mathewhe/aqua_rat huggingface dataset:
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 15,000?
(A) 50,000
(B) 750,000
(C) 850,000
(D) 7,500,000
(E) 750,000,000
Rationale: number of cars sold = x=800000-50y
y=15000
x=800000-750000=50000
revenue from 50000 cars=15000*50000=750000000
ANSWER:E
Answer: (E) 750,000,000
Question: 7, 26, 63, 124, 215, 342, (....)
(A) 481
(B) 391
(C) 511
(D) 421
(E) 452
Rationale: Explanation :
The series is (2^3 - 1), (3^3 - 1), (4^3 - 1), (5^3 - 1), (6^3 - 1), (7^3 - 1), ...
Hence, next number is (8^3 - 1) = 511
Answer : Option C
Answer: (C) 511
Question: 240 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?
(A) 1~10
(B) 10~20
(C) 20~30
(D) 55~65
(E) 65~75
Rationale: 240 = 2^4*3*5
There are factors in each range except for 65~75
The answer is E.
Answer: (E) 65~75
Question: The average weight of 9 person's increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg. What might be the weight of the new person?
(A) 72 kg
(B) 77.5 kg
(C) 135.5 kg
(D) Data inadequate
(E) None of these
Rationale: Total weight increased = (9 x 5.5) kg = 49.5 kg.
Weight of new person = (86 + 49.5) kg = 135.5 kg.
Answer: Option C
Answer: (C) 135.5 kg
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 2.06
(B) 2.09
(C) 2.03
(D) 2.01
(E) 2.02
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:D
Answer: (D) 2.01
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 12+11 = 23.
The answer is D.
Answer: (D) 23
Question: what is the remainder when 89001 is divided by 18
(A) 3
(B) 8
(C) 9
(D) 4
(E) 6
Rationale: 89001 / 18
89001 / 9*2
9889 / 2 => rem = 1
we have cancelled it by 9
reqd remainder = 9*1 = 9
ANSWER:B
Answer: (B) 8
Question: Arrange the given words in the sequence in which they occur in the dictionary and choose the correct sequence.
(A) 3, 5, 2, 1, 4
(B) 3, 5, 2, 1, 8
(C) 3, 5, 2, 1, 2
(D) 3, 5, 2, 1, 5
(E) 3, 5, 2, 5, 5
Rationale: Explanation:
The correct alphabetical order is
Each, Eager, Earlier, Economic, Edition
ANSWER: A
Answer: (A) 3, 5, 2, 1, 4
Question: What will be the day of the week 15th August, 2010?
(A) Thursday
(B) Sunday
(C) Monday
(D) Saturday
(E) Friday
Rationale: Explanation:
15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2009
= 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day
Days from 1-Jan-2010 to 15-Aug-2010
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227
227 days = 32 weeks + 3 day = 3 odd day
Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday.
Answer: Option B
Answer: (B) Sunday
Question: A man can row a boat at 10 kmph in still water and the speed of the stream is 8 kmph. What is then time taken to row a distance of 90 km down the stream ?
(A) 8hrs
(B) 5 hrs
(C) 15 hrs
(D) 15 hrs
(E) 20 hrs
Rationale: Speed in down stream = 10 +8 = 18
Time taken to cover 90 km down stream = 90/18 = 5 hrs.
ANSWER:B
Answer: (B) 5 hrs
Question: The angles of a triangle are in the ratio 1:9:8. Find the measurement of the largest of three angles of triangle.
(A) 90°
(B) 100°
(C) 120°
(D) 140°
(E) 160°
Rationale: If the ratio of the three angles is 1:9:8, then the measures of these angles can be written as x, 9x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 9x + 8x = 180
Solve for x
18x = 180
x = 10
The measures of the three angles are
x = 10°
9x = 9 × 10 = 90°
8x = 8 × 10 = 80°
A
Answer: (A) 90°
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 1/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
(A) 1/35
(B) 2/3
(C) 7/35
(D) 5/7
(E) 7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 1/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 1/7 x 1/5 = 1/35
ANSWER:A
Answer: (A) 1/35
Question: Person X joins a job at 20 yrs. First 3 years salary = 10,000 p.a. Afterwards every year increment of 2,000 per year for 10 years. Then salary becomes constant till retirement. At retirement average salary is 25,000. (throughout career). At what age he retires?
