mathewhe/aqua_rat huggingface dataset:
Question: In an Examination there are three subject of 100 marks each. A student scores 60% in the 1st subject and 80% in the second subject. He scored 70% in aggregate. His percentage of marks in the third subject is:
(A) 70
(B) 80
(C) 60
(D) 65
(E) 66
Rationale: Explanation :
Let be the score of third subject = X
A student of score in first subject = 60% = 60 x 100/100 = 60
A student of score in second subject = 80% = 80 x 100/100 = 80
70% of 300 = 300 x 70/100 = 210
score of third subject = 210 – ( 60 + 80)
= 210 – 140 = 70
Percentage of score in third subject = 70 x 100/100 = 70%
Hence, the answer is 70%
Answer : A
Answer: (A) 70
Question: The arithmetic mean of the scores of a group of students in a test was 62. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
(A) A)61.4.
(B) B)51.7
(C) C)69.54
(D) D)51.1
(E) E)51.2
Rationale: Let the required mean score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 62 * 100
= 1600 + 775 + 55x = 6200
= 55x = 3825
= x = 69.54
Answer:C
Answer: (C) C)69.54
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) 1/0
(B) 1/3
(C) 1/1
(D) 1/7
(E) 1/5
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer: B
Answer: (B) 1/3
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1240. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A) 2480
(B) 3490
(C) 6785
(D) 8215
(E) 9255
Rationale: sum of square of n numbers is found using the formula [n (n+1) (2n+1)]/6
we have sum of 1st 15 numbers = 1240
we need to find sum of squares from 16 to 30 which is = sum of squares of 1st 30 +ve integers - sum of squares of 1st 15 +ve integers.
we will get D - 8215;ANSWER:D
Answer: (D) 8215
Question: Eight men, ten women and six boys together can complete a piece of work in eight days. In how many days can 20 women complete the same work if 20 men can complete it in 12 days?
(A) 33
(B) 77
(C) 66
(D) 22
(E) 99
Rationale: Let the number of units which can be completed by each man, each women and each boy be m/day, w/day and b/day respectively.
Work = 8(8m + 10w +6b)units = 12(20m)
10w +6b = 22m
b is unknown.
We cannot find the relation between m and w.
We cannot answer the question.
Answer:D
Answer: (D) 22
Question: Which of the following is divisible by the first five positive integer multiples of 23?
(i) 11110
(ii) 102120
(iii) 307740
(A) None
(B) iii only
(C) i and iii only
(D) ii and iii only
(E) i, ii and iii
Rationale: A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 3*4*5*23=60*23=1380.
The sum of the integers of 11110 is 4 so 11110 is not divisible by 3, hence not divisible by 1380.
102=17*6 and 120=20*6, so 102120=60*(1700+2)=60*1702=60*2*851. Now, 851-30*23=851-690=161=7*23, so 102120 is divisibly by 60*23=1380.
Finally, 102120*3=306360, and 306360+1380=307740, so (iii) is also divisible by 1380.
Answer D.
Answer: (D) ii and iii only
Question: A local bank that has 20 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 20 codes?
(A) 3
(B) 4
(C) 7
(D) 6
(E) 5
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Add one more integer: 5
55, 15, 51, 25, 52, 35, 53,54,45 = 9 Codes
Total = 25 Codes. Enough.
Answer: E
Answer: (E) 5
Question: If 3/p = 6 and 3/q = 15 then p – q = ?
(A) 3/19
(B) 3/11
(C) 3/17
(D) 3/10
(E) 3/13
Rationale: Explanation:
3p3p = 6 , p = 3636 = 1212and
3q3q = 15 , q = 315315 = 1515 then
p – q = 1/2 – 1/5 = 3/10
Answer: D
Answer: (D) 3/10
Question: The cost of the paint is rs.50 per kg. if 1kg of paint covers 20 sq.ft, how much will it cost to paint outside of a cube having 20 feet each side
(A) Rs.962
(B) Rs.6000
(C) Rs.546
(D) Rs.876
(E) None of these
Rationale: Explanation:
surface area of a cube= 6 x 20^2 = 2400 sq.ft
quantity of paint required=(2400/20)=120 kg
cost of painting= 50x 120= Rs.6000
Answer: B
Answer: (B) Rs.6000
Question: If the city centers of Tokyo and Rome are 6124 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)
(A) 1.7 × 10^7
(B) 4.8 × 10^7
(C) 3.9 × 10^8
(D) 2.7 × 10^9
(E) 1.5 × 10^10
Rationale: 6124 miles = 6124 x 5280 feet/mile x 12 inches/foot which is about 3.9 x 10^8 inches.
