mathewhe/aqua_rat huggingface dataset:
Question: There are 10 balls in a box: 5 balls are green, 3 are blue and 2 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a white ball is selected at random from the box?
(A) 1/13
(B) 4/13
(C) 3/13
(D) 5/13
(E) 2/8
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 4 green, 2 blue and 2 white balls, a total of 8 balls. If one ball is selected at random, the probability that it is white is given by 2 / 8
Answer : E
Answer: (E) 2/8
Question: Each of the 43 points is placed either inside or on the surface of a perfect sphere. If 16% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
(A) 3
(B) 11
(C) 13
(D) 23
(E) 38
Rationale: Maximum number of points on the surface is 16%*43 = 6.88 ... or 6 since it has to be an integer
Now note that if two points form a diameter, they cannot be part of any other diameter.
So in the best case we can pair up the points
We have 6 points, so at best we can form 3 pairs (6).
So, answer is (A)
Answer: (A) 3
Question: On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 160 is how many times an intensity corresponding to a magnitude of 125?
(A) 40
(B) 100
(C) 400
(D) 1000
(E) 10 000
Rationale: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 160 it'll be 10*10*10*10*x=10^3*x.
Answer: D.
Answer: (D) 1000
Question: Working together, printer M and printer N would finish the task in 24 minutes. Printer M alone would finish the task in 60 minutes. How many pages does the task contain if printer N prints 5 pages a minute more than printer M?
(A) 400
(B) 450
(C) 600
(D) 1200
(E) 1500
Rationale: 24*M + 24*N = x pages
in 24 mins printer M will print = 24/60 * x pages = 2/5*x pages
thus in 24 mins printer printer N will print x - 2/5*x = 3/5*x pages
Also it is given that printer N prints 5 more pages per min that printer M. In 24 mins printer N will print 120 more pages than printer M
thus 3/5*x - 2/5*x = 120 => x = 600 pages
C)
Answer: (C) 600
Question: If 'a' and 'b' are non-zero numbers such that their sum is ten times the product, what is the value of 1/a + 1/b?
(A) 2
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: a+b = 10ab
1/a + 1/b = (b + a)/(ab) = 10.
The answer is C.
Answer: (C) 10
Question: Two friends plan to walk along a 22-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: If Q complete x kilometers, then P completes 1.2x kilometers.
x + 1.2x = 22
2.2x=22
x = 10
Then P will have have walked 1.2*10=12 km.
The answer is C.
Answer: (C) 12
Question: 1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is ?
(A) 63.3%
(B) 52.4%
(C) 81.2%
(D) 75.4%
(E) 69.1%
Rationale: Total number of students = 1100+700 = 1800
Number of students passed = (42% of 1100+30% of 700) = 462+210 = 672
number of failures = 1128*100/1800 = 190/3%= 63.3%
Answer is A
Answer: (A) 63.3%
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
(A) 36
(B) 27
(C) 72
(D) 29
(E) 22
Rationale: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase =
4 * 10 = 40
The new sum = 230 + 40 = 270 The new average = 270/10
= 27.
Answer:B
Answer: (B) 27
Question: Find the odd man out. 18, 16, 12, 24, 11, 34, 46
(A) 16
(B) 46
(C) 16
(D) 11
(E) 12
Rationale: Explanation :
11 is the only odd number in the given series. Answer : Option D
Answer: (D) 11
Question: Out of a world population of approximately 6.6 billion, 1.2 billion people live in the richer countries of Europe, North America, Japan and Oceania and is growing at the rate of 0.25% per year, while the other 5.4 billion people live in the lees developed countries and is growing at the rate of 1.5%. What will be the world population in 5 years if we assume that these rates of increase will stay constant for the next 5 years. (round answer to 3 significant digits)
(A) 7.02 billion.
(B) 7.03 billion.
(C) 7.04 billion.
(D) 7.05 billion.
(E) 7.06 billion.
Rationale: Solution to Problem 12:
Let us first calculate the population PR in 5 years in the richer countries
PR = (1.2 + 0.25% * 1.2) = 1.2(1 + 0.25%) after one year
PR = 1.2(1 + 0.25%) + 0.25% * 1.2(1 + 0.25%)
= 1.2(1 + 0.25%) 2after two years
Continue with the above and after 5 years, PR will be
PR = 1.2(1 + 0.25%) 5 after 5 years
Similar calculations can be used to find the population PL in less developed countries after 5 years.
PL = 5.4(1 + 1.5%) 5 after 5 years
The world population P after 5 years will be
P = PR + PL = 1.2(1 + 0.25%) 5 + 5.4(1 + 1.5%) 5 = 7.03 billion.
Answer B
Answer: (B) 7.03 billion.