(A) 50
(B) 60
(C) 40
(D) 70
(E) 80
Rationale: Let age of retirement = x
so according to the given condition 25000*(x-20)
=10000*3+12000+14000+16000+18000+20000+22000+24000+26000+28000+30000+30000(x-33)
= 30000+210000+30000x-990000
= 30000x-750000
or 25000x-500000=30000x-750000
or 5000x = 250000
or x = 50
ANSWER:A
Answer: (A) 50
Question: If 25% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 500
(B) 600
(C) 620
(D) 640
(E) 660
Rationale: We know 25 % people study biology,therefore the no of people not studying = 100 - 25 = 75%
> Therefore the people not studying biology out of a total 880 people are = 75 % of 880
> (75/100)*880 = 660 people
E
Answer: (E) 660
Question: The area of a square is 4761 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
(A) 5:28
(B) 5:19
(C) 15:12
(D) 5:13
(E) 15:46
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4761
a = 69
L = 2a and b = a - 24
b : l = a - 24 : 2a = 45 : 138
= 15:46
Answer:E
Answer: (E) 15:46
Question: The ratio between the length and the breadth of a rectangular park is 1 : 3. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 124545 m
(B) 134561 m
(C) 156787 m
(D) 15450 m
(E) 120000 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 1x metres and breadth = 3x metres.
Then, 2(1x + 3x) = 1600 or x = 200.
Length = 200 m and Breadth = 600 m.
Area = (600 x 200) m2 = 120000 m
E
Answer: (E) 120000 m
Question: Calculate the average of first 12 even numbers is?
(A) 15
(B) 14
(C) 12
(D) 11
(E) 13
Rationale: Explanation:
Sum of 12 even numbers = 12 * 13 = 156
Average = 156/12 = 13
Answer: Option E
Answer: (E) 13
Question: Jessica can text 75 words per minute, while Maurice can text 10 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
(A) 0.3
(B) 1.3
(C) 3.5
(D) 9
(E) 11.3
Rationale: Since the answer choices are reasonably spaced out, we can approximate and save time
Combined words per day = 85*60*24 which should be something close to 122400 (i.e 100*25*60)
410400/122400 will be closest to only 3.5,
So, Answer should be C.
Answer: (C) 3.5
Question: How many positive integers less than 23 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
(A) 17
(B) 25
(C) 24
(D) 22
(E) 20
Rationale: 8 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19}
2 odd multiples of 5: {5, 15}
9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 8+1+9-1=17.
Answer: A.
Answer: (A) 17
Question: At a certain high school, the senior class is three times the size of the junior class. If 1/3 of the seniors and 3/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese?
(A) 1/2
(B) 3/8
(C) 5/16
(D) 1/4
(E) 7/16
Rationale: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 300 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (1/3)*300=100 and (3/4)*100=75. 100+75=175. There are a total of 400 students in the junior class and senior class combined (100+300=300), and there are 175 total students in Japanese, so 175 students in Japanese / 400 total students equals 7/16 of the students in both classes that study Japanese.
Answer: E
Answer: (E) 7/16
Question: A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
(A) 4 days
(B) 3 days
(C) 5 days
(D) 6 days
(E) 8 days
Rationale: B
3 days
A can complete the work in (7*9) = 63 days
B can complete the work in (6*7) = 42 days
--> A’s one hour’s work = 1/63 and B’s one hour work = 1/42.
(A+B)’s one hour work = 1/63+1/42 = 5/126
Therefore, Both can finish the work in 126/5 hours.
Number of days of 8 2/5 hours each = (126*5/(5*42)) = 3 days
Answer: (B) 3 days
Question: If the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 4, what is the ratio of apples to cucumbers?
