mathewhe/aqua_rat huggingface dataset:
Question: In store A there are 10 pairs of pants for every 50 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
(A) 4:15.
(B) 2:3.
(C) 1:3.
(D) 3:4.
(E) 2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
10x : 50x
X:5X
Price :
4y:3y
Total revenue
4xy : 15xy
4:15
Answer is A
Answer: (A) 4:15.
Question: A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let the total money be $x
B's 1day work = $ x/12
C's 1day work = $ x/24
A+B 1day work = $ x/8
Money is sufficient to pay the wages of both for 8days
Answer is C
Answer: (C) 8
Question: If 45% of z is 72% of y and y is 75% of x, what percent of x is z?
(A) 200
(B) 120
(C) 100
(D) 65
(E) 50
Rationale: (45/100)z = (72/100)y
and y = (75/100)x i.e. y = (3/4)x
i.e. (45/100)z = (72/100)*(3/4)x
i.e. z = (72*3)x/(45*4)
i.e. z = (1.2)x = (120/100)x
i.e. z is 120% of x
Answer: Option B
Answer: (B) 120
Question: The ratio of number of boys and girls in a class is 3 : 2. In the 1st semester exam 20% of boys and 25% of girls get more than or equal to 90% marks. What percentage of students get less than 90% marks ?
(A) 56
(B) 70
(C) 78
(D) 80
(E) 85
Rationale: Let boys =3x and girls =2x.
Number of those who get less than 90% mark =(80% of 3x) + (75% of 2x)
=(80/100 )*3x +(75/100 *2x) =39x/10
Required percentage = (39x/10 *1/5x *100)% = 78%.
ANSWER:C
Answer: (C) 78
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer: C
Answer: (C) 1/5
Question: Find the odd number. 15, 25, 30, 51, 85, 90, 115
(A) 12
(B) 42
(C) 46
(D) 47
(E) 51
Rationale: All numbers are multiples of 5 except 51
so answer is 51
answer E
Answer: (E) 51
Question: If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+4) for all positive integers n, what is the third term of the sequence?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Tn = nth term
T1 = 1st term
T2 = 2nd term
and so on...
Sn = Sum of first n terms of the sequence
Sn = 1st term + 2nd term + 3rd term + ... + nth term
Sn = T1 + T2 + T3 + ....Tn
You are given here thatSn is the SUM of first n terms...So you have
Sn = T1 + T2 + T3 + ....Tn = n(n+1)
So S1 = T1
S2 = T1 + T2
S3 = T1 + T2 + T3
and so on
S1 = T1 = 1*(1+1) = 2
S2 = T1 + T2 = 2 + T2 = 2*(2+1) = 6
So T2 = 4
S3 = T1 + T2 + T3 = 2 + 4 + T3 = 3*(3+1) = 12
So T3 = 9
(This is what we wanted)
The third term is 9.
E
Answer: (E) 9
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
(A) 567
(B) 564
(C) 645
(D) 735
(E) 756
Rationale: we have 3m and 2w
or
4m and 1w
or
5m
no of ways =(7C3 x 6C2) + (7C4 x 6C1) + (7C5)=	= (525 + 210 + 21)
= 756.
ANSWER:E
Answer: (E) 756
Question: 2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 1/2 of the red fish and 1/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
(A) 3/20
(B) 7/30
(C) 5/16
(D) 1/4
(E) 2/5
Rationale: 1/2*2/5 + 1/5*1/4 = 1/4
The answer is D.
Answer: (D) 1/4
Question: Venus travels around the Sun at an approximate speed of 21 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
(A) 84,000
(B) 126,000
(C) 135,000
(D) 148,000
(E) 162,000
Rationale: The speed is 21 miles/s. Then 21/0.6 = 35 km/s
35*3600 = 126,000 kph
The answer is B.
Answer: (B) 126,000
Question: Find the product of the localvalue and absolutevalue of 3 in 20368?
(A) 1000
(B) 1100
(C) 1200
(D) 900
(E) 10000
Rationale: Local value of 3 = 3 x 100 = 300
Place value of 3 = 3
There fore = 3 x 300 = 900
D
Answer: (D) 900
Question: A number when divided by 17 leaves 11 as a remainder. This number is greater than fifty but less than seventy. What will be the remainder if the number is divided by 10?
(A) 5
(B) 8
(C) 2
(D) 17
(E) 11
Rationale: Let 17 + 11 = 28 be the smallest number divisible by 17 with a remainder of 11.
Since 17 is prime, we need only add 17 to 28 until we enter the specified range.
17 + 17+ 11= 45 That doesn't fit.
17 +17 +17 +11=62 Bingo!
Now, 62 divided evenly into tens leaves a remainder of 2.
The answer is C.
Answer: (C) 2
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 42 years. What is the age of Deepak at present?
