mathewhe/aqua_rat huggingface dataset:
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 2/3 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
(A) 4/15
(B) 3/40
(C) 13/40
(D) 7/20
(E) 13/22
Rationale: P(1 and not 2)=2/3*(1-3/5)=4/15.
Answer: A.
Answer: (A) 4/15
Question: A little girl is numbering her collection of butterflies by placing single-digit stickers under each specimen. If the girl has 330 butterflies, how many stickers does she need? (The numbers are consecutive and the number of the first butterfly is 1).
(A) 882
(B) 901
(C) 1,001
(D) 1,003
(E) 1,346
Rationale: For the first 9 butterflies we need 9 stickers.
For the next 90 we need 2 stickers each or 180 stickers.
For the next 900 butterflies we need 3 stickers each.
The first 99 butterflies correspond to 189 stickers.
Subtract 99 from the total number of butterflies (330).
This leaves 231 butterflies that use 3 stickers each. So, multiply 231 by 3 to get 693.
Add 693 to 189 stickers to get 882 stickers.
Answer: A
Answer: (A) 882
Question: On a journey across Bombay, a tourist bus averages 10 km/h for 20% of the distance, 30 km/h for 60% of it and 20 km/h for the remainder. The average speed for the whole journey was
(A) 10 km/h
(B) 30 km/h
(C) 5 km/h
(D) 20 km/h
(E) None of these
Rationale: explanation
Let the average speed be x km/h.
and Total distance = y km. Then,
0.2⁄10y + 0.6⁄30y + 0.2⁄20y = y⁄x
⇒ x = 1⁄0.05 = 20 km/h
Answer D
Answer: (D) 20 km/h
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 24km/h, what is the circumference of the tire?
(A) 1 meters
(B) 9 meters
(C) 8 meters
(D) 5 meters
(E) 3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 24,000 m : C is the circumference
C = 1 meters
correct answer A
Answer: (A) 1 meters
Question: What is the remainder when 3^33 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}
33 has the form 4k+1, so the units digit of 3^33 is 3.
The remainder when dividing by 5 is 3.
The answer is D.
Answer: (D) 3
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
(A) difference=24
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
A
Answer: (A) difference=24
Question: A man in a train notices that he can count 21 telephone posts in one minute.If they are known to be 50 meters apart , then at what speed is the train travelling ?
(A) 55 km/hr
(B) 57 km/hr
(C) 60 km/hr
(D) 63 km/hr
(E) None of these
Rationale: Solution
Number of gaps between 21 telephone posts = 20.
Distance travelled in 1 minute =(50x20)m = 1000 m = 1 km.
∴ Speed = 60 km/hr.
Answer C
Answer: (C) 60 km/hr
Question: Prove the theorem, due to Kraitchik, asserting that 13|2^70+3^70
(A) 1^70+3^70 == 0 (mod 13), or 1|2^70+3^70
(B) 2
(C) 1
(D) 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70
(E) 1
Rationale: By Fermat's theorem we have 2^12 == 1 (mod 13), hence 2^60 == 1 (mod 13), and since 2^5 == 6 (mod 13), which implies 2^10 == -3 (mod 13), we get 2^70 == -3 (mod 13). On the other hand, 3^3 == 1 (mod 13), hence 3^69 == 1 (mod 13) and 3^70 == 3 (mod 13). Therefore 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70, which was to be proved.
So Answer is D 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70
Answer: (D) 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70
Question: If selling price is doubled, the profit triples. Find the profit percent
(A) 128%
(B) 100%
(C) 126%
(D) 276%
(E) 262%
Rationale: Explanation:
Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%
.Answer:B
Answer: (B) 100%
Question: 10 one question was x*y^2*z<0 then
(A) x<0
(B) xyz<0
(C) xz<0
(D) xy<0
(E) None of these
Rationale: if we take y^2 then it will always greater than zero so only one option z left i.e. xz
ANSWER:C
Answer: (C) xz<0
Question: How long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length?
