mathewhe/aqua_rat huggingface dataset:
Question: Julie and his friends wants to play Team Carrom board. Julie has 7 friends.In how many possible ways to divide into team?
(A) 282
(B) 521
(C) 100
(D) 105
(E) 90
Rationale: This question is little different from other question.The sentence "julie has 7 friends and they need to play Team carrom",Here they describes both julie and her 7 friends. so 8 members are there to play to carrom.
The question is How many different ways can the group be divided into 4 teams of 2 people?
Group = A(julie) B C D E F G H. Again, A must be on a team--there are 7 possibilities. For each of those possibilities, there are 15 ways of dividing the remaining 6 members into 3 teams. So total possibilities = 7 * 15 = 105.
The answer is Option D
Answer: (D) 105
Question: The salaries of A and B together amount to $7000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?
(A) $1000
(B) $5250
(C) $2500
(D) $4500
(E) $1200
Rationale: Let A's salary is x
B's salary = 7000-x
(100-95)% of x = (100-85)% of (7000-x)
x = $5250
Answer is B
Answer: (B) $5250
Question: Line J has a y-intercept of 9 and passes through point (a,b). What is the slope of Line J in terms of a and b?
(A) (a−6)/b
(B) (a−b)/6
(C) (b-9)/a
(D) (6−b)/a
(E) (b−6)/a
Rationale: You know that the line goes through point (a,b) and the y-intercept of 9 tells you that the line also goes through point (0,9).
slope m = (y-y1)/(x-x1) = (b-9)/(a-0)= (b-9)/a
C
Answer: (C) (b-9)/a
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Total number of outcomes possible, n(S) = 10 + 25 = 35
Total number of prizes, n(E) = 10
E)
Answer: (E) 10
Question: A train traveling with constant speed crosses a 90m long platform in 12 seconds and a 120m long platform in 15 seconds.Find the length of the train and its speed.
(A) 30
(B) 40
(C) 60
(D) 50
(E) NOne
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 12 => y = x/12
(x + 90)/12 = x+120/15 => x = 30 m.
Answer:A
Answer: (A) 30
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
(A) 120
(B) 350
(C) 700
(D) 2,520
(E) 5,040
Rationale: Number of ways to choose 2 colors among 5 - 5c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations - 5c2 * 2* 7c4 = 700 ANS:C
Answer: (C) 700
Question: In a race where 18 cars are running, the chance that car X will win is 1/8, that Y will win is 1/12 and that Z will win is 1/6. Assuming that a dead heat is impossible, find the chance that one of them will win.
(A) 1/140
(B) 1/180
(C) 3/12
(D) 3/8
(E) 57/120
Rationale: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).
= 1/8 + 1/12 + 1/6
= 3/8
ANSWER:D
Answer: (D) 3/8
Question: A starts business with Rs.4500 and after 7 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Bâ€™s contribution in the Capital ?
(A) 24887
(B) 20778
(C) 16200
(D) 9000
(E) 2811
Rationale: Explanation:
A invested Rs.3500 for 12 months.
Let B joined with investment x. And he invested for 12 - 7 = 5 months.
So there profit ratio = (4500 Ã— 12) : (5x) = 2 : 3
â‡’ x = 16200
Answer: C
Answer: (C) 16200
Question: How many keystrokes are needed to type the numbers from 1 to 1500?
(A) 2805
(B) 3224
(C) 3897
(D) 4562
(E) 4893
Rationale: There are 9 one-digit numbers from 1 to 9.
There are 90 two-digit numbers from 10 to 99.
There are 900 three-digit numbers from 100 to 999.
There are 501 four-digit numbers from 1000 to 1500.
9 + 90(2) + 900(3) + 501(4) = 4893
The answer is E.
Answer: (E) 4893
Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio T of milk and water in the resultant mixture?
(A) 17 : 3
(B) 9 : 1
(C) 3 : 17
(D) 5 : 3
(E) 11: 2
Rationale: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1.
When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.
Step 2.
When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
Shortcut.
We are essentially replacing water in the mixture with pure milk.
Let W_o be the amount of water in the mixture originally = 8 litres.
Let W_r be the amount of water in the mixture after the replacements have taken place.
Then,{W_r}/{W_o}= (1-R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore,TW_r ={W_o}/4= 8/4 = 2 litres.B
Answer: (B) 9 : 1
Question: The product of the prime integers between 42 and 50, inclusive, is:
(A) 50! – 40!
(B) 99,029
(C) 2,021
(D) 2,303
(E) 2,000
Rationale: only prime number bet ween 43 and 50 inclusive are 43 and 47
thus 43*47 = 2021
Ans: C
Answer: (C) 2,021
Question: 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container H?