The answer is C.
Answer: (C) 3.9 × 10^8
Question: Aman started a business investing Rs. 70,000. 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) 12:15:16
(C) 12:15:10
(D) 12:15:12
(E) 12:15:11
Rationale: Explanation:
Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B
Answer: (B) 12:15:16
Question: The mean of 50 observations was 36. it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :
(A) 35.2
(B) 36.1
(C) 36.5
(D) 39.1
(E) None of these
Rationale: Solution
Correct sum = (36 × 50 + 48 - 23) = 1525.
∴ correct mean = 1825/50=36.5 Answer C
Answer: (C) 36.5
Question: Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 7%. What is the approximate interest he pays annually?
(A) 1000
(B) 1500
(C) 3000
(D) 2500
(E) 2400
Rationale: An easy way too attempt this is by approximation:
For the first quarter, he pays 7% of 10,000 which is $700.
So for the four quarters in the year, he will approximately play 700*4=2800 over the entire year.
Because of compound interest it will be more than 2800. Approx. option C is correct.
Answer : C
Answer: (C) 3000
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A)  2:9
(B)  2:7
(C)  1:6
(D)  1:4
(E)  1:3
Rationale: (10/100)A+(3/100)B = (4/100)(A+B)
6A =B
=> A/B = 1/6
Answer is C.
Answer: (C)  1:6
Question: If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)?
(A) 0.36
(B) 0.4
(C) 0.42
(D) 0.43
(E) 0.64
Rationale: P(B|A) = P(A n B)/P(A)
P(A n B) = P(B|A) × P(A)
P(A n B) = 0.2 × 0.18
P(A n B) = 0.36
A
Answer: (A) 0.36
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 8200, then what will be the share of Sameer in the profit?
(A) s.2323
(B) s.2380
(C) s.2800
(D) s.2329
(E) s.2312
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 8200 * 14/41
= Rs.2800.
Answer: C
Answer: (C) s.2800
Question: The difference between the local value and the face value of 7 in the numeral 32675149 is
(A) 69950
(B) 69993
(C) 69997
(D) 70000
(E) 01000
Rationale: (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
B
Answer: (B) 69993
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 4 fantasy books, there are 5 reference books. If the proportion of history to fantasy books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
(A) 6
(B) 21
(C) 24
(D) 32
(E) 36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7. After the change, H:F = 4:7 = 16:28
For every 4 fantasy books, there are 5 reference books:
F:R = 4:5 = 28:35
H:F:R = 16:28:35
There are fewer than 60 fantasy books, so there are 28 or 56 fantasy books.
The number of history books could be 16 or 32.
The answer is D.
Answer: (D) 32
Question: One side of a triangle has length 9 and a second side has length 4. Which of the following could be the area of the triangle?
I. 30
II. 20
III. 10
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 9 and 4 are the base and height of triangle .
Area = 1/2 * 9 * 4 = 18
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 18
The answer is C.
Answer: (C) III only
Question: Calculate the L.C.M of 1/5, 6/ 7, 5/6, 3/5 is :
(A) 15
(B) 30
(C) 20
(D) 40
(E) 10
Rationale: Required L.C.M =L.C.M. of 1, 6, 5, 3/H.C.F. of 5, 7, 6, 5 =30/1=30
Answer is B
Answer: (B) 30
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
(A) 37.6
(B) 37.5
(C) 37.7
(D) 37.2
(E) 37.1
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%.Answer: B
Answer: (B) 37.5
Question: If the two-digit integers F and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of F and N?
(A) 181
(B) 165
(C) 121
(D) 99
(E) 44
Rationale: Since the question asks for the answer that CANNOT be the sum of F and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that F and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of F and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Answer: (A) 181
Question: There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?
(A) A)55%
(B) B)60%
(C) C)80%
(D) D)72%
(E) E)70%
Rationale: There is a 10% chance that Tigers will not win at all during the whole season
We can infer that there is 90% chance Tigers will win .
Similarly There is a 30% chance that Federer will not play at all in the whole season
We can also infer that there is 70% chance that Federer will play.
Answer E
Answer: (E) E)70%
Question: Solve below question 2x + 1 = -17
(A) 7
(B) -9
(C) 10
(D) -1
(E) 2
Rationale: 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
Answer: (B) -9
Question: To be elected president of a certain organization, a candidate needs the votes of at least 2/3 of its 1,331 members. What is the least number of votes the candidate needs to be elected?