(A) 82.5
(B) 27
(C) 55
(D) 18
(E) 12
Rationale: T = (660 + 165)/36 * 18/5
T = 82.5
Answer: A
Answer: (A) 82.5
Question: Which of the following is an irrational numbers?
(A) √16
(B) √25
(C) √45
(D) √64
(E) √100
Rationale: Clearly √45 is an irrational number. Ans : C
Answer: (C) √45
Question: A bakery opened yesterday with its daily supply of 50 dozen rolls. Half of the rolls were sold by noon, and 84 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
(A)  5
(B)  4
(C)  3
(D)  2
(E)  1
Rationale: answer is B ...4 dozens ....
half sold by noon --> 25 dozens (25 *12 =300)
remaining --> 25 dozens i.e 300 eggs...
84% sold --> 84*300/100 =252 eggs
remaining 16% --> 48 eggs (4 dozens ) --> answer
Answer: (B)  4
Question: A certain fruit stand sold apples for $0.70 each and cherry for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
(A) 12
(B) 11
(C) 13
(D) 14
(E) 15
Rationale: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.
63 is a direct multiple of 7, however in this case there won't be any cherry. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7
B
Answer: (B) 11
Question: Three flats of the same type were advertised to be let in a housing complex. Three men made separate applications for a flat. What is the probability that each of them applied for the same house.
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/3
(E) 1/9
Rationale: Since each of the flat has same probability of getting selected so for each men proability of selecting a flat out of 3 flats
Let us consider case where all 3 men choose flat no 1
So for First men it will be 1/3,second men 1/3 and third men also 1/3
So probability of selecting flat no 1 is 1/3*1/3*1/3= 1/27
And since there are 3 such flats so probability that each men select the same flat is 3*1/27 or 1/9
Ans is D
Answer: (D) 1/3
Question: In one hour a boat goes 13 km long the stream and 9 km against the stream.The speed of the boat in still water is?
(A) 17
(B) 18
(C) 16
(D) 15
(E) 11
Rationale: Speed in still water A = ½ ( 13+9) km/hr A= 11 kmph
Answer: E
Answer: (E) 11
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?
(A) 108 sq.cm
(B) 112 sq.cm
(C) 116 sq.cm
(D) 120 sq.cm
(E) 122 sq.cm
Rationale: Explanation:
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm
ANSWER IS D
Answer: (D) 120 sq.cm
Question: Today is Thursday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
(A) SUNDAY
(B) MONDAY
(C) TUESDAY
(D) WEDNESDAY
(E) FRIDAY
Rationale: Today is Thursday
after three days--->Sunday
now, (sunday)after before day--->saturday
then, (saturday)day after tomorrow--->monday
ANSWER:B
Answer: (B) MONDAY
Question: Mapy bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
(A) $10
(B) $11
(C) $12
(D) $13
(E) $14
Rationale: From the given information,we can conclude that Mapy bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Answer: (B) $11
Question: Students are asked to create a record of the recital of a poem for English class in groups of three. The tape length should be 1,200 seconds. The students assigned different stanzas of the poem to each member, and the individual records were compiled. If member three took 3 times longer than member two, and member two took equal time as member one, how many seconds did member three record for his/her reading?
(A) 720
(B) 240
(C) 1200
(D) 40
(E) 500
Rationale: member one, two and three as m1, m2 and m3 respectively.
m2=m1 as eq.a
m3=m2*3 as eq.b
m3+m2+m1=1,200 as eq.c
Substitute eq.b into eq. c, making (m2*3) + m2+ m2=1,200
(m2*5)/5=1,200/5 reduces to m2=240 seconds.
m3 is then m2*3, which is 720 seconds.
Answer is A.
Answer: (A) 720
Question: What is the missing number in this series?