(A) 77 years
(B) 15 years
(C) 66 years
(D) 88 years
(E) 27 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 42 => x = 9
Deepak's age = 3x = 27 years.
Answer: E
Answer: (E) 27 years
Question: Two dogsled teams raced across a 700-mile course in Alaska. Team A finished the course in 7 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: Let v be team B's average speed.
Time = Distance/Rate and the time difference was 7 hours.
700/v - 700/(v+5)= 7
700v + 3500 - 700v = 7(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D.
Answer: (D) 20
Question: Find the invalid no.from the following series 3, 7, 15, 31, 61, 127, 255
(A) 3
(B) 61
(C) 27
(D) 63
(E) 127
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 61 is wrong.
B
Answer: (B) 61
Question: Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 25 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
(A) 10.5
(B) 0.5
(C) 25.5
(D) 30
(E) 60
Rationale: The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 25
x=0.5 minutes
Answer: B
Answer: (B) 0.5
Question: A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a
passenger train leaves the same station for Chicago traveling 60 mph. How long before the
passenger train overtakes the freight train?
(A) 6hours
(B) 5hours
(C) 9ours
(D) 2hours
(E) 4 hours
Rationale: Read the problem. It is a time, rate, and distance problem. (Use D=r*t)
The question asks, “how long?” (which means time) for the passenger train.
Let t=the time it takes the passenger train to overtake the freight train
t+2=the number of hours the freight train had traveled when overtaken.
Draw a sketch and make a table.
Time Rate Distance
Freight t+2- 40 mph- 40(t+2)
Passengert- 60 mph-60t
Equation: When the passenger train overtakes the freight train, they have both traveled
the same distance. Write each of their distances in terms of ratetime (as seen in the
table above), then set them equal to each other to create an equation. Then solve the
equation.
40(t+2)=60t
40t+80=60t
80=20t
t=4
The answer: It takes the passenger train 4 hours to overtake the freight train.
Check by substituting 4 into the original equation.
40(4+2)=60(4)
40(6)=240
240=240
true
Thus, 4 hours is the correct answer.
correct answer E
Answer: (E) 4 hours
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 96288
(C) 26667
(D) 1662
(E) 2882
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
Answer:A
Answer: (A) 9680
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:
(A) Rs. 1800
(B) Rs. 1450
(C) Rs. 1360
(D) Rs. 6800
(E) Rs. 7800
Rationale: sum=si*td/(si-td)
sum=80*85/(85-80)
sum=1360
ANSWER:C
Answer: (C) Rs. 1360
Question: A car drove from Town A to Town B without stopping. The car traveled the first 90 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 70 miles if the car’s average speed for the entire trip was 40 miles per hour?
(A) 128
(B) 148
(C) 150
(D) 155
(E) 175
Rationale: KAPLANOFFICIAL SOLUTION:
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.
For the first 90 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 90/25, because distance divided by rate equals time.
For the last 70 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 70 miles is 70/R.
If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(90/25 + 70/R) = 40. We can now solve for R and reach our answer.
160/(90/25 + 70/R) = 40
R = 175 is choice (E) and that’s our correct answer.
Answer: (E) 175
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?
(A) 40%
(B) 55%
(C) 57%
(D) 60%
(E) 62%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: Which among the following fractions below has the highest value?
(A) A)23/77
(B) B)23/78
(C) C)23/84
(D) D)23/87
(E) E)23/27
Rationale: 23/27.
Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.
Answer (E).
Answer: (E) E)23/27
Question: What is the value of 3x^2 − 2.4x + 0.3 for x = 0.6?
(A) −0.3
(B) 0
(C) 0.06
(D) 1.08
(E) 2.46
Rationale: 3x^2-2.4x+0.3 for x=0.6
=3(0.6*0.6)-4*0.6*(0.6)+0.3
=-0.6*0.6+0.3
=0.06
Correct Option : C
Answer: (C) 0.06
Question: Aman started a business investing Rs. 60,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 12:15:18
(B) 72:105:112
(C) 52:105:112
(D) 62:105:112
(E) 12:105:112
Rationale: Explanation:
Aman : Rakhi : Sagar = (60000 * 36) : (105000 * 30) : (140000 * 24)
= 72:105:112
Answer: B
Answer: (B) 72:105:112
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 42 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 229
(B) 288
(C) 787.5
(D) 888
(E) 121
Rationale: D = 30 * 5 = 150
RS = 42 – 30 = 8
T = 150/8 = 18.75
D = 42 * 18.75 = 787.5 km
Answer: C
Answer: (C) 787.5
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 8, if the digits are allowed to repeat within a number?
(A) 12,987
(B) 13,876
(C) 14,765
(D) 15,654
(E) 16,543
Rationale: The number of these 3-digit numbers is 3*3*3 = 27
Each digit 1, 4, and 8 will appear in the ones, tens, and hundreds place 9 times each.
