mathewhe/aqua_rat huggingface dataset:
Question: A company recently conducted a survey and found that 40,000 of its customers live in rural areas. If the number of customers who live in urban areas is 137 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
(A) 90,000
(B) 91,200
(C) 92,400
(D) 93,600
(E) 94,800
Rationale: The number of customers in urban areas is 40,000+1.37*40,000=94,800.
The answer is E.
Answer: (E) 94,800
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 880 grams per kg, what is his percent?
(A) 15%
(B) 13.6%
(C) 65%
(D) 45%
(E) 35%
Rationale: Explanation:
880 --- 120
100 --- ? => 13.6%
Answer: B
Answer: (B) 13.6%
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability T that at least one will be orange?
(A) T=7/10
(B) T=3/5
(C) T=2/5
(D) 3/10
(E) 1/10
Rationale: Method 1
Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue)* P(Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: (A) T=7/10
Question: Judy ate 20g of chocolate on Monday, and 30g of chocolate on Tuesday. How much chocolate on average did she eat on those two days?
(A) 50g
(B) 6g
(C) 600g
(D) 25g
(E) 1kg
Rationale: (20g + 30g)/2 = 25g
The correct answer is D
Answer: (D) 25g
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
(A) 65 days
(B) 16 days
(C) 15 days
(D) 19 days
(E) 20 days
Rationale: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x => x= 16 days.
Hence, Tanya takes 16 days to complete the work.
Answer: B
Answer: (B) 16 days
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:4 . Find their incomes?
(A) 112.5, 158.5
(B) 180.5, 150
(C) 100, 200
(D) 112.5, 150
(E) 122.5, 150
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:4
(3P - 100):(4P - 100) = 1:4
8P = 300 => P = 37.5
Their incomes = 112.5, 150
ANSWER:D
Answer: (D) 112.5, 150
Question: If Jake loses 15 pounds, he will weigh twice as much as his sister. Together they now weigh 132 pounds. What is Jake’s present weight, in pounds?
(A) 63
(B) 93
(C) 139
(D) 147
(E) 188
Rationale: Lets say J is the weight of Jack and S is the wt of his sister.
If he loses 15 pounds, he s twice as heavy as his sister.
J-15=2*S
Also, together they weight 132 pounds
J+S=132
solvong the 2 equation ,we get J=93 pounds !
B
Answer: (B) 93
Question: The average of the two-digit numbers, which remain the same when the digits interchange their positions, is?
(A) 22
(B) 89
(C) 55
(D) 38
(E) 13
Rationale: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9
= [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9
= [(4 * 110) + 55]/9 = 495/9
= 55.
Answer:C
Answer: (C) 55
Question: Salaries of Ram and Sham are in the ratio of 4 : 5. If the salary of each is increased by Rs. 5000, then the new ratio becomes 50 : 60. What is Sham's present salary?
(A) Rs. 20,000
(B) Rs. 25,000
(C) Rs. 30,000
(D) Rs. 35,000
(E) Rs. 40,000
Rationale: EXPLANATION:
Assume original salaries of Ram and Sham as 4x and 5x respectively.
Therefore,
(4x + 5000)/(5x +5000)	=	50 /60
60 (4x + 5000) = 50 (5x + 5000)
10 x = 50,000
5x = 25, 000
Sham's present salary = 5x + 5000 = 25,000 + 5000
Sham's present salary = Rs. 30,000
ANSWER IS C
Answer: (C) Rs. 30,000
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $140, how much more remains to be paid?
(A) $880
(B) $990
(C) $1,000
(D) $1,100
(E) $1,260
Rationale: 10/100P = 140 >> p= 140*100/10 = 1400
1400 - 140 = 1260
ANSWER:E
Answer: (E) $1,260
Question: How many different positive integers exist between 10^5 and 10^6, the sum of whose digits is equal to 2?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 18
Rationale: So, the numbers should be from 100,000 to 1,000,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
100,001
100,010
100,100
101,000
110,000
5numbers.