(A) 443
(B) 444
(C) 887
(D) 888
(E) 889
Rationale: required votes>= 1331∗2/3
votes should be an integer, thus we can take
required votes = 1332∗2/3( because 1332/3 will be an integer )
= 888
ANSWER:D
Answer: (D) 888
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
(A) 148
(B) 150
(C) 152
(D) 158
(E) 160
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: (D) 158
Question: An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks?
(A) 1200
(B) 1680
(C) 2102
(D) 4020
(E) 1840
Rationale: Number of ways of choosing 4 stocks = 8C4
Number of ways of ranking the chosen stocks = 4!
Hence total ways of chosing and ranking = 8C4 * 4! = 1680
Correct Option: B
Answer: (B) 1680
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 118
(B) 110
(C) 112
(D) 113
(E) 115
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: (C) 112
Question: Today John is 3 times older than Mark. If in 13 years, John will be one year younger than twice the age of Mark on that day, how old is Mark today?
(A) 12
(B) 33
(C) 36
(D) 38
(E) 39
Rationale: today +13yrs
J =3M 3M+13
M M+13
Given after 13yrs john will be 1 year younger than twice mark's age
i.e 3M+13 = 2(M+13)-1
M=12
Answer is A.
Answer: (A) 12
Question: A train moves fast a telegraph post and a bridge 245 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 73.5
(B) 39.5
(C) 79.9
(D) 79.2
(E) 79.1
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 245)/20 = y
y = 20.42
Speed = 20.42 m/sec = 20.42 * 18/5 = 73.5 km/hr.
Answer:A
Answer: (A) 73.5
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 52.65
(B) 56.25
(C) 50.75
(D) 42.75
(E) 52.75
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
ANSWER:B
Answer: (B) 56.25
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
(A) 1:7
(B) 2:15
(C) 9:31
(D) 8:17
(E) 9:19
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
C
Answer: (C) 9:31
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches?
(A) 50%
(B) 87%
(C) 100%
(D) 187%
(E) 200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 11 is twice 5.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: (C) 100%
Question: To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 10 cents
(B) Separately, with a saving of 10 cents
(C) Combined, with a saving of 15 cents
(D) Separately, with a saving of 15 cents
(E) Combined, with a saving of 5 cents
Rationale: 5 pounds = 1*20+4*5 = 40
10 pounds = 1*20+9*5 =65
total = 105
15 pound = 1*20+14*5 = 90
dif. 15
Answer : C
Answer: (C) Combined, with a saving of 15 cents
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2800, what will be the difference between Q and R's share?
(A) 2788
(B) 3500
(C) 7282
(D) 2782
(E) 2729
Rationale: 4 --- 2800
5 --- ? => 3500
Answer:B
Answer: (B) 3500
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 20 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
C
Answer: (C) 14 years
Question: On average, the bottle-nosed dolphin comes up for air once every four minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: Dolphin once in 4 min;
Beluga once in 6 min;
So, dolphin comes up 1.5 times frequently than beluga, which is 100% (6-4)/2*100.
Answer: B.
Answer: (B) 100%
Question: What is the sum of all the composite numbers up to 8?
(A) 16
(B) 6
(C) 10
(D) 12
(E) 6
Rationale: Explanation:
4 + 6+8 = 16
Answer: A
Answer: (A) 16
Question: The mean of (54,822)^2 and (54,824)^2 =
(A) (54,821)^2
(B) (54,821.5)^2
(C) (54,820.5)^2
(D) (54,823)^2 + 1
(E) (54,821)^2 – 1
Rationale: 54822^2 = (54823-1)^2 = 54823^2 + 1^2 - 2*54823*1
54824^2 = (54823+1)^2 = 54823^2 +1^2 + 2*54821*1
Taking the average of above 2 , we get (54823)^2 +1
hence the answer is D
Answer: (D) (54,823)^2 + 1
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 40 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/200
(C) 1/25
(D) 1/50
(E) 1/900
Rationale: So there are 900 cars that they have to search.. Each takes 40mins, total of 36000 mins.. Have to find in 180 mins.. Prob180/36000 = 1/200 (ANSWER B)
Answer: (B) 1/200
Question: Tina has 12 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 5 specific shirts with 3 specific pants?
(A) 93
(B) 66
(C) 36
(D) 85
(E) 108
Rationale: Total no of combinations available is= 12 shirts X 9 pants = 108
Eliminate the 5 shirts X 3 pants combo = 15 which gives.......>> 108-15=93
ANSWER:A
Answer: (A) 93
Question: The contents of a certain box consist of 14 apples and 12 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
(A) 3
(B) 6
(C) 14
(D) 17
(E) 20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 12 oranges, so to get to 6 oranges, we should remove 12 - 6 = 6 oranges.