Question: A right triangle AWC has to be constructed in the xy-plane so that the right angle is at A and AW is parallel to x axis. The coordinates of A, W and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
(A) 63
(B) 336
(C) 567
(D) 3024
(E) 5040
Rationale: All the cordinates are integer hence,
possible AW values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Answer: (D) 3024
Question: At a wedding reception, 125 guests ate chicken and 75 guests ate beef. If exactly 100 guests ate only one of the two types of meat, how many guests ate both types of meat?
(A) 5
(B) 100
(C) 7
(D) 4
(E) 50
Rationale: Say x guests ate both types of meat.
(125 - x) + (75 - x) = 100 --> x = 50.
Answer: E.
Answer: (E) 50
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago.What is the difference between the ages of the replaced and the new member?
(A) 2 years
(B) 4 years
(C) 8 years
(D) 15 years
(E) 25 years
Rationale: the age 5 members will be 13,14,15,16 and 17
3 years before there age was 10,11,12,13 and 14 hence the average is 12(10+11+12+13+14/5=60/5=12).
now if the oldest man 17 is replaced by 2 the the average is become same as three years ago the are .
as (13+14+15+16+2)/5 = 60/5=12.
hence the difference between the ages of the replaced and the new member is 17-2=15.
ANSWER:D
Answer: (D) 15 years
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
(A) 50
(B) 874
(C) 168
(D) 578
(E) 120
Rationale: Explanation:
Let speed of the car be x kmph
hen, speed of the train =150/100X=3/2X kmph
75/x-75/(3/2)x=125/(10*60)
75/x-50/x=5/24
x=25*24/5=120 kmph
Answer E
Answer: (E) 120
Question: 70 students are required to paint a picture. 52 use green color and some children use red, 38 students use both the colors. How many students use red color?
(A) 53
(B) 54
(C) 55
(D) 56
(E) 57
Rationale: 70 = red +green -both
Red = 70-green+both = 70-52+38=56
ANSWER:D
Answer: (D) 56
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?
(A) 500
(B) 560
(C) 670
(D) 800
(E) 900
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
D
Answer: (D) 800
Question: A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is
(A) 22030
(B) 220030
(C) 23030
(D) 24030
(E) 20303
Rationale: Explanation:
(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
Option B
Answer: (B) 220030
Question: The Racing magic takes 40 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Time taken by Racing magic to make one circle = 40 seconds
Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 40 seconds = 360 seconds = 6 mins
Time taken for them to meet at the starting point for the second time = 6 mins *2 = 12 mins
Answer D
Answer: (D) 12
Question: Balls are bought at 11 for Rs.10/- and sold at 10 for Rs.11/-. Find the gain or loss percentage?
(A) 21 % Profit
(B) 22 % Profit
(C) 24 % Profit
(D) 31 % Profit
(E) 32 % Profit
Rationale: 11 balls -----> Rs.10/-
10 balls -----> Rs.11/-
Note: Number of articles bought is must equal to number of articles sold.
10(11 10) ==> 110 100 = Cost price
11(10 11) ==> 110 121 = Selling price
Then, 21/100 × 100 = 21 % Profit
A)
Answer: (A) 21 % Profit
Question: if there is one larger cube with surface area 600 and no. of smaller cubes with surface area 24.then how many small cubes are required to make a larger cube with surface area of 600?
(A) 5
(B) 125
(C) 4
(D) 100
(E) 24
Rationale: the ratio between larger and smaller is
6a12:6a22=600:24
a12:a22=100:4
a1:a2=10:2
then length of cube is 10 and 2
so make a cube with length 10, we have to 5 small cubes each in length, breadth and height. so total 125 cubes are required.
then the answer is B
Answer: (B) 125
Question: In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is?
(A) 11
(B) 20
(C) 28
(D) 17
(E) 13
Rationale: Explanation:
It is the same as a person with 20 years more age replaces an existing person of the group ( or village)
Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.
Alternatively : ( n x 42 ) + 20 = ( n x 43 )
=> n=20
Answer: B
Answer: (B) 20
Question: Harry started a 7-mile hike with a full 11-cup canteen of water and finished the hike in 3 hours with 2 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 6 miles of the hike?
(A) 2/6
(B) 3/6
(C) 4/6
(D) 6/4
(E) 5/6
Rationale: No of cups leaked during the trip = 3 cups.
No of cups Harry drank = 6 cups.
No of cups harry drank during the first 6 miles = 3.
drink / mile = 3/6
Answer: B
Answer: (B) 3/6
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 55000. What is the share of C?
(A) Rs. 12250
(B) Rs. 13375
(C) Rs. 16750
(D) Rs. 15000
(E) None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 55000] = Rs. 15000
Answer: Option D
Answer: (D) Rs. 15000
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 25% premium.If the company declares 5% dividend at the end of the year,then how much does he get ?