(A) A:45
(B) B:25
(C) C:37.5
(D) D:36
(E) E:42
Rationale: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.
1st Replacement
After the first replacement you have 37.5-15=22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.
The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.
Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.
Final Replacement
The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.
Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. Choice C is correct.
Answer: (C) C:37.5
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 7 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
(A) 15 litres
(B) 14 litres
(C) 30 litres
(D) 22 litres
(E) 8 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+7)=4/5
20x=4(3x+7)
8x=28
x=3.5
Quantity of alcohol = (4 x 3.5) litres = 14 litres.
Answer is B.
Answer: (B) 14 litres
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 8 2 1/2 kmph
(B) 2 2 1/8 kmph
(C) 2 2 7/2 kmph
(D) 2 2 1/2 kmph
(E) 2 3 1/2 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: D
Answer: (D) 2 2 1/2 kmph
Question: 8 teams.each teams play twice with other teams.win =2poins. lose =0 points. no draw/match abandonment.top four go semis.if same points runrate considered. whats the minimum num of points with which a team may go to semis
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Minumum points for (may condition): 4
ANSWER:C
Answer: (C) 4
Question: Which of the following expressions CANNOT have a negative value
(A) |a + b| – |a – b|
(B) |a + b| – |a|
(C) |2a + b| – |a + b|
(D) a^2 + b^2 |+ 2|ab|
(E) |a^3 + b^3| – a – b
Rationale: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
a^2+b^2+2|ab| = |a|^2 + |b|^2 + 2|a||b| = (|a| +|b|)^2.
This will always be positive.
Correct Option: D
Answer: (D) a^2 + b^2 |+ 2|ab|
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team?
(A) 23 years
(B) 17 years
(C) 16 years
(D) 19 years
(E) 15 years
Rationale: Let the average of the whole team be x years.
11x - (26 + 29) = 9(x - 1)
= 11x - 9x = 46
= 2x = 46 => x = 23
So, average age of the team is 23 years.
Answer: A
Answer: (A) 23 years
Question: A milk man has 20 liters of milk. If he mixes 25 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
(A) 20%
(B) 45%
(C) 33.33%
(D) 18%
(E) None of these
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.
Therefore, profit percentage = 45 %. Answer: B
Answer: (B) 45%
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability T that the new color will be one of theJaunecolors?
(A) 5/42
(B) 37/42
(C) 1/21
(D) 4/9
(E) 5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability T of Jaune = (40 + 34)/84 = 37/42.B
Answer: (B) 37/42
Question: Look at this series: 15, __, 27, 27, 39, 39, ... What number should fill the blank?
(A) 10
(B) 16
(C) 18
(D) 11
(E) 15
Rationale: E
11
In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: (E) 15
Question: A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 20 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?
(A) 36%
(B) 40%
(C) 44%
(D) 48%
(E) 52%
Rationale: Let x be the number of stamps in the original collection.
The percentage of the collection given away is:
0.2x + 0.2(0.8x) = 0.2x + 0.16x = 0.36x = 36%
The answer is A.
Answer: (A) 36%
Question: A container can hold 4 quarts of fruit juice and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts fruit juice to 5 parts water by volume?
(A) 4/3
(B) 5/3
(C) 7/3
(D) 8/3
(E) 10/3
Rationale: An alternate to the alligation method is the more direct/algebraic method:
Let x be the amount of water to be added.
New total amount of water = 4+x
Total amount of fruit juice = 4
New total = 4+4+x=8+x
Final ratio required (for water) = 5/(5+3)=5/8
Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.
D is thus the correct answer.
Answer: (D) 8/3
Question: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 63,000 different outfits, then for how many garments does Dave have exactly five choices?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: There are 9 different kinds of clothes.
so if you find the prime factors of 63000
i.e. 3 * 3 * 7 * 2 * 2 *2 *5 * 5 *5 * 1
But the guy has everything greater than 1... so ignoring that there are exactly
9 factors.
and 5 is 3 times.
so Answer is D.
Answer: (D) 3
Question: Three unbiased coins are tossed. What is the probability of getting all tails?
(A) 7/8
(B) 1/2
(C) 3/8
(D) 1/4
(E) 1/8
Rationale: Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting two heads
Then E = {TTT}
P(E) = n(E)/n(S) =1/8
Answer: (E) 1/8
Question: The function f is defined for all the positive integers g by the following rule: f(g) is the number of positive integers each of which is less than g and has no positive factor in common with g other than 1 . if p is a prime number then f(p)?
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The moment you put a prime number in the function f(g), notice that all the numbers lesser than g have no divisor clashing with divisor of g since g is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: (A) p-1
Question: A can do a work in 3days. B can do in 6days. If both A&B are working together in how many days they can finish the work?