8 2 14 6 11 ? 14 6 18 12
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: by taking pairs (8,2),(14,6),(11,?),(14,6),(18,16)
the difference of pairs follow the sequence like 6,8,?,8,6...
therefore the pair is (11,5) which makes the difference 6
ANSWER:E
Answer: (E) 5
Question: There are 7 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
(A) 15
(B) 16
(C) 28
(D) 42
(E) 64
Rationale: Every team plays with 6 teams...so total no of matches = 7 x 6 = 42.
Now, each match is played twice => 42 x 2
But 2 teams play a match => 42 x 2 /2 = 42.
Answer: D
Answer: (D) 42
Question: The percentage increase in the area of rectangle , if each of its side is increased by 10% is?
(A) 21%
(B) 30%
(C) 25%
(D) 40%
(E) 50%
Rationale: Let original length = x meters
original breadth = y meters
original area = xy m^2
New length = 110x/100
New breadth = 110y/100 = 11y/10
New area = 11x/10 * 11y/10 = 121xy/100 m^2
Increase percent = 21xy/100 * 1/xy *100 = 21%
Answer is A
Answer: (A) 21%
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
(A) 38
(B) 37
(C) 22
(D) 69
(E) 21
Rationale: Let the ten's digit be x and unit's digit by y
Then, x + y = 15 and x - y = 3 or y - x = 3
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9
So, the number is either 96 or 69.
Hence, the number cannot be determined.
Answer: D
Answer: (D) 69
Question: If 50% of (x-y) = 30% of (x+y), then what percent of x is y?
(A) 20%
(B) 30%
(C) 25%
(D) 15%
(E) 50%
Rationale: 50% of (x-y) = 30% of (x+y)
50/100 (x-y) = 30/100 (x+y)
x = 4y
Required percentage = y/x *100 = y/4y * 100 = 25%
Answer is C
Answer: (C) 25%
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
(A) 22
(B) 02
(C) 78
(D) 50
(E) 18
Rationale: 5 * 46 – 4 * 45 = 50
Answer: D
Answer: (D) 50
Question: The difference between two numbers 1365.When the larger
number is divided by the smaller one the quotient is 6 and
the remainder is 15.The smaller number is?
(A) 270
(B) 170
(C) 230
(D) 130
(E) 420
Rationale: Let the smaller number be x, then larger number =1365+x
Therefore 1365+x=6x+15
5x=1350 => x=270
Required number is 270.
ANSWER A 270
Answer: (A) 270
Question: Find the perimeter and area of a square of side 11 cm.
(A) 11 cm²
(B) 81 cm²
(C) 121cm²
(D) 144 cm²
(E) 151 cm²
Rationale: We know that the perimeter of square = 4 × side
Side= 11 cm
Therefore, perimeter = 4 × 11 cm = 44 cm
Now, area of the square = (side × side) sq. units
= 11 × 11 cm²
= 121 cm²
ANSWER : C
Answer: (C) 121cm²
Question: Tim and Stacy need to select seats in a row of chairs that are numbered in order from 1 to 5. If Tim cannot sit in an even-numbered seat and Stacy cannot sit in an odd-numbered seat, how many arrangements are possible if the two cannot sit adjacent to each other and Tim and Stacy are the only people to be seated?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 20
Rationale: The total number if there is no restriction is = 2X3= 6
and if both are sitting together, the combination is = 2X2= 4
So, the way they can not sit together is 6-4=2
ANSWER:B
Answer: (B) 2
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 36 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
(A)  16%
(B)  32%
(C)  68%
(D)  84%
(E)  92%
Rationale: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 36% is one st.Dev, then on either side of m we have 36/2 = 18%. So,18% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 18= 68% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 68% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
C
Answer: (C)  68%
Question: A can do a certain job in 14 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
(A) 7 1/2 days
(B) 8 3/4 days
(C) 5 days
(D) 9 days
(E) None of them
Rationale: Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 14 : x = 8x = 5 x 14 =x = 8 3/4 days.