(A) 1:3
(B) 2:5
(C) 3:5
(D) 5:8
(E) 4:7
Rationale: The ratio of bananas to cucumbers is 1 to 4 which equals 2 to 8.
The ratio of apples to bananas to cucumbers is 5 to 2 to 8.
The ratio of apples to cucumbers is 5 to 8.
The answer is D.
Answer: (D) 5:8
Question: If s and t are integers and s^2 – t^2 is an odd integer, which of the following must be an even integer?
I. s + t + 2
II. s^2 + 2st + t^2
III. s^2 + t^2
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III
Rationale: s^2–t^2 is an odd integer means that either s is even and t is odd or s is odd and t is even.
Check all options:
I. s + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. s^2 + 2st + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. s^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Answer: (A) None
Question: A new savings account offers 8 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
(A) $80.00
(B) $84.40
(C) $360.00
(D) $6,360.00
(E) $6,489.60
Rationale: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.08) (1/2) = $240(Note: the 6 months are “1/2” in the equation since 8% is a yearly rate, not a bi-yearly one).
Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,240. The interest earned during the final 6 months of the year is $6,240(.08)(1/2) = $249.6. Therefore, the total balance is the original amount ($6000) + $240 + $249.60 = $6,489.60.
The correct answer is E.
Answer: (E) $6,489.60
Question: The cost of 200 kgs. of sugar is Rs.3000. What is the cost of3.525 kgs. of sugar?
(A) Rs.54
(B) Rs.48.875
(C) Rs.55
(D) Rs.52
(E) Rs.52.875
Rationale: Explanation:.
The cost of 3.525kgs. of sugar = 3000x 3.525/200= Rs.52.875
Answer: Option:E
Answer: (E) Rs.52.875
Question: A,B,C can do a piece of work in 11days, 20days and 55days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?
(A) 2
(B) 4
(C) 8
(D) 10
(E) 12
Rationale: A+B 1day work = 1/11 + 1/20 = 31/220
A+C 1day work = 1/11 + 1/55 = 6/55
work done in 2 days = 31/220 + 6/55 = 55/220 = 1/4
1/4 work is done by A in 2days
Whole work will be done in 2*4 = 8days
Answer is C
Answer: (C) 8
Question: A grocery shop has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 4857
(B) 4184
(C) 4012
(D) 4991
(E) 5291
Rationale: Let the sale in the sixth month =x
Then
(6435+6927+6855+7230+6562+x)/6 =6500
=>6435+6927+6855+7230+6562+x =6×6500
=> 34009+x=39000
=> x=39000−34009
=4991
ANSWER:D
Answer: (D) 4991
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 50%
(C) 57%
(D) 64%
(E) 78%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?
(A) 9, 46
(B) 9, 50
(C) 10, 46
(D) 10, 50
(E) 10, 56
Rationale: Explanation:
We have : A = 3B ...(i) and
C - 4 = 2 (A - 4) ...(ii)
Also, A + 4 = 31 or A= 31-4 = 27.
Putting A = 27 in (i), we get: B = 9.
Putting A = 27 in (ii), we get C = 50.
Answer: B
Answer: (B) 9, 50
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 96. what is sum of the numbers?
(A) 48
(B) 56
(C) 76
(D) 84
(E) 85
Rationale: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 96
=> 12x = 96
=> x = 96/12 = 8
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 8 = 56
Answer: Option B
Answer: (B) 56
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 19 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) 1/10
(B) 3/10
(C) 1/2
(D) 7/10
(E) 29/100
Rationale: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-19 -2CMB = 100
B-CB-MB-2CMB = 29
hence the probability = 29/100.
E
Answer: (E) 29/100
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
(A) 1/8
(B) 1/2
(C) 1/9
(D) 11/1
(E) 1/12
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer:B
Answer: (B) 1/2
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total expenditure of the company over these items during the year 2000 is?