(A) 1
(B) 3
(C) 2
(D) 4
(E) 5
Rationale: 1day work of A = 1/3
1day work of B = 1/6
1day work of A&B = 1/3 + 1/6 = 1/2
A&B finish the work in 2days
Answer is C
Answer: (C) 2
Question: The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?
(A) 552 km
(B) 502 km
(C) 492 km
(D) 422 km
(E) 487 km
Rationale: Explanation:
Given that distance travelled in 1st hour = 35 km
and speed of the bus increases by 2 km after every one hour
Hence distance travelled in 2nd hour = 37 km
Hence distance travelled in 3rd hour = 39 km
..
Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term, a=35, number of terms,n = 12 and common difference, d=2.
The sequence a , (a + d), (a + 2d), (a + 3d), (a + 4d), . . .
is called an Arithmetic Progression(AP)
where a is the first term and d is the common difference of the AP
Sum of the first n terms of an Arithmetic Progression(AP),
Sn = n/2[2a+(n−1)d]
where n = number of terms
Hence, [35+37+39+... (12 terms)]
= S12 = 122[2 × 35 +(12 − 1)2]
= 6[70 + 22] = 6 × 92 = 552
Hence the total distance travelled = 552 km
Answer: Option A
Answer: (A) 552 km
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?
(A) 2 days
(B) 76 days
(C) 8 days
(D) 6 days
(E) 4 days
Rationale: 1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 * 6 = 2/3
Remaining work = 1 - 2/3 = 1/3
18 men's 1 day work = 1/108 * 18 = 1/6
1/6 work is done by them in 1 day.
1/3 work is done by them in 6 * 1/3 = 2 days.
Answer: A
Answer: (A) 2 days
Question: A train has a length of 150 meters . it is passing a man who is moving at 6 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
(A) 182 km/hr
(B) 180 km/hr
(C) 152 km/hr
(D) 186 km/hr
(E) 179 km/hr
Rationale: Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 6 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 6
=> Vt = 180 + 6 = 186 km/hr
Answer: Option D
Answer: (D) 186 km/hr
Question: Three friends A,B and C invested Rs. 40,000, Rs.60,000 and 80,000 respectively in a business. If the annual profit is Rs. 18000 then share of B is
(A) Rs. 5000
(B) Rs. 5400
(C) Rs. 5500
(D) Rs. 6000
(E) Rs. 7000
Rationale: the ratio of investment is 2:3:4 and sum of the investment ratio is 9
then the ratio of b is 3 then 3/9*18000=6000
so the share of B is rs.6000
ANSWER:D
Answer: (D) Rs. 6000
Question: What is the remainder when 220*165*110*55 is divided by 15?
(A) 12
(B) 15
(C) 10
(D) 11
(E) 18
Rationale: OA is 'C'.
OE:
take the remainder from each of 220/15, 165/15 and so on..
220/15 gives remainder = 10
165/15 gives remainder = 0
110/15 gives remainder = 5
55/15 gives remainder = 10
the net remainder is the product of above individual remainders. i.e = 10*0*5*10
break them into pairs 10*0/15 gives remainder 10
and 5*10/15 gives remainder 5
so 10*5/15 gives remainder 5.
Answer: C
Answer: (C) 10
Question: A train travels 325 km in 3.5 hours and 470 km in 4 hours. Find the average speed of train ?
(A) 116 kmph
(B) 106 kmph
(C) 186 kmph
(D) 126 kmph
(E) 176 kmph
Rationale: Explanation:
As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 325 + 470 = 795 km
Thus, Total Speed = 7.5 hrs
Average Speed = 795/7.5 => 106 kmph.
Answer: B
Answer: (B) 106 kmph
Question: A cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 4hours. If both the taps are opened simultaneously then after how much time will the cistern get filled?
(A) 2hr
(B) 5hr
(C) 7hr
(D) 1hr
(E) 4hr
Rationale: Net part filled in 1 hour 1/2 - 1/4 = 1/4
The cistern will be filled in 4 hr
Answer is E
Answer: (E) 4hr
Question: In a class of 25 students in an examination in maths 3 students scored 95 marks each, 5 get zero each and the average of the rest was 45. What is the average of the whole class?
(A) A)47
(B) B)45.6
(C) C)42
(D) D)48
(E) E)49
Rationale: Explanation:
Total marks obtained by a class of 25 students
= 3*95 + 5*0 + 17* 45 =1050
Average marks of whole class = 1050/25 =42
Answer: Option C
Answer: (C) C)42
Question: A restaurant meal cost $100 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
(A)  $100 and $110
(B)  $105 and $109
(C)  $109 and $116
(D)  $115 and $120
(E)  $111 and $115
Rationale: Hence it will be between 100 * (1+10/100) and 100 * (1+15/100).
i.e b/w 110 and 115. Hence the answer C (b/w 109 and 116).
