mathewhe/aqua_rat huggingface dataset:
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2240 less than the principal. What was the principal?
(A) 1500
(B) 2500
(C) 2507
(D) 2800
(E) 11500
Rationale: P - 2240 = (P*5*4)/100
P = 2800
Answer: D
Answer: (D) 2800
Question: Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 50 years. The age of E is?
(A) 50
(B) 47
(C) 48
(D) 49
(E) 46
Rationale: Solution
5 years ago average age of A,B,C,D = 45 years
=> 5 years ago total age of A, B, C, D = 45 x 4 = 180 years
=> Total present age of A, B, C, D = 180 + 5x4 = 200 years
If E's present age is x years = 200+x/5= 50
x=50 years. Answer A
Answer: (A) 50
Question: A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio E of students per class?
(A) E=3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Another way to look at the problem...
Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)
we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)
(ii)-(i)....
C=10R+10 = 10(R+1).......
so # of classes has to be multiple of 10
AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..
so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3
A
Answer: (A) E=3
Question: A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a women alone in 18 days, how long will a boy take to complete the work?
(A) 6days
(B) 8days
(C) 9days
(D) 7days
(E) 5days
Rationale: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3
1 man’s 1 day work = 1/6
1womans 1 day’s work = 1/18
(1 Man + 1 woman) ‘s 1 day’s work = 1/6 + 1/18 = 2/9
Therefore, 1 boys 1 day’s work = 1/3 – 2/9 = 3-2/9 = 1/9
Therefore, the boy alone can finish the work in 9 days.
Answer: Option C
Answer: (C) 9days
Question: If n is an integer and 5^n > 50,000,000, what is the least possible value of n?
(A) 12
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: When you seperate the 50000000 into factors of 5 and 2 you get - > 10^7 x 5^1 = 5^8 x 2^7
2 to the ^ 7 = 128 so its 128 x 5^8
that means 5^8 x 5^x must be greater
5^x > 128
5^1=5
5^2=25
5^4= 625
- > so x must be at least 4
5^(8+4)= 5^12
A
Answer: (A) 12
Question: If a coin is tossed twice, what is the probability that the coin lands on tails on both tosses?
(A) 1/6
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1
Rationale: P(2 tails) = 1/2*1/2=1/4
The answer is C.
Answer: (C) 1/4
Question: The price of a certain painting increased by 20% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
(A) 102%
(B) 105%
(C) 120%
(D) 135%
(E) 140%
Rationale: Assume that price is 100
Price at the end of yr 1: 100+ 20 = 120
Price at the end of year 2 = 120 - 120*0.15 = 120*0.85 = 102
Hence required answer = (102/100)*100% = 102%
Answer is A.
Answer: (A) 102%
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 55 km more than the other. What is the distance between the two stations?
(A) 540 km
(B) 495 km
(C) 276 km
(D) 178 km
(E) 176 km
Rationale: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 55 km more than the other,
25x â€“ 20x = 55
5x = 55
x = 11hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*11 = 495 km.
ANSWER: B
Answer: (B) 495 km
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 80 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
(A) 79
(B) 89
(C) 95
(D) 90.91
(E) 97.2
Rationale: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 80*5 = 400
Student's average = (600+400)/11 = 90.91
Answer D
Answer: (D) 90.91
Question: A single refined oil can contains 20% impurities. After double – refining it contains 4% impurities. How much of double- refined oil can be obtained from 30 litres of single refined oil?
(A) 24.0 litres
(B) 24.8 litres
(C) 25.0 litres
(D) 25.5 litres
(E) 35.0 litres
Rationale: Exp. On double- refining impurity decreases from 20% to 4%., but the
amount of pure oil in both cases remains constant,
i.e, 96% of double refined oil = 80% of single refined oil.
Let x be the quantity of double-refined oil
Then 96*x/100 = 80*30/100, x = 30*80 /96 = 25
Answer:C
Answer: (C) 25.0 litres
Question: In 2005, 20 percent of the math department’s 45 students were female, and in 2007, 40 percent of the math department’s 705 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
(A) 85%
(B) 130%
(C) 211.1%
(D) 220%
(E) 260%
Rationale: Female students in 2005 = 20% of 45 = 9
Female students in 2007 = 40% of 70 = 28
Percentage increase = [(28 - 9)/9] *100 % = 211.1%
Correct Option: C
Answer: (C) 211.1%
Question: Find the average of the series : 130, 160, 328, 180 and 162?
(A) 186
(B) 196
(C) 190
(D) 198
(E) 192
Rationale: Average = (130 + 160 + 328 + 180 + 162)/5
= 960/5
= 192
Answer: E
Answer: (E) 192
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a red and the second card is black is?