2. One 2 and the rest are 0's:
200,000
1 number.
Total = 6 numbers.
Answer: A
Answer: (A) 6
Question: A train passes a station platform in 45 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 180 m
(B) 240 m
(C) 260 m
(D) 280 m
(E) 375 m
Rationale: Speed = 54 x 5/18 = 15 m/s
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/45 = 15
--> x + 300 = 675
x = 375m.
Answer : E.
Answer: (E) 375 m
Question: A present value of a machine is $128000. Its value depletiation rate is 25% per annum then find the machine value after 3 years?
(A) $54000
(B) $48000
(C) $36520
(D) $32450
(E) $42500
Rationale: P= $128000
R = 25%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=128000*3/4 * 3/4 * 3/4
=$54000
Answer is A
Answer: (A) $54000
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 187.5 m
(B) 127.5 m
(C) 127.3 m
(D) 122.5 m
(E) 197.3 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 * 212.5)/1000
= 127.5 m.
Answer:B
Answer: (B) 127.5 m
Question: A parking space have 10 different slots. 10 cars has to arrange in 8 slots. But there are exactly 4 cars between 6 specified cars. In how many ways cars can be arranged?
(A) 17280
(B) 65000
(C) 1500
(D) 1640
(E) 1440
Rationale: we arranged 2 specified cars in 4 slots = 4!
remaining 6 cars in 6 slots = 6!
number of ways = 4!*6! = 17280
correct option is A
Answer: (A) 17280
Question: There are 10 women and 15 men in an office. In how many ways a team of a man and a woman can be selected?
(A) 55
(B) 25
(C) 150
(D) 28
(E) None of these
Rationale: Number of ways in which a team of a man and a woman can be selected
= 15 × 10 = 150
Answer is C
Answer: (C) 150
Question: In what time will a railway train 60 m long moving at the rate of 72 kmph pass a telegraph post on its way?
(A) 8 sec
(B) 3 sec
(C) 2 sec
(D) 6 sec
(E) 9 sec
Rationale: T = 60/72 * 18/5
= 3 sec
Answer:B
Answer: (B) 3 sec
Question: A retailer bought a machine at a wholesale price of $90 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) 160
Rationale: My solution: Wholesale Price= 90
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 = 90+ 1/5(90)
x=120;
ANSWER:C
Answer: (C) 120
Question: Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $50 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?
(A)  $752
(B)  $755
(C)  $765
(D)  $788
(E)  $775
Rationale: = (750*6+ 800 *20)/26
= 788
Answer is D.
Posted from my mobile device
Answer: (D)  $788
Question: In the reading room of a library, there are 24 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?
(A) 8
(B) 16
(C) 15
(D) 14
(E) 9
Rationale: 1+2+3+4+5+6+7+8 = 36
so, 8 spots are occupied by users
24-8 = 16,
ANSWER:B
Answer: (B) 16
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
(A) 2989
(B) 2789
(C) 1210
(D) 1288
(E) 1211
Rationale: π (232 – 122)
= 1210
Answer: C
Answer: (C) 1210
Question: What could be the range of a set consisting of odd multiples of 5?
(A) 21
(B) 24
(C) 35
(D) 62
(E) 60
Rationale: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 5*(2n+1) where n is any positive integer.
Range = 5*(2m + 1) - 5*(2n + 1) = 5*2*(m-n) = 10 * (m-n).
m, n - any positive integers
The answer must be divisible by 10, which is only 60.
The correct answer is E.
Answer: (E) 60
Question: Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.4 meters high. What is Mr. Wayne's speed in meters per second?
(A) 3
(B) 3.75
(C) 4
(D) 4.25
(E) 5
Rationale: IMO: D
15 Floors * 3.4 Meter/Floor = 51 Meters
Time= 12 sec
Rate * 12 = 51
Rate= 51/12
=4.25
Answer D
Answer: (D) 4.25
Question: If there is exactly one root of the equation ax^2 + x + b, where a and b are positive constants, what is b in terms of a?