Answer: (C)  $109 and $116
Question: Which of the following CANNOT be the median of the 3 positive integers x, y, and z?
(A) x
(B) z
(C) x+z
(D) (x+z)/2
(E) (x+z)/3
Rationale: The median of a set with odd number of terms is justa middle term, so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+z)/2 and (x+z)/3 (for example: {1, 2, 3} and {1, 2, 5}).
But since x, y, and z arepositiveintegers then it no way can be x+z. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and z) in a set with 3 terms.
Answer: C.
Answer: (C) x+z
Question: Which of the following points is closest to line y=x
(A) (2, -1)
(B) (2, 4)
(C) (-1, 1)
(D) (-2, -1)
(E) (-2, 0)
Rationale: Attachment:
m12-20.pngAs you can see point (-2, -1) is the closest to line y=x.
Answer: D.
Answer: (D) (-2, -1)
Question: A bag contains 6 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4
(B) 4/3
(C) 4/5
(D) 4/9
(E) 5/11
Rationale: Let number of balls = (6 + 5) = 11.
Number of white balls = 5.
P (drawing a white ball) = 5/11
Hence Answer is E
Answer: (E) 5/11
Question: Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $80.00 on four CDs and five tapes, how much does one tape cost?
(A) $5.00
(B) $6.25
(C) $12.00
(D) $8.00
(E) $100.00
Rationale: CD => C
Type => T
Carol: 4C+5T=80
Anna: 12C+5T=160
12C-4C=80
8C=80
C=10
4C+5T=80
40+5T=80
5T=40
T=8
Answer is D
Answer: (D) $8.00
Question: If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10?
(A) A.0
(B) B.1
(C) C.3
(D) D.4
(E) E.5
Rationale: 92p × 5p+w + 11w × 6pw--1=B
Answer: (B) B.1
Question: If the mean of numbers 28, x, 42, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?
(A) 78
(B) 58
(C) 390
(D) 310
(E) 66
Rationale: x is common to both the series. So, x is not going to make a difference to the average.
Only the remaining 4 numbers will contribute to the difference in average between the two series.
Sum of the 4 numbers, excluding x, of the first series is 28 + 42 + 78 + 104 = 252
Sum of the 4 numbers, excluding x, of the second series is 48 + 62 + 98 + 124 = 332
The difference between the sum of the two sets of numbers = 332 - 252 = 80
The sum of the second series is 80 more than the sum of the first series.
If the sum of the second series is 80 more, the average of the second series will be 80/5 = 16 more than the first series.
Therefore, the average of the second series = 62 + 16 = 78.
Answer A
Answer: (A) 78
Question: A certain tax rate is $.42 per $100.00. What is the rate, expressed as a percent?
(A) .42%
(B) 4.2%
(C) 0.82%
(D) 0.042%
(E) 0.0082%
Rationale: Here in question it is asking $.42 is what percent of $ 100.Suppose $ .42 is x% of 100 means
100* (x/100) = .42
Hence x = .82 %
So answer is A
Answer: (A) .42%
Question: if the ratio of two no. is 5:4.and addition of that no. is 36.then tell the bigger number.
(A) 15
(B) 20
(C) 18
(D) 12
(E) 24
Rationale: let the ratio constant be x,
5x+4x=36
9x=36
x=4
bigger number=20
answer B
Answer: (B) 20
Question: Of three numbers, the third is four times the second and the second is two times the first. If their average is 165, the second number of the three numbers is:
(A) 18
(B) 100
(C) 90
(D) 45
(E) 120
Rationale: Explanation:
Let first number be x.
So,2nd no. = 2x & 3rd no.=8x.
So,x+2x+8x=165 × 3 = 495
11x = 495/11
x = 495/11
Hence,first Number is x=45
so, second number is = 2 x 45=90
Answer: C
Answer: (C) 90
Question: The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice athe age of the son. Find the present age of the father.
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: Sol. Let the son’s present age be x years. Then, father’s present age = (3x + 3) years.
Therefore (3x + 3 + 3) = 2 (x + 3) + 10
‹=› 3x + 6 = 2x + 16 ‹=› x = 10
Hence, father’s present age = (3x + 3) = (3 x 10 + 3) years
= 33 years.
Answer A
Answer: (A) 33
Question: A sum of money at simple interest amounts to Rs. 815 in 4 years and to Rs. 854 in 5 years. The sum is:
(A) s. 650
(B) s. 659
(C) s. 698
(D) s. 700
(E) s. 720
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 4 years = Rs.(39 x 4) = Rs. 156.
Principal = Rs. (815 - 156) = Rs. 659.
Answer: Option B
Answer: (B) s. 659