6⁄7
Question: The average height of 30 girls out of a class of 40 is 160 cm. and that of the remaining girls is 156 cm. The average height of the whole class is :
(A) 159
(B) 377
(C) 888
(D) 266
(E) 277
Rationale: Explanation:
Average height of the whole class =(36×160+10×15640)=159(36×160+10×15640)=159 cms
Answer:A
Answer: (A) 159
Question: The ratio of the radius of two circles is 5: 3, and then the ratio of their areas is?
(A) 1: 8
(B) 1: 6
(C) 25: 9
(D) 1: 3
(E) 1: 2
Rationale: r1: r2 = 5: 3
Πr12: Πr22
r12: r22 = 25: 9
Answer:C
Answer: (C) 25: 9
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 11758
(B) 11756
(C) 11753
(D) 11750
(E) 11751
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Answer: (D) 11750
Question: A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%?
(A) 7
(B) 6
(C) 5
(D) 9
(E) 8
Rationale: C
5
C.P. of 6 toffees = $ 1
S.P. of 6 toffees = 120% of $ 1 = $ 6/5
For $ 6/5, toffees sold = 6. For $ 1.
Toffees sold = 6 * 5/6 = 5
Answer: (C) 5
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 40 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 333$
(B) 380$
(C) 420$
(D) 450$
(E) 480$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 40 ) = 21 + 312 => 333
Hence answer will be (A) 333
Answer: (A) 333$
Question: In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−2, −3)?
(A) 4
(B) 2
(C) 0
(D) −2
(E) −4
Rationale: slope = rise/run = 6/12 = 1/2
The equation of the line is y = (1/2)x + b
3 = (1/2)(10) + b
b = -2
The equation of the line is y = (1/2)x - 2
To find the x-intercept, let y = 0:
0 = (1/2)x - 2
x = 4
The answer is A.
Answer: (A) 4
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 30 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) 90
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 30 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
30 = 180/4t
t = 90
B-C = 90mph
Answer A
Answer: (A) 90
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
(A) 46
(B) 83
(C) 45
(D) 53
(E) 64
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
Answer:A
Answer: (A) 46
Question: The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is :
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation:
Let the numbers be 13a and 13b.
Then, 13a * 13b = 2028
=> ab = 12. Now, co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 * 1, 13 * 12) and (13 * 3, 13 * 4).
Clearly, there are 2 such pairs.
ANSWER IS B
Answer: (B) 2
Question: Ravi purchased 20 dozens of toys at the rate of Rs. 360 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 23%
(B) 12%
(C) 10%
(D) 34.1%
(E) 12.2%
Rationale: C
C.P. of 1 toy = 360/12 = Rs. 30
S.P of 1 toy = Rs. 33
Profit = 3/31.25 * 100 = 10%
Answer: (C) 10%
Question: What is the least integer greater than –2+0.5?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: irst, let's take care of the Arithmetic:
(-2) + (0.5) = -1.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -2 to -1.5).
Next, the question asks for the LEAST integer that is GREATER than -1.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -1.5 is -1.
Final Answer:B
Answer: (B) –1
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
(A) 814
(B) 820
(C) 840
(D) 844
(E) None of these
Rationale: Explanation:
Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 × 41) cm2
Answer: A
Answer: (A) 814
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 12:40 a.m., how long will the conference last if there are a total of 6 seminars that day?
(A) hours and 15 minutes
(B) hours and 20 minutes
(C) hours and 25 minutes
(D) hours and 30 minutes
(E) hours and 35 minutes
Rationale: Well its like this S B S B S B S B S B S
the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5=150
Time of 1 seminar =150 /3=50 min .
So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 20 min .
Answer is B.
Answer: (B) hours and 20 minutes
Question: When which digit in 467*15*23 is added 1, the product changes by least value?
(A) 1
(B) 2
(C) 6
(D) 7
(E) 5
Rationale: let volume of cuboid = 8*9*10 =720
which value(8/9/10) should be added 1 so the net result is least affected.
let add 1 to 8
vol= 9*9*10= 810 (change from original = 810-720 = 90)
let add 1 to 9
vol: 8*10*10 = 800 (change from original = 800-720 = 80)
let add 1 to 10
vol = 8*9*11 = 792 (change from original = 792-720 = 72)
so take away:
in order to have least effect always change the maximum value.
now in our example to have least effect on 467∗15∗23467∗15∗23
we need to keep 2 thing in mind
1)change the unit digit(Because if you change tens or hundred place then it will have larger effect that's common sense)
2)change the biggest number
so biggest number is 467 and unit digit of this 7.
ANSWER:D
Answer: (D) 7
Question: A man got killed in his office. The suspects are Edison, Maxis, Jason, Janna, Sofia.
A calendar near the man has blood, written 6, 4, 9,
10, 11.
Who is the killer?
(A) Jason
(B) Janna
(C) Sofia
(D) Edison
(E) Maxis
Rationale: Jan:1
Feb:2
March: 3
April:4
...
...
June:6
and so on...j = june(6)
a = april(4)
and...
ANSWER:A
Answer: (A) Jason
Question: If |x+y|=|x-y|, then x*y must be equal to:
(A) -1
(B) 1
(C) 2
(D) 0
(E) -2
Rationale: Solution 1: Distance perspective
|x-y| = |x+y| ==> The distance of x and y is equal to the distance of x and -y.
<=======(-y)=======0=======(y)======>
Only 0 is the value that has a distance equal to y and -y.
Solution 2:
|x-y| = |x+y| (square both)
x^2 -2xy + y^2 = x^2 + 2xy + y^2
4xy = 0
xy = 0
Answer: D
Answer: (D) 0
Question: If an article with marked price of $300 is sold at successive discount of 10%,25% and 15%,what is the price the customer has to pay?
(A) 243
(B) 151
(C) 230
(D) 201
(E) 171
Rationale: discount=0.9*.75*.85=.57
so .57*300=171
ANSWER:E
Answer: (E) 171
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 112
(B) 177
(C) 127
(D) 150
(E) 881
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 9) m
= 150 m.
Answer:D
Answer: (D) 150