(A) 1/4
(B) 1/52
(C) 1/26
(D) 1/13
(E) 1/169
Rationale: Probability of a queen = 4/52 = 1/2
Probability of a red card = 26/52 = 1/2
Probability of both = P1*P2 = 1/(2*2) = 1/4
Answer is A.
Answer: (A) 1/4
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 4%
(B) 5%
(C) 2%
(D) 9%
(E) 1%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R =5%
Answer:B
Answer: (B) 5%
Question: If 0 < a < b and k = (2a + b)/b , which of the following must be true?
(A) k < 3
(B) k < 7
(C) k < 9
(D) k > 9
(E) k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a<b, you get k = (2+2)/2 = 2. This eliminates all but option A , making it the correct answer.
Answer: (A) k < 3
Question: A box contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 25/36. How many marbles are in the bag?
(A) 24
(B) 48
(C) 60
(D) 72
(E) 84
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 25/36
-->(x-12)^2= 25/36
x^2
square rooting u have x-12/x = 5/6 or x = 72
E
Answer: (E) 84
Question: Platinum is 19 times as heavy as bronze and silver is 9 times as heavy as bronze. In what ratio these two metals be mixed so that the alloy is 15 times as heavy as bronze is
(A) 2:1
(B) 3:2
(C) 1:2
(D) 2:3
(E) 3:4
Rationale: Let the proportion of weight of platinum in the mixture = x
then the proportion of weight of silver in the mixture = 1 - x
According to the question
19 X x + 9 (1 - x) = 15 X 1
19x + 9 - 9x = 15
10x = 15 - 9 = 6
x = 6/10 = 3/5
Therefore the proportion of weight of platinum in the mixture = x = 3/5
and the proportion of weight of silver in the mixture = 1 - x = 1 - 3/5 = 2/5
The required ratio of platinum : silver = 3/5 : 2/5
= 3 : 2
ANSWER:B
Answer: (B) 3:2
Question: Chauncy, an English bulldog, received 1200 votes in the Mr. Bulldog USA competition, giving him approximately 30 percent of the vote. Approximately what percent of the remaining votes would he have needed to receive in order to win 70 percent of the total votes?
(A) 56.14%
(B) 57.14%
(C) 58.14%
(D) 59.14%
(E) 60.14%
Rationale: let the total vote is x.then 30% of x=(30/100)*x=1200,
or,x=(1200*100)/30;
or,x=4000;
now, 30% of votes already given...so other 70% of x votes=(70/100) *4000=2800 votes. now other needed votes=(70-30)%=40% votes. so 40% votes of x=(40/100)*4000=1600; now he have needed only % of votes=(100*1600)/2800=160000/2800;=57.14285714%
ANSWER:B
Answer: (B) 57.14%
Question: Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
(A) 33277
(B) 6888
(C) 6000
(D) 2777
(E) 27812
Rationale: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
Answer: C
Answer: (C) 6000
Question: The sum of three numbers is 98. If the ratio of the first to second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is
(A) 33
(B) 28
(C) 30
(D) 88
(E) 287
Rationale: Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 ==
A : B : C = 2 : 3 : = 10 : 15 : 24
B = = 30
Answer: C) 30
Answer: (C) 30
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 11 a.m.
(B) 10 a.m.
(C) 12 a.m.
(D) 9 a.m.
(E) 8 a.m.
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: Option B
Answer: (B) 10 a.m.
Question: 80 ? 860 1550 2440 3530
(A) 370
(B) 840
(C) 750
(D) 860
(E) 960
Rationale: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530.
ANSWER:A
Answer: (A) 370
Question: If each number in the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is used exactly once, in how many ways can the numbers be arranged?
(A) 3,228,400
(B) 3,328,500
(C) 3,428,600
(D) 3,528,700
(E) 3,628,800
Rationale: 10! = 3,628,800
The answer is E.
Answer: (E) 3,628,800
Question: Tom can hit a target 3times in 6 shots, Karan can hit the target 2 times in 6shots & Ashwini can hit 4 times in 4 shots.What is the probability that at least 2 shots hit the target ?
(A) 1/2
(B) 2/5
(C) 2/3
(D) 2/7
(E) 3/7
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: (C) 2/3
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/2 and |b| = 2/3, which of the following CANNOT be the result of a + b?
(A) 7/6
(B) -1/6
(C) 1/6
(D) 2/6
(E) -7/6
Rationale: |a| = 1/2
Absolute value of 'a' can have two values = 1/2 and -(1/2)
|b| = 2/3
Absolute value of 'b' can have two values = 2/3 and -(2/3)
Now different combinations of a + b are as follows:
a + b = (1/2) + (2/3) = 7/6
- a - b = -(1/2) - (2/3) = -7/6
a - b = (1/2) - (2/3) = -(1/6)
-a + b = -(1/2) + (2/3) = 1/6
Cross verifying with the given options, left over option is D.