(A) Rs. 544.44 lakhs
(B) Rs. 544.54 lakhs
(C) Rs. 544.79 lakhs
(D) Rs. 545 lakhs
(E) Rs. 546 lakhs
Rationale: Total expenditure of the Company during 2000
= Rs. (324 + 101 + 3.84 + 41.6 + 74) lakhs
= Rs. 544.44 lakhs.
A)
Answer: (A) Rs. 544.44 lakhs
Question: 3/5 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?
(A) 1/5
(B) 1/4
(C) 7/20
(D) 3/5
(E) It cannot be determined from the given information.
Rationale: Plug in simple numbers. Take 100 couples for example.
3/5 of 100 couples have more than one child = 60 couples.
2/5 of 100 couples have more than 3 kids = 40 couples.
This implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples, which equals 20 couples have either one or no kids at all.
We need to find couples that have 2 or 3 kids, so essentially, it is 60 - 40 = 20. Fraction will be 20/100 = 1/5.
Option A
Answer: (A) 1/5
Question: The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 8340 for a computer table, then what was the cost price of the computer table?
(A) Rs.6672
(B) Rs.6727
(C) Rs.6908
(D) Rs.6725
(E) Rs.6728
Rationale: CP = SP * (100/(100 + profit%))
= 8340(100/125) = Rs.6672.
Answer: A
Answer: (A) Rs.6672
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 18%?
(A) 20%
(B) 26%
(C) 42%
(D) 27%
(E) 23%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 82
2/3 SP1 = 82
SP1 = 123
100 --- 23 => 23%
Answer: E
Answer: (E) 23%
Question: If k is the sum of the digits of integer m, and m=16n, where n is an integer, which of the following must be true?
(A) k is not divisible by 9
(B) The sum of the digits of k is 9
(C) m is a multiple of 2k
(D) k is a multiple of 9
(E) k is a multiple of 6
Rationale: m= 16n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m 16,32,48,64 or -16 ,-32 ,-48 ,-64 then k 7,5 12,10 or -(1+6) , -(3+2) , -(4+8) ,-(6+4)
ans A
Answer: (A) k is not divisible by 9
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 17603
(B) 17608
(C) 17628
(D) 17600
(E) 176023
Rationale: Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375
= Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100
= Rs. 17600
Answer: D
Answer: (D) 17600
Question: A train covers a distance of 12 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
(A) 298
(B) 288
(C) 120
(D) 776
(E) 180
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 9
= 180 m.
Answer:E
Answer: (E) 180
Question: HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 48, then the other number is?
(A) 99
(B) 66
(C) 132
(D) 264
(E) 364
Rationale: 12 * 396 = 48 * x
x = 99
ANSWER:A
Answer: (A) 99
Question: The length of a room is 5 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
(A) 21375
(B) 25750
(C) 26550
(D) 26750
(E) 25725
Rationale: Area = 5 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 5 × 4.75 × 900
= 5 × 4275 = Rs. 21375
Answer is A.
Answer: (A) 21375
Question: A circular rim 28 inches in a diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes B revilutions per second, how many revilutions per minute does the larger rim makes in terms of B?
(A) a) 48pi/B
(B) b) 75m
(C) c) 48B
(D) d) 24B
(E) e) B/75
Rationale: distance covered by a circular wheel per sec* = 2*pi* r * n
where n is number of revolution
So we know the smaller rim makes B rev per sec so the inches coverd SR per sec = 28 * pi* B
the problem the say SR rotates the same number of inches as the LR.
The inches covered by the LR per sec = 35 * pi*Y
So equate both u will get Y = 4/5 B
Theis is in sec we need the answer in min so 48B
answer is C
Answer: (C) c) 48B
Question: for every correct answer 4 is awarded but for a wrong answer 2 is deducted. If there are a total of 150 questions and sukanya scores 480 how many answers of sukanya were correct?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: If x questions are correct, then
4x-2(150-x) = 480
6x= 780
x=130
so 130 questions are correct.
ANSWER:C
Answer: (C) 130
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle
(A) 18 cm
(B) 16 cm
(C) 40 cm
(D) 20cm
(E) 28 cm
Rationale: Explanation:
Let breadth =x cm
Then, length =2x cm
Area =x×2x=2x^2 sq.cm.