Answer B
Answer: (B) 6
Question: (0.0088)(4.5) / (0.05)(0.1)(0.008)=
(A) 950
(B) 940
(C) 980
(D) 960
(E) 990
Rationale: (0.0088)(4.5) / (0.05)(0.1)(0.008)=0.0088 * 450/5 * (0.1)(0.008)
= 0.088*90/1 * 0.008 = 88*90/8 = 11*90
=990
Answer : E
Answer: (E) 990
Question: X and Y put in 3,000 and 4,000 respectively into a business. X reinvests into the business his share of the first year?s profit of 2,100 whereas Y does not reinvest. In what ratio should they share the second year?s profit?
(A) 39 : 40
(B) 3 : 4
(C) 3 : 7
(D) 40 : 79
(E) None of these
Rationale: For first year, ratio of profit = 3 : 4
X?s profit of first year = 3?7 � 2100 = 900
Now, for second year,Now, for second year,
ratio of profit = 3000 � 12 + 900 � 12 : 4000 � 12
= 46800 : 48000 = 39 :40
Answer A
Answer: (A) 39 : 40
Question: One computer can upload 100 megabytes worth of data in 3 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 30 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
(A)  6
(B)  10
(C)  9
(D)  11
(E)  13
Rationale: Since the first computer can upload 100 megabytes worth of data in 3 seconds then in 3*10=30 seconds it can upload 10*100=1000 megabytes worth of data, hence the second computer in 30 seconds uploads 1300-1000=300 megabytes worth of data. The second computer can upload 100 megabytes of data in 10 seconds.
Answer: B.
Answer: (B)  10
Question: Liz drove from point A to point B at 40 Km/h. On her way back she drove at 50 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?
(A) 150
(B) 200
(C) 450
(D) 500
(E) 600
Rationale: Distance is same
S1t1=s2t2
40t= 50 (t-1)
t=5
distance= speed *time
40*5= 200
ANSWER:B
Answer: (B) 200
Question: Pipe A can fill a tank in 12 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 18
(B) 27
(C) 98
(D) 27
(E) 36
Rationale: Let the pipe B be closed after x minutes.
30/12 - x/24 = 1 => x/24 = 30/12 - 1 = 3/2
=> x = 3/2 * 24
= 36.
Answer:E
Answer: (E) 36
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are
(A) 42,30
(B) 42,31
(C) 42,32
(D) 42,33
(E) 42,55
Rationale: Explanation:
Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
Answer: Option D
Answer: (D) 42,33
Question: In a throw of coin what is the probability of getting tails.
(A) 1
(B) 2
(C) 1/2
(D) 0
(E) None of these
Rationale: Explanation:
Total cases = [H,T] - 2
Favourable cases = [T] -1
So probability of geƫng tails = 1/2
Answer: C
Answer: (C) 1/2
Question: A person's present age is one-fifth of the age of his mother. After 8years, he will be one - half of the age of his mother. How old is the mother at present ?
(A) A)25
(B) B)44
(C) C)32
(D) D)45
(E) E)40
Rationale: Let the mother's present age be x years
Then the person's present age = 2x/5
(3x/5)+8 = 1/2(x+8)
2(3x+40) = 5 (x+8)
x = 40
Answer is E
Answer: (E) E)40
Question: If a fair coin is tossed six times, what is the probability of getting exactly four heads in a row?
(A) 5/64
(B) 3/32
(C) 3/16
(D) 3/8
(E) 1/8
Rationale: Let X represent either H or T (it doesn't matter which).
P(HHHHTX) = 1/32
P(THHHHT) = 1/64
P(XTHHHH) = 1/32
The sum of these three probabilities is 5/64
The answer is A.
Answer: (A) 5/64
Question: The average of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?
(A) 79 years
(B) 18 years
(C) 19 years
(D) 19 years
(E) 13 years
Rationale: Sum of the ages of 14 students
= (16 * 35) - (14 * 21) = 560 - 294 = 266
Required average = (266/14) = 19 years.
Answer:D
Answer: (D) 19 years
Question: An uneducated retailer marks all his goods at 60% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
(A) 20 %
(B) 13.50 %
(C) 14 %
(D) 14.50 %
(E) None
Rationale: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 160.
S.P. = 75% of Rs. 160 = Rs. 120.
∴ Gain% = 20%.
Answer A
Answer: (A) 20 %
Question: If x < z < -1, which of the following is true?
(A) x/z > xz
(B) z/x > x+z
(C) z/x > xz
(D) z/x < x+z
(E) z/x > x/z
Rationale: Consider :
x= -3
z= -2
then put for every option. U'll get ans B.
Answer: (B) z/x > x+z