Answer: (D) 2/6
Question: The sale price watches listed for Rs.4500 after successive discount is 10% and 20% is?
(A) 3240
(B) 3420
(C) 4320
(D) 4230
(E) 3140
Rationale: 4500*(90/100)*(80/100)
= 342
Answer: A
Answer: (A) 3240
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
(A) 20 years
(B) 21 years
(C) 22 years
(D) 23 years
(E) 24 years
Rationale: Let present age of the son =x years
Then, present age the man =(x+24) years
Given that, in 2 years, man's age will be twice the age of his son
=(x+24)+2=2(x+2)
=x=22
Answer: Option C
Answer: (C) 22 years
Question: A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 15
(B) 61
(C) 21
(D) 14
(E) 12
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [385 * 3/55] sec = 21 sec
Answer: C
Answer: (C) 21
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 12 minutes
(B) 18 minutes
(C) 10 minutes
(D) 15 minutes
(E) 42 minutes
Rationale: Part filled by A in 1 min. = 1/20
Part filled by B in 1 min. = 1/30
part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.
Both the pipes can fill the tank in 12 minutes.
Answer:A
Answer: (A) 12 minutes
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287 m
(B) 350 m
(C) 187 m
(D) 197 m
(E) 186 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x
= 350 m.
Answer: B
Answer: (B) 350 m
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 20%
(B) 45%
(C) 44%
(D) 48%
(E) 49%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
ANSWER:C
Answer: (C) 44%
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2700 sq m, then what is the breadth of the rectangular plot?
(A) 11
(B) 17
(C) 18
(D) 101
(E) 30
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 2700
3b2 = 2700
b2 = 900 = 30 (b > 0)
b = 30 m.
Answer: E
Answer: (E) 30
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 227
(B) 350
(C) 771
(D) 176
(E) 125
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B
Answer: (B) 350
Question: 10% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 6514, how much was it in the beginning?
(A) 8545
(B) 8770
(C) 8515
(D) 7999
(E) 7989
Rationale: X * (90/100) * (85/100) = 6514
X = 8515
Answer: C
Answer: (C) 8515
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999 ?
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) None of these
Rationale: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(15000x2/6) = Rs. 50,000. Answer B
Answer: (B) Rs.50,000
Question: If a > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - a) =
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4
(E) 1
Rationale: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have a-x=2t. So y-x=-t, y-a=-3t. ---> (y - x)/(y - a) = 1/3.
The answer is (B).
Answer: (B) 1/3
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 10 to produce 60 units?
(A) 9
(B) 10
(C) 15
(D) 25
(E) 30
Rationale: 5 machines would produce 60 units in 30 hours. Increasing the amount of machines by 2 would mean dividing 30 hours by 2.
30/2 = 15
Answer : C
Answer: (C) 15
Question: Sami's investment portfolio consists of three stocks: an airline, a bank, and a computer company. In the month of February, the price of the airline's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 15%, but the overall value of her portfolio increased. If Sami owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order airline, bank, and computer company respectively?
(A) $55, $85, $40
(B) $60, $60, $60
(C) $65, $55, $90
(D) none of these
(E) $25, $60, $70
Rationale: Since Sami owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased.
Answer is D.
Answer: (D) none of these
Question: What is the total surface area in square meters of a rectangular solid whose length is 8 meters, width is 7 meters, and depth is 4 meters?
(A) 132 m2
(B) 145 m2
(C) 165 m2
(D) 152 m2
(E) 120 m2
Rationale: Surface Area of a cuboid = 2(lb+bh+lh) = 2(8*7+7*4+8*4)=2(56+28+32)=2*116=132 m2
Answer : A
Answer: (A) 132 m2
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 828
(B) 788
(C) 378
(D) 750
(E) 288
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min.
= 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60
= 25 è x = 25 * 60 / 2
= 750
Answer: D
Answer: (D) 750
Question: Find the number of numbers from 1 to 100 which are not divisible by any one of 2,3,5,7.
(A) 16
(B) 17
(C) 18
(D) 19
(E) 21
Rationale: All Prime Numbers between 1 to 100 - (4)= 25-4
=> 21
ANSWER:E
Answer: (E) 21
Question: B and C started a business by investing Rs.3300/- and Rs.8800/- respectively. Find the C’s share out of a total profit of Rs.2200:
(A) 500
(B) 600
(C) 700
(D) 800
(E) 900
Rationale: B = Rs.3300/-
C = Rs.8800/-
B share 3 parts & C share 8 parts
Total 11 parts -----> Rs.2200/-
----> 1 part -------> Rs.200/-
C share = 3 parts -----> Rs.600/-
B
Answer: (B) 600
Question: On dividing 23 by a number, the quotient is 5 and the remainder is 3. Find the divisor.