(A) 1/4a
(B) a
(C) 3a/2
(D) a^2/2
(E) a^2/4
Rationale: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here
c= b
b = 1
substituting these values in 1, we have
1^2 = 4ab => b =1/4a
Answer is A.
Answer: (A) 1/4a
Question: A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) 35
(B) 77
(C) 28
(D) 50
(E) 22
Rationale: Explanation:
SP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre
= 45 + 5
= Rs. 50
Answer: D
Answer: (D) 50
Question: How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 4
(B) 3
(C) 6
(D) 8
(E) 9
Rationale: Explanation :
Here 3, 4 and 11 are pairwise co-prime numbers. 132 = 3 × 4 × 11 . Also 3,4 and 11 are
factors of 132. Hence
if a number is divisible by 3, 4 and 11, the number will be divisible by their product 132 also.
If a number is not divisible by 3 or 4 or 11, it is not divisible by 132
You must learn Divisibility Rules to say whether a given number is divisible by another number
without actually performing the division.
further.
264 is divisible by 3, 4 and 11 => 264 is divisible by 132
396 is divisible by 3, 4 and 11 => 396 is divisible by 132
462 is divisible by 3 and 11, but not divisible by 4 => 462 is not divisible by 132
792 is divisible by 3, 4 and 11 => 792 is divisible by 132
968 is divisible by 4 and 11, but not divisible by 3 => 968 is not divisible by 132
2178 is divisible by 3 and 11, but not divisible by 4 => 2178 is not divisible by 132
5184 is divisible by 3 and 4, but not divisible by 11 => 5184 is not divisible by 132
6336 is divisible by 3, 4 and 11 => 6336 is divisible by 132
Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is 4. Answer : Option A
Answer: (A) 4
Question: A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train in going?
(A) 5 sec
(B) 7 sec
(C) 6 sec
(D) 10 sec
(E) none
Rationale: speed of train relative to man=(60+6)km/hr=66 km/ hr.
(66*5/18)m/sec.
(55/3)m/sec.
Time taken to pass the man=(110*3/55)sec=6 sec.
Answer: C
Answer: (C) 6 sec
Question: Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 2 scones must be equal to which of the following?
(A) Y/20
(B) 200/Y
(C) 100Y/(15X)
(D) XY/250
(E) Y/(5X)
Rationale: Rachel eats 4 scones/10 minutes = 2/5 scones per minute
The time for Rachel to eat 1 scone is 5/2 minutes.
The time for Rachel to eat Y scones is 5Y/2 minutes.
The time for Henry to eat X scones is 5YX/200 minutes.
The time for Henry to eat 1 scone is 5Y/200 minutes.
The time for Henry to eat 2 scones is 10Y/200 = Y/20 minutes.
The answer is A.
Answer: (A) Y/20
Question: In what ratio must water be mixed with milk costing Rs.12 per litre in order to get a mixture worth of
Rs.8 per litre?
(A) 1 : 3
(B) 2 : 2
(C) 1 : 2
(D) 3 : 1
(E) 3 : 2
Rationale: Explanation :
By the rule of alligation, we have
Cost Price of 1 litre of water Cost Price of 1 litre of milk
0 12
Mean Price
8
12-8=4 8-0=8
Required Ratio = 4 : 8 = 1 : 2
Answer : Option C
Answer: (C) 1 : 2
Question: A person took some amount with some interest for 3 years, but increase the interest for 1%, he paid Rs.120/- extra, then how much amount he took?
(A) s.5500/-
(B) s.6000/-
(C) s.4000/-
(D) s.7000/-
(E) s.8000/-
Rationale: Explanation:
3 years = Rs.120/-
year = 120/3
Rate of Interest = 1%
100/1% × 120/3 = Rs.4000/-
P = Rs.4000/-
Answer: Option C
Answer: (C) s.4000/-
Question: If 60 percent of 500 is 50 percent of x, then x=?