The sum equals 9(111) + 9(444) + 9(888) = 12,987
The answer is A.
Answer: (A) 12,987
Question: What is the unit digit in the product (245 x 122 x 431)?
(A) 2
(B) 3
(C) 0
(D) 1
(E) Can't be determined
Rationale: Explanation:
Product of unit digits = 5 x 2 x 1 = 10
Required digit = 0
Answer: Option C
Answer: (C) 0
Question: A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?
(A) 8
(B) 24
(C) 58
(D) 80
(E) 210
Rationale: 6!/3!(6-3)! = 20
4!/1!(4-1)!=4
so number of different committees equals 20*4=80
ANS:D
Answer: (D) 80
Question: One fourth of a solution that was 10 percent RICE by weight was replaced by a second solution resulting in a solution that was 16 percent RICE by weight. The second solution was what percent RICE by weight ?
(A) 34%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of RICE in 2nd sol)=34%=A
Answer: (A) 34%
Question: The H.C.F. of two numbers is 25 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 350
Rationale: Clearly, the numbers are (25 x 13) and (25 x 14).
Larger number = (25 x 14) = 350.
Answer: Option E
Answer: (E) 350
Question: In racing over a given distance d at uniform speed, A can beat B by 20 meters, B can beat C by 6 meters, and A can beat C by 23 meters. What is the distance d in meters?
(A) 32
(B) 36
(C) 40
(D) 48
(E) 60
Rationale: When A is at the finish line, B is 20 meters back, and C is 23 meters back.
When B runs another 20 meters to the finish line, C is 6 meters back.
So B gains 3 meters every 20 meters covered.
To gain a final difference of 6 meters, B runs a total of 40 meters.
The answer is C.
Answer: (C) 40
Question: A company decreased the price of its main product by 10%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
(A) 4.3
(B) 5.6
(C) 6.2
(D) 10.0
(E) 12.0
Rationale: For the total revenue to remain the same when the price is 1/10, the number of products sold must 1/10 times. Therefore increase in the number of products sold is 100%
=> The required ratio = 100%/10% = 10.0
Answer : D
Answer: (D) 10.0
Question: At Deluxe paint store, Fuchsia paint is made by mixing 6 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?
(A) 9
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: in 24 liters, Red = 6/9 * 24 = 16 and Blue = 8
so, 16/(8+x) = 4/5
or, x = 12 (Answer B)
Answer: (B) 12
Question: A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 19}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
(A) 15
(B) 16
(C) 19
(D) 24
(E) 36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 24
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
D
Answer: (D) 24
Question: Three printing presses, L, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take L, working alone at its constant rate, to do the same job?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: =1/4-1/5=1/20
L can do 1/20 job in 1 hour
L can do the whole job in 20 hours=E
Answer: (E) 20
Question: Some of the people in Town V are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town V, three times as many people are tall as are tall in Town V, three times as many people are both as are both in Town V, but no one is neither. If the total number of people in Town V is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town V who are neither left-handed nor tall?
(A)  23
(B)  39
(C)  72
(D)  143
(E)  199
Rationale: Yes, correct answer is indeed D.
{V}={Left} + {Tall} - {Both} + {Neither};
{Y} = 3*{Left} + 3*{Tall} - 3*{Both};
Since the total number of people in Town V is four times greater than the total number of people in Town Y, then:
{Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});
{Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town V who are neither left-handed nor tall must be a multiple of 11.
Only answer choice D, is a multiple of 11: 143=11*13.
Answer: D.
Answer: (D)  143
Question: There are 1000 buildings in a street. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?
(A) 190
(B) 191
(C) 192
(D) 193
(E) 194
Rationale: divide as (1-100)(100-200)....(900-1000)
total 192
ANSWER:C
Answer: (C) 192
Question: Seven years ago the average age of a family of 2 members was 22 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
(A) 30years
(B) 33years
(C) 35years
(D) 37years
(E) 40years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 22
= (22+ 7) * 2 = 36 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 36 = 33 years
Answer: Option B
Answer: (B) 33years
Question: Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B?
(A) 8,000
(B) 8,600
(C) 8,150
(D) Data inadequate
(E) None of these
Rationale: % interest on total amount per annum
= 3620×100/16500×2=362/33%
Now, use Alligation method.
Hence, ratio of amount invested in schemes A and B
= (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16
Hence, amount invested in B = 16×16500/(17+16)=8000
Answer A
Answer: (A) 8,000
Question: A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?
(A) 5 m
(B) 6 m
(C) 4 m
(D) 7 m
(E) 8 m
Rationale: Let radius of the outer circle be R and radius of the inner circle be r.