New length =(2x−5) cm
New breadth =(x+5) cm
New area =(2x−5)(x+5) sq.cm.
Given that, new area = initial area +75 sq.cm.
⇒(2x−5)(x+5)=2x^2+75
⇒2x^2+10x−5x−25=2x^2+75
⇒5x−25=75
⇒5x=75+25=100
⇒x=1005=20 cm
Length =2x=2×20=40 cm
Answer: Option C
Answer: (C) 40 cm
Question: Two vessels A and B contain milk and water mixed in the ratio 4:3 and 2:3 in what ratio must these mixtures be mixed to form new mixture containing half milk and half water?
(A) 7:6
(B) 7:1
(C) 7:5
(D) 7:2
(E) 7:8
Rationale: Answer with Explanation: Step (i): Let C.P. of 1 liter milk be Re.1 Ratio of mixture in A = 4:3  Milk in 1 litre mixture in A = 4/7 lit,  C.P of 1 litre mix of A = Rs. 4/7 Ratio of mix in B = 2:3  Milk in 1 litre mixture in B = 2/5 lit,  C.P of 1 litre mix of B = Rs. 2/5 Ratio of new mixture = 1:1  Milk in 1 litre mixture = 1/2 lit,  C.P of 1 litre mix = Rs. ½ (Mean price = re. ½ ) Step (ii) By the rule of alligation C.P. of 1 lit mix. In A (d) C.P. of 1 lit mix. In B (c) 4/7 2/5
Mean Price (m)
m-c (1/2 – 2/5) = 1/10 1/2 d-m (4/7 – 1/2) = 1/14
Required Ratio = 1/14 : 1/10 = 7 : 5
Answer:C
Answer: (C) 7:5
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
(A) 28 ways
(B) 35 ways
(C) 67 ways
(D) 23 ways
(E) 30 ways
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3
=30 ways.
Answer:E
Answer: (E) 30 ways
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.14.70 less, he would have gained 30%. Find the cost of the article.
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 14.70 when C.P=(100*14.70)/21=70
ANSWER:E
Answer: (E) 70
Question: In how many ways Chief Minister and Minister be elected from a team of 14 members?
(A) 162 ways
(B) 192 ways
(C) 182 ways
(D) 172 ways
(E) 152 ways
Rationale: To do this, if captain is elected first, then we have 14 ways of doing this.
For election of vice-captain, we have only 13 ways left, Bcoz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 14*13= 182 ways.
C
Answer: (C) 182 ways
Question: y selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 9
(C) 7
(D) 5
(E) 4
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: (A) 8
Question: The sum of the ages of 5 children born at the intervals of 4 years each is 50 years. what is the age of the eldest child ?
(A) 15
(B) 8
(C) 18
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Let x = the youngest child. Each of the other four children will then be x+4, x+8, x+12, x+16.
We know that the sum of their ages is 50 .
so, x+(x+4)+(x+8)+(x+12)+(x+16) = 50
x= 2
The youngest child is 2 years old.
Age of eldest child is = 2+16 = 18
Answer: C
Answer: (C) 18
Question: (64 - 12)2 + 4 x 64 x 12 = ?
(A) 5246
(B) 4406
(C) 5126
(D) 5776
(E) None of these
Rationale: Explanation :
Here, the given statement is like (a - b)2 + 4ab where a= 64 and b = 12
(a - b)2 + 4ab = (a2 - 2ab + b2) + 4ab = a2 + 2ab + b2 = (a + b)2
Hence (64 - 12)2 + 4 x 64 x 12 = (64 + 12)2 = 762 = 5776. Answer : Option D
Answer: (D) 5776
Question: The forth proportional to 10,8,15 is?
(A) 15
(B) 12
(C) 18
(D) 20
(E) 24
Rationale: Let the fourth proportional to 10,8,15 be x
then 10:8::15:x
10x = 8*15
x = 12
Answer is B
Answer: (B) 12