Answer is B.
Answer: (B) 8 3/4 days
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross-section is 630 square meters, what is the depth of the channel (in meters)?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 1/2 * d * (12 + 6) = 630
d = 70
The answer is C.
Answer: (C) 70
Question: Set J consists of 18 consecutive even numbers. If the smallest term in the set is -12, what is the range of the positive integers in set J?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Since there are only 18 integers, another approach is the just list all 18.
We get:-12, -10, -8, -6, -4, -2,0,2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Range of POSITIVE INTEGERS =22 - 2= 20
Answer: C
Answer: (C) 20
Question: In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 20 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?
(A) 2%
(B) 5%
(C) 8%
(D) 10%
(E) 12%
Rationale: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 30:20 represents the number ratio of Republicans:Democrats. If 80% of Republicans (which is (60*0.8) = 48) and 20% of Democrats (40*0.2 = 8) voted for candidate X, means that out of total of 100 voters; 56 (48 + 8) voters voted for candidate X and 44 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 12 (56-44) votes. Therefore candidate X is expected to win the election by (12/100) votes which is equivalent to 12%.
I think the answer is E.
Answer: (E) 12%
Question: The variables a and b are non-zero integers Q. If a = 2b^3/c, what happens to c when a is halved and b is doubled?
(A) c is not changed.
(B) c is halved.
(C) c is doubled.
(D) c is multiplied by 4.
(E) c is multiplied by 16.
Rationale: a=2b^3/c
c=2b^3/a
when a is halved and b is doubled
c=2(2b)^3/(a/2)
c=16*2b^3/a
Ans. E c is multiplied by 16.
Answer: (E) c is multiplied by 16.
Question: Abbey has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
(A)  32
(B)  30
(C)  29
(D)  28
(E)  27
Rationale: 5c + 10d= 460
c > d
Pick an easy number to work with.
suppose c=30.
Then you have 150.
You need another 310 and that means you need d=31 which is greater than c.
Therefore, c > 30.
The only answer choice where c > 30 is if c = 32.
A is the answer.
Answer: (A)  32
Question: In the xy-coordinate system, what is the slope of the line that goes through the point (1, 1) and is equidistant from the two points P = (3, 7) and Q = (9, 11)?
(A) 0.5
(B) 0.625
(C) 0.75
(D) 0.875
(E) 1.0
Rationale: First, get the middle coordinate between (3,7) and (9,11)...
x = 3 + (9-3)/2 = 6
y = 7 + (11-7)/2 = 9
Second, get the slope of (9,6) and (1,1). m = 6-1 / 9-1 = 5/8 = 0.625
Answer: B
Answer: (B) 0.625
Question: A man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 2 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 4
Rationale: When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 2*15/60 =1/2 miles and the man walks the distance mM, which is 2*5/60 = 1/6 mile.
The difference of 1/2 - 1/6 =1/3 miles (MW) will be covered by the man in (1/3)/5 = 1/15 of an hour, which is 4 minutes.
Answer E.
Answer: (E) 4
Question: A tank has a capacity of 20 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find how much spirit is left in the resulting mixture finally?
(A) 6(257/525) gallons
(B) 20(346/625) gallons
(C) 6.5 gallons
(D) 6.25 gallons
(E) None of these
Rationale: There is a direct formula to calculate such repetition:
Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:
Left QTY / 20 = (20 -4)^5 / 20^5
Left QTY = 20 (16/20)^5
Left QTY = 20 ( 4/5 )^5
Left QTY = 20(346/625)
Answer is B
Answer: (B) 20(346/625) gallons
Question: A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
Rationale: {total} = {M} + {S} + {R} - {Both} + {Neither}
We want to maximize Neither, so Both has to be as large as possible. The max of {Both} is 5 because {R} = 5.