(A) 600
(B) 620
(C) 650
(D) 700
(E) 720
Rationale: 0.6 * 500 = 0.5 * x
x = 6/5 * 500 = 600
Answer: (A) 600
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 4:7
(C) 7:1
(D) 2:5
(E) 1:6
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
ANSWER:A
Answer: (A) 9:1
Question: John bought a total of 24 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 24 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 14
Rationale: Let number of mangoes be x, number of oranges be 24-x
0.80x +(24-x)0.60/24 = 0.65
solving for x, we get x = 6 --> Mangoes 6, Oranges 18
Now, number of oranges to be returned be y
0.80*6 + (18-y)*0.60/24-y = 0.72
solving for y, y = 14
Ans: E
Answer: (E) 14
Question: A tank contains 9,000 gallons of a solution that is 6 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A)  6%
(B)  7%
(C)  8%
(D)  9%
(E)  10%
Rationale: We start with 9,000 gallons of a solution that is 6% sodium chloride by volume. This means that there are 0.06 x 9,000 = 54 gallons of sodium chloride.
When 3,000 gallons of water evaporate we are left with 6,000 gallons of solution. From here we can determine what percent of the 6,000 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(540/6,000) x 100 = ?
9/100 x 100 = ?
= 9%
Answer is D.
Answer: (D)  9%
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by A are?
(A) 11
(B) 18
(C) 13
(D) 17
(E) 12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
4/25 * 75 = 12
Answer:E
Answer: (E) 12
Question: Rs 3600 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
(A) s 4000
(B) s 2800
(C) s 1800
(D) s 3500
(E) s 3100
Rationale: Explanation :
Average rate = (144/3600)*100 = 4
Ratio = 1:1
So, first part = (1/2)*3600 = Rs 1800.
Answer : C
Answer: (C) s 1800
Question: Alex takes a loan of $8,000 to buy a used truck at the rate of 6 % simple Interest.Calculate the annual interest to be paid for the loan amount.
(A) 480
(B) 520
(C) 460
(D) 400
(E) 520
Rationale: From the details given in the problem Principle = P = $8,000 and R = 6% or 0.06 expressed as a decimal.
As the annual Interest is to be calculated, the time period T =1.
Plugging these values in the simple Interest formula,
I = P x T x R
= 8,000 x 1 x 0.06
= 480.00
Annual Interest to be paid = $480
answer :A
Answer: (A) 480
Question: On a track for remote controlled racing cars, racing car A completes the track in 57 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
(A) 275
(B) 325
(C) 1995
(D) 425
(E) None of these
Rationale: Time required in seconds will be LCM ( 35, 57 ) = 1995
Hence, answer will be (C) 1995
Answer: (C) 1995
Question: A train covers a distance of 54 km in 15 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?
(A) 470
(B) 480
(C) 490
(D) 500
(E) 510
Rationale: Speed = (54/15 * 60) km/hr = (216 * 5/18) m/sec = 60 m/sec.
Length of the train = 60 * 8 = 480 m.
Answer: Option B
Answer: (B) 480
Question: Four friends built a colony for themselves. They built their own houses at different distances from each other.
Chris lived 60 km away from Alex.
Darren lived 40 km away from Bill.
Chris lived 10 km nearer to Darren than he lived to Bill.
Can you find out how far was Darren's house from Alex?
(A) 75 km
(B) 60 km
(C) 45 km
(D) 50 km
(E) 85 km
Rationale: A
75 km
Explanation:
Distance between Bill and Darren = 40 km
Distance between Bill and Chris + Distance between Chris and Darren = 40 km
Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km
2 * Distance between Bill and Chris = 50 km
Distance between Bill and Chris = 25
Distance between Chris and Darren = 15 km
Therefore, distance between Darren's house and Alex's house = 60 + 15 = 75 km.