(A) Rs. 576
(B) Rs. 600
(C) Rs. 650
(D) Rs. 720
(E) None
Rationale: Solution
Number of shares = (14400/125) = 115.2.
Face value = Rs. (100x115.2 ) = Rs. 11520.
Annual income = Rs.(5/100x11520) = Rs. 576.
Answer A
Answer: (A) Rs. 576
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 5
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: E
Answer: (E) 5
Question: If the sum and difference of two numbers are 5 and 10 respectively, then the difference of their square is:
(A) 50
(B) 28
(C) 160
(D) 180
(E) 18
Rationale: Let the numbers be x and y.
Then, x + y = 5 and x - y = 10
x2 - y2 = (x + y)(x - y) = 5 * 10 = 50.
ANSWER:A
Answer: (A) 50
Question: 47% of the students in a class of 38 students has glasses or contacts. How many students in the class have either glasses or contacts?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: a=r⋅b
47%=0.47a
=0.47⋅34
a≈18
Option D is correct.
Answer: (D) 18
Question: A person travels at a speed of 10 mph from one city to another. However while returning as there was not much traffic. He came with a speed of 15mph. what is his average speed?
(A) 10Kmph
(B) 11Kmph
(C) 12Kmph
(D) 13Kmph
(E) 14Kmph
Rationale: Average speed = 2xy/(x+y) = (2*15*10)/25 = 12Kmph
ANSWER:C
Answer: (C) 12Kmph
Question: In a barrel of juice there is 20 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:3.
(E) 3:4
Rationale: Price of 20 L juice= 3x
1L= 3x/20
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/20/4x/80= 3:1
C is the answer
Answer: (C) 3:1.
Question: A fruit seller had some oranges. He sells 10% oranges and still has 360 oranges. How many oranges he had originally?
(A) 420
(B) 700
(C) 220
(D) 400
(E) None of these
Rationale: Explanation :
He sells 10% of oranges and still there are 360 oranges remaining
=> 90% of oranges = 360
⇒ (90 × Total Oranges)/100 = 360
⇒ Total Oranges/100 = 4
⇒ Total Oranges = 4 × 100 = 400
Answer : Option D
Answer: (D) 400
Question: A dog takes 2 leaps for every 3 leaps of a hare. If one leap of the dog is equal to 5 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 9 : 3
(B) 3 : 10
(C) 2 : 3
(D) 6 : 3
(E) 10 : 3
Rationale: Explanation:
Dog : Hare = (2*5) leaps of hare : 3 leaps of hare = 10 : 3
Answer: E
Answer: (E) 10 : 3
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?
(A) 1/3
(B) 2by3
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3.
Hence, B is the correct answer.
Answer: (B) 2by3
Question: A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 288
(B) 165
(C) 881
(D) 1277
(E) 121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer: B
Answer: (B) 165
Question: What is 2/5 of 5/9 of 1/2?
(A) 1/4
(B) 1/9
(C) 9/16
(D) 5/8
(E) 16/9
Rationale: 2/5 * 5/9 * 1/2= 1/9
Answer: B
Answer: (B) 1/9
Question: If q = 50! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 29
III. 41
(A) I​ only
(B) III only
(C) II and III
(D) I and II
(E) I​, II, and III
Rationale: The numbers 11, 29, and 41 are all factors of 50!
Therefore they can not be factors of 50! + 1.
The answer is E.
Answer: (E) I​, II, and III
Question: There are 19 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
(A) 1710
(B) 1920
(C) 2440
(D) 2860
(E) 3260
Rationale: The number of ways to choose two teams is 19C2 = 19*18/2 = 171
The total number of games in the season is 10*171 = 1710.
The answer is A.
Answer: (A) 1710
Question: The food in a camp lasts for 36 men for 45 days. If twelve more men join, how many days will the food last?
(A) 80 days
(B) 30 days
(C) 65 days
(D) 34 days
(E) 15 days
Rationale: one man can consume the same food in 36*45 = 1620 days.
12 more men join, the total number of men = 48
The number of days the food will last = 1620/48
= 34 days.
Answer:D
Answer: (D) 34 days
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
(A) 71 years
(B) 72 years
(C) 74 years
(D) 77 years
(E) 78 years
Rationale: Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
Answer: Option A
Answer: (A) 71 years
Question: The “c-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^c, where c is the c-number of the result of his die roll, and plots 3^c on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
(A)  3/8
(B)  13/36
(C)  17/36
(D)  19/36
(E)  23/36
Rationale: If you calculate 3^c for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: (B)  13/36
Question: If the LCM of 9, 12, 5, and x is 180, which of the following could be x?