Circumference of the outer circle =
Circumference of the inner circle =
But,
or, R - r =
Thus, width of the road = 7 m
D
Answer: (D) 7 m
Question: If a number is 35% more than the another, how much % is the smaller number less than the first ?
(A) 24%
(B) 28%
(C) 16(1/3)%
(D) 16(4/3)%
(E) 26%
Rationale: Take a number 100,
Then the other number is 135
% the smaller number is less than the first = [(35/(135)) x 100]% = 26%.
ANSWER:E
Answer: (E) 26%
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes Q, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
(A)  6
(B)  9
(C)  10
(D)  12
(E)  15
Rationale: This is an inverse proportional problem......
5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15
So, Q=15-5 = 10.C
Answer: (C)  10
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
(A) 65 ways
(B) 54 ways
(C) 88 ways
(D) 14 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 .3³C2 ways i.e., 10 * 3
= 30 ways.
Answer:E
Answer: (E) 30 ways
Question: If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
(A) 500
(B) 1000
(C) 1500
(D) 2000
(E) 3000
Rationale: Explanation:
Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.
Then, 2x + 3y = 3500 ...(i)
and 3x + 2y = 4000 .....(ii)
solving (i) and (ii) we get x = 1000, y = 500
ANSWER IS B
Answer: (B) 1000
Question: A boat can move upstream at 25 kmph and downstream at 30 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 2.5
(E) 9
Rationale: US = 25
DS = 30
M = (35 - 25)/2 = 2.5
Answer: D
Answer: (D) 2.5
Question: Ron has had 3 pay cuts in her salary in the past 6 months. If the first pay cut was 5%, the second pay cut was 10% and the third was 15%. What will be the percentage decrease, if the salary is decreased in a single shot?
(A) 29.33%
(B) 27.33%
(C) 17.33%
(D) 27.99%
(E) 29.33%
Rationale: Let Rs.100 be initial salary.
Salary After 1st decrease, 5% = 95
Salary After 2nd decrease, 10% = 85.5 i.e. reduced by 10 percent of 95
Salary After 3rd decrease, 15% = 72.675 i.e. reduced by 15 percent of 85.5
So if its decreased in single shot =
i = ( ( b - a ) /b ) * 100
=27.33%
ANSWER:B
Answer: (B) 27.33%
Question: tipli and pikli are a married couple (dont ask me who he is and who she is)
They have two children, one of the child is a boy. Assume safely that the probability of each gender is 1/2.
What is the probability that the other child is also a boy?
Hint: It is not 1/2 as you would first think.
(A) 1/1
(B) 1/2
(C) 1/3
(D) 1/4
(E) 1/5
Rationale: Solution:
1/3
This is a famous question in understanding conditional probability, which simply means that given some information you might be able to get a better estimate.
The following are possible combinations of two children that form a sample space in any earthly family:
Boy - Girl
Girl - Boy
Boy - Boy
Girl - Girl
Since we know one of the children is a boy, we will drop the girl-girl possibility from the sample space.
This leaves only three possibilities, one of which is two boys. Hence the probability is 1/3
Answer C
Answer: (C) 1/3
Question: Find the sum of the following series,
1,4/5,16/25,64/125 ……………..
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: It is a G.P with infinite terms. The common ratio is (4/5) and this is less than 1. The sum to infinity of a series with first term ‘a ‘ and common ratio ‘r’ =[ a/( 1-r) ], The sum to infinity = 1/ (1 – 4/5 ) = 5
ANSWER:C
Answer: (C) 5
Question: Evaluate combination
97C95=97/(95)!(2)!
(A) 4656
(B) 5176
(C) 4176
(D) 3176
(E) None of these
Rationale: Explanation:
nCr=n!/(r)!(n−r)!
97C95=97!/(95)!(2)!
=97*96*95!/(95)!(2)!
=97*96/2∗1
=4656
Option A
Answer: (A) 4656
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 4 : 3. If C gets Rs. 500 more than D, what is A's share?
(A) Rs. 2500
(B) Rs. 1000
(C) Rs. 1500
(D) Rs. 2000
(E) NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 500 ⇔ x = 500.
∴ A's share = Rs. 5x= Rs. (5x500) = Rs. 2500.
Answer A
Answer: (A) Rs. 2500
Question: How many four letter words are formed using the letters of the word SHORT?
(A) 95
(B) 100
(C) 115
(D) 110
(E) 120
Rationale: The number of letters in the given word is five.
The number of four letter words that can be formed using these five letters is 5P4
= 5 * 4* 3* 2 = 120.
Answer: E
Answer: (E) 120
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c âˆ’ a?
(A) 25
(B) 70
(C) 90
(D) 140
(E) It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=160 --2
subtracting 1 from 2 we have
c-a=70;
ANSWER:B
Answer: (B) 70