Answer: (A) 75 km
Question: Today is Monday. After 61 days, it will be:
(A) SUNDAY
(B) SATURSDAY
(C) FRIDAY
(D) THURSDAY
(E) MONDAY
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option B
Answer: (B) SATURSDAY
Question: Graph G has a line of symmetry of x = –5. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
(A)  –8
(B)  –7
(C)  –5
(D)  –4
(E)  -13
Rationale: Line of symmetry is X=-5; one point is (3,3)
Right side distance =5+3(distance from origin) = 8; therefore Left side distance should be same from line of symmetry =8;
therefore left side co-ordinate=8+5(distance from origin) = 13; as the X coordinate is in 2nd quadrant hence -13
Therefore answer is E
Answer: (E)  -13
Question: Which of the numbers below is the odd one out
1,5,13,17,25,41,61.
(A) 17
(B) 13
(C) 5
(D) 25
(E) 61
Rationale: 17 is the odd man.. diff between sucessive no.s are multiples of 4
ANSWER:A
Answer: (A) 17
Question: Today Roseline, who is 50 years old, and her daughter, who is 20 years old, celebrate their birthdays. How many years will pass before Roseline’s age is twice her daughter’s age?
(A) 12
(B) 13
(C) 10
(D) 15
(E) 18
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes Roseline’s age will be (50+x) years old, and her daughter’s age will be (20+x) years old. Since the Roseline’s age is twice her daughter’s age (50+x)= 2 * (20+x) ---> 50+x=40+2x ---> x= 10
The answer is (C).
Answer: (C) 10
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.52 if each film contains 36 photos?
(A) 4 films and 10 photos
(B) 5 films and 6 photos
(C) 5 films and 14 photos
(D) 6 films and 4 photos
(E) 6 films and 28 photos
Rationale: 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.52-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->4 full films and 1+11=12 photos
Answer: A
Answer: (A) 4 films and 10 photos
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7
(A) 1/2
(B) 7/12
(C) 5/13
(D) 5/12
(E) 6/17
Rationale: Total number of cases = 6*6 = 36
Favourable cases = [(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,4),(5,6),(5,3),(5,5),(6,2),(6,3),(6,4),(6,5),(6,6)] = 15
So Probability = 15/36 = 5/12
Answer is D
Answer: (D) 5/12
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs. 1090
(B) Rs. 1160
(C) Rs. 1190
(D) Rs. 1202
(E) Rs. 1204
Rationale: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
15=(1400-s.p)/1400*100
so,after solving answer=1190.
ANSWER:C
Answer: (C) Rs. 1190
Question: total dinning bill of 8 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
(A) 11.84
(B) 12.84
(C) 23.84
(D) 19.11
(E) 10.12
Rationale: dinner bill of 8 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/8 = $ 19.11
ANSWER:D
Answer: (D) 19.11
Question: The number of arrangements that can be made with the letters of the word JOHNNIE so that the vowels occupy the even places?
(A) A)122
(B) B)134
(C) C)144
(D) D)156
(E) E)176
Rationale: Explanation:
The word JOHNNIE has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
C
Answer: (C) C)144
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 8?
(A) 1
(B) 3
(C) 5
(D) 4
(E) 6
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2,3 and 4 then no two numbers out of these 5 add up to 8.
Now, the next, 6th number whatever it'll be (5,6,7,8 or 9) will guarantee that two number WILL add up to 8. So, 6 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 8
Answer: E
Answer: (E) 6
Question: In what proportion must wheat at Rs. 15 per kg. be mixed with wheat at Rs. 18 per kg. So that the mixture will be worth Rs. 17 per kg. ?
(A) 1 : 9
(B) 1 : 3
(C) 1 : 2
(D) 1 : 1
(E) 1 : 8
Rationale: Explanation:
Wheat/Rs. 15 per kg.
Wheat/Rs. 18 per kg.
For the mixture to be worth Rs. 17 per kg. The ratio should be:
(18 – 17) : (17 – 15)
1 : 2
ANSWER:C
Answer: (C) 1 : 2
Question: What is the remainder of R=3^19 when divided by 10?
(A) 0
(B) 1
(C) 5
(D) 7
(E) 9
Rationale: I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3
hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or
^18 - units digit 9
and ^19 - units digit 7
therefore, R=when divided by 10, the remainder must be 7.D
Answer: (D) 7