30 = 8 + 12 + 5 - 5 + Neither
Neither = 10
ANSWER:D
Answer: (D) 10
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 78 minutes. The waste pipe can empty the full cistern in?
(A) 8 min
(B) 7 min
(C) 5 min
(D) 9 min
(E) 6.5 min
Rationale: 1/10 + 1/15 - 1/x
= 1/78
x = 6.5
Answer:E
Answer: (E) 6.5 min
Question: N and M are each 3-digit integers. Each of the numbers 2, 3,4,5, 6, and 7 is a digit of either N or M. What is the smallest possible positive difference between N and M?
(A) 59
(B) 49
(C) 58
(D) 113
(E) 131
Rationale: You have 6 digits: 2, 3, 4, 5, 6, 7
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 2 and 7 in the hundreds places and reserve them for the tens places . Now what are the options?
Try and make a pair with (3** and 4**). Make the 3** number as large as possible and make the 4** number as small as possible.
376 and 425 (difference is 49) or
Try and make a pair with (5** and 6**). Make the 5** number as large as possible and make the 6** number as small as possible. We get 574 and 623 (difference is 49)
B
Answer: (B) 49
Question: A department of eleven people - five men and six women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?
(A) 250
(B) 270
(C) 300
(D) 320
(E) 350
Rationale: They can make a team of 3 men and 2 women.
The number of ways to do this is 5C3*6C2=10*15 = 150
They can make a team of 2 men and 3 women.
The number of ways to do this is 5C2*6C3=10*20 = 200
The total number of distinct groups is 350.
The answer is E.
Answer: (E) 350
Question: A baseball team won 45 percent of the first 80 games it played. How many of the remaining 85 games will the team have to win in order to have won exactly 40 percent of all the games it played?
(A) 30
(B) 45
(C) 50
(D) 55
(E) 81
Rationale: Games won out of first 80 questions = (45/100)*80 = 36
Total Games = 80+85 = 165
Games to be won = (40/100)*165 = 66
Remaining games to be won = 66-36 = 30
Answer: Option A
Answer: (A) 30
Question: A person decided to build a house in 100 days. He employed 100 men in the beginning and 100 more after 20 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
(A) 40
(B) 80
(C) 70
(D) 60
(E) 50
Rationale: 200 men do the rest of the work in 100-40 = 60 days
100 men can do the rest of the work in 60*200/100 = 120 days
Required number of days = 120-60 = 60 days
Answer is D
Answer: (D) 60
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6936, how much amount did Raghu invest ?
(A) 1287
(B) 2887
(C) 2000
(D) 1129
(E) 2400
Rationale: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 6936
= x= 6936/2.89 = 2000
Therefore, amount invested by Raghu is Rs. 2400.
Answer: E
Answer: (E) 2400
Question: The CI on a certain sum for 2yrs at 10 percent/annum is Rs. 525. The SI on the same sum for double the time at 1/2 the rate % per annum is:
(A) Rs. 100
(B) Rs. 300
(C) Rs. 400
(D) Rs. 500
(E) Rs. 550
Rationale: Let the sum be Rs. P.
Then, P 1 +	10 2	- P = 525
100
P 11 2	- 1 = 525
10
P = 525 x 100 = 2500.
21
Sum = Rs . 2500.
So, S.I. = Rs. 2500 x 5 x 4 = Rs. 500
100
D
Answer: (D) Rs. 500
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.9
(B) 4.6
(C) 4.1
(D) 4.2
(E) 4.3
Rationale: Explanation:
Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
Answer: B
Answer: (B) 4.6
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 18. Find the sum :
(A) 4500
(B) 7500
(C) 5000
(D) 7200
(E) None of these
Rationale: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2100=10100×5×2100=10
and CI = 100(1+5100)2−100100(1+5100)2−100
∴ =100×21×2120×20−100=414=100×21×2120×20−100=414
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 18, the sum
= 400 × 18 = 7200 Answer D
Answer: (D) 7200