(A) 10
(B) 12
(C) 13
(D) 9
(E) 13
Rationale: Using elimination method, eliminate the option to arrive at 10
if x is replaced by 10 and the LCM is calculated you arrive at 180
A
Answer: (A) 10
Question: Last week we got 3.5 inches of snow. Six-tenths of an inch melted before another storm added
8.3 inches. Since then we have lost 4.2 inches to melting or evaporation. How may inches of snow
are left on the ground?
(A) 7" remaining
(B) 5" remaining
(C) 8" remaining
(D) 6" remaining
(E) 10" remaining
Rationale: 3.5 - .6 = 2.9"
2.9 + 8.3 = 11.2"
11.2 - 4.2 = 7" remaining
correct answer A
Answer: (A) 7" remaining
Question: A man buy a book in Rs50 & sale it Rs100. What is the rate of profit ???
(A) 10%
(B) 100%
(C) 30%
(D) 25%
(E) 28%
Rationale: cp=50
sp=100
profit=100-50=50
%=50/50*100=100%
ANSWER:B
Answer: (B) 100%
Question: Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are?
(A) 12, 24, 38
(B) 12, 24, 56
(C) 12, 24, 31
(D) 12, 24, 36
(E) 12, 24, 32
Rationale: Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 12.
The numbers are 12, 24, 36.
Answer: D
Answer: (D) 12, 24, 36
Question: When a train travels at a speed of 90kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
(A) 18.75km
(B) 50km
(C) 60km
(D) 85km
(E) 95km
Rationale: Let x be the time reached with the speed 90km/h
50km/h ----> x+15
Distance is equal so
90(km/h)× xhr = 50(km/h) × (x+15) hr
So
90 x = 50x + 750
So the would be in km
And x = 18.75
ANSWER:A
Answer: (A) 18.75km
Question: A man has Rs.680 in the denominations of two-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 160
(B) 40
(C) 680
(D) 120
(E) 180
Rationale: Let number of notes of each denomination be x.
Then 2x + 5x + 10x = 680
17x = 680
x = 40
Hence, total number of notes = 3x = 120.
Answer is D
Answer: (D) 120
Question: R is the set of positive even integers less than 201, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A)  None
(B)  Two
(C)  Four
(D)  Five
(E)  Seven
Rationale: R is the set of positive even integers less than 201, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=2,4,6,8,10,12...
S=4,16,36,64...
Numbers: 4, 16, 36, 64, 100, 144, and 196 are even integers (less than 201) that are in both sets.
Solution: Seven
Answer: E
Answer: (E)  Seven
Question: Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700);
A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9);
C. all three are alike = 3 (777, 888, 999).
So, 299-216-3=80.
Answer: C.
Answer: (C) 80
Question: The difference between the squares of two consecutive numbers is 35. The numbers are
(A) 14,15
(B) 15,16
(C) 17,18
(D) 18,19
(E) None
Rationale: Explanation:
Let the numbers be a and (a+1)
(a+1)2−a2=35
⇒a2+2a+1−a2=35
⇒2a=34⇒2a=34 or a = 17
The numbers are 17 & 18.
Correct Option: C
Answer: (C) 17,18
Question: A and B started a business with investments of Rs. 42000, and Rs. 63000 respectively. After 4 months B withdraws from the business. At the end of a year they got Rs. 9600 as total profit. Find the share of B.
(A) Rs. 5600
(B) Rs. 2800
(C) Rs. 3200
(D) Rs. 6400
(E) None of these
Rationale: Explanation:
Ratio of capitals of A and B = (42000 × 12) : (63000 × 4) = 2 : 1
B's share = Rs. [(1/3) × 9600] = Rs. 3200
Answer: Option C
Answer: (C) Rs. 3200
Question: A watch was sold at a profit of 15%. If its cost had been 5% less and it had been sold for Rs. 21 less, than the profit would have been 10%. Find the cost price of the watch
(A) 100
(B) 200
(C) 120
(D) 140
(E) 160
Rationale: let the price of the watch is x
it was sold at a profit of 15%
then the price of the watch is 1.15x
again cost had been decreased by 5% i.e 0.95x
according to the question
1.15x=0.95x*(110/100)+21
then x=200
ANSWER:B
Answer: (B) 200
Question: If a/b = 4, b/c = 2/5, c/d = 6/5, d/e = 5/2 and e/f = 3, then what is the value of abc/def ?
(A)  2704/4124
(B)  4561/8645
(C)  3235/7456
(D)  475/8456
(E)  3125/41472
Rationale: Say a = 2. Then:
a/b = 4 --> b = 1/2;
b/c = 2/5 --> c = 5/4;
c/d = 6/5 --> d = 25/24;
d/e = 5/2 --> e = 5/12;
e/f = 3 --> f = 5/36.
abc/def = (2*1/2*5/4)/(25/24*5/12*5/36) = 3125/41472.
Answer: E.
Answer: (E)  3125/41472