(A) 1
(B) 2
(C) 4
(D) 6
(E) 7
Rationale: d = (D-R)/Q
= (23 - 3)/5
= 20/5 = 4
C
Answer: (C) 4
Question: There are 160 horses and 340 sheep on a certain farm. If 20% of the horses and 35% of the sheep are eight years old or older, what percent of the horses and sheep on the farm are under the age of eight?
(A) 15.6%
(B) 30.2%
(C) 55%
(D) 56%
(E) 69.8%
Rationale: 2 horses are eight years or older, thus 128 are younger.
119 sheeps are eight years or older, thus 221 are younger.
Total sheeps and horses younger than eight: 349
Total sheeps and horses 500.
349/500 is very close to 350/500 which is 70%. Considering the error chose E.
Answer E.
Answer: (E) 69.8%
Question: If a + b - c =-2d, and if a - b + c = 2e, then a =
(A) 2(d + e)
(B) d – e
(C) (d + e)/2
(D) d-2e
(E) e-d
Rationale: Add both equations:
a + b - c =-2d
a - b + c = 2e
a+b-c+a-b+c=-2d+2e
2a=2e-2d
a=e-d
Ans:E
Answer: (E) e-d
Question: How many integers between 324,700 and 387,600 have tens digit 1 and units digit 3?
(A) 438
(B) 629
(C) 780
(D) 879
(E) 924
Rationale: The integers are:
324,713
324,813
etc...
387,513
The number of integers is 3876 - 3247 = 629
The answer is B.
Answer: (B) 629
Question: A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 126 Kmph
(B) 136 Kmph
(C) 172 Kmph
(D) 128 Kmph
(E) 19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 700/20
S = 35 M/Sec
Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 126 Kmph
Answer: A
Answer: (A) 126 Kmph
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 9, what is the least possible value of n?
(A) 7
(B) 6
(C) 9
(D) 12
(E) 7
Rationale: We need at least 2 factors of three, which means n must be at least 6, so B is the correct answer.
Answer: (B) 6
Question: 16 +17+18+19=70. How many such 4 consecutive numbers are there less than 1000 when added gives a sum which is divisible by 10?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: since 1+2+3+4=10 & 6+7+8+9=30
any combination with these no be will give u desirable result...
so total no in 100 will be 20 & that's why in in 1000,it will be 200
ANSWER:B
Answer: (B) 200
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 23.5
(B) 24.5
(C) 12.5
(D) 14.5
(E) 16.5
Rationale: Explanation:
If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Answer: Option B
Answer: (B) 24.5
Question: Find the number of factors Q of 180 that are in the form (4*k + 2), where k is a non-negative integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) Q=6
Rationale: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 Q (=2^2*3^2*5) = 18. So listing the factors gives us:
1, 180
2, 90
3, 60
4, 45
5, 36
6, 30
9, 20
10, 18
12, 15
As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with
2,4,6,10,12,18,20,30,36,60,90,180
For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.
For checking any particular factor whether they conform to the form 4k+2---> do the following
4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.
E is thus the correct answer.
Answer: (E) Q=6
Question: Find the reminder when 333666777888999 divided by 3 or 9 or 11
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: the sum of the digits is 3+3+3+6+6+6+7+7+7+8+8+8+9+9+9=99, which is a multiple of 3 & 9, hence divisible by 3 & 9. hence the remainder is 0.
the difference of the sum of even place digits and odd place digits is (3+3+6+7+7+8+9+9)-(3+6+6+7+8+8+9)=5. hence not divisible by 11. so, the remainder is the difference, which is 5.
ANSWER:D
Answer: (D) 5
Question: Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 192 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 4
(D) Cannot be determined
(E) None of these
Rationale: Let rate = R% and time = R years.
Then,1200 x R x R/100= 192
12R2 = 192
R2 = 16
R = 4.
Answer:C
Answer: (C) 4
Question: Sandy had $217 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?
(A) $270
(B) $290
(C) $310
(D) $330
(E) $350
Rationale: Let the money Sandy took for shopping be x.
0.7x = 217
x = 310
The answer is C.
Answer: (C) $310
Question: Peeta asks Katniss, 'It is 12 pm as per my watch right now.Do you know what will be the time 23, 999, 996 hours later?'
Katniss knows the answer. Do you ?
(A) 9am
(B) 6pm
(C) 4am
(D) 7am
(E) 8pm
Rationale: A
9pm
The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: (A) 9am