mathewhe/aqua_rat huggingface dataset:
Question: How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits?
(A)  48
(B)  52
(C)  66
(D)  68
(E)  84
Rationale: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
2 5 5
Number of possibilities = 3*4*4 = 48.
Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52.
Answer: B
Answer: (B)  52
Question: 70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 25.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
(A) one
(B) two
(C) three
(D) four
(E) five
Rationale: The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-25,4=74,6. There are only two numbers below 74,6. The answer is B
Answer: (B) two
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 2 employees to 3 different offices?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans. Each employee can go into any of the two offices. Thus we have
=> 3 * 3 = 9
Answer : E
Answer: (E) 9
Question: Simplify the following 515*515*515-221*221*221/(515*515+515*221+221*221)
(A) 294
(B) 394
(C) 284
(D) 274
(E) 264
Rationale: 515*515*515-221*221*221/(515*515+515*221*221+221)
=[(515)^3 - (221)^3 ] / [(515)^2 + 515*221 + (221)^2]
if x = 515 & y = 221 then exp is
(x^3 - y^3)/(x^2 + xy + y^2) which is equal to (x-y)
(x^3 - y^3)/(x^2 + xy + y^2)=(x-y)
[(515)^3 - (221)^3 ] / [(515)^2 + 515*221 + (221)^2] = (515-221)= 294
ANSWER:A
Answer: (A) 294
Question: f1 (x) = x 0 ≤ x ≤ 1
= 1 x ≥ 1
= 0 otherwise
f2 (x) = f1(–x) for all x
f3 (x) = –f2(x) for all x
f4 (x) = f3(–x) for all x
How many of the following products are necessarily zero for every x:
f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Explanation :
We have to consider positive and negative numbers for all the cases.
f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)
f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)
f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)
f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)
So, we see that, out of the 3 products in the question, f1(x)*f2(x) and f2(x)*f4(x) are always zero, for any x.
Answer : C
Answer: (C) 2
Question: If the simple interest on a certain sum of money for 6 years is one–fifth of the sum, then the rate of interest per annum is
(A) 3.3%
(B) 7.2%
(C) 6.1%
(D) 5.0%
(E) 3.1%
Rationale: Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 6 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 6) = 20/6 = 3.3%
Answer: Option A
Answer: (A) 3.3%
Question: The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 50% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 25% less than the number there from 10 a.m. to 11 a.m. If 75 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: No of people from 10 - 11 is x
No of people from 11 - 12 is 3x/4
No of people from 12 to 1 is (3/2)(3x/4)
Given that 3x/4 + (3/2)(3x/4) = (3x/4)(5/2) = 75
Then x = 40
D
Answer: (D) 40
Question: The speed at which a man can row a boat in still water is 22 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres?
(A) 12.59
(B) 11.53
(C) 15.69
(D) 14.56
(E) 18.98
Rationale: Speed of the boat downstream = 22 + 3 = 25 kmph= 25 * 5/18 = 6.94 m/sHence time taken to cover 80 m = 80/6.94= 11.53 seconds.Answer:B
Answer: (B) 11.53
Question: In measuring the sides of a rectangle, one side is taken 20% in excess and the other 10% in deficit. Find the error per cent in area calculated from the measurement?
(A) 12% deficit
(B) 10% excess
(C) 8% excess
(D) 9% excess
(E) none of these
Rationale: Since Side1 x Side2 = Area
Therefore, error% in area
= ( x + y + xy/100) %
= [20 - 10 + ( -10 x 20)/100]% or 8%
i.e., 8% excess
ANSWER:C
Answer: (C) 8% excess
Question: Insert the missing number
2, 4, 8, ..., 32, 64, 128, 256
(A) 15
(B) 14
(C) 16
(D) 13
(E) 18
Rationale: series is 2* Previous Number.
ANSWER:C
Answer: (C) 16
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15%, in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 3436521
(B) 3546577
(C) 3546546
(D) 7565643
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 7 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: if n =8
mark sold 1 box
and Ann sold 6 boxes
total 7 < 8
Answer:E
Answer: (E) 8
Question: The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 11 years
(B) 17 years
(C) 18 years
(D) 20 years
(E) 58 years
Rationale: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
6x = 84 => x = 14
Son's age after 6 years = (x + 6) = 20 years.
Answer:D
Answer: (D) 20 years
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $2,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A)  19,500
(B)  24,500
(C)  25,500
(D)  26,500
(E)  27,500
Rationale: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 2,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 2,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 160 = 0.10x
Combine terms and subtract 0.08x from both sides:
390 = 0.02x
Divide both sides by 0.02:
19,500 = x
Your answer is A.
Answer: (A)  19,500
Question: What is the value of (12 + 22 + 32 + 42 + ----- + 102)
(A) 295
(B) 324
(C) 385
(D) 391
(E) 399
Rationale: Explanation:
(12 + 22 + ….. + n2) = (1/6) n(n + 1) (2n + 1)
Here, n = 10
Therefore,
(12 + 22 + ….. + 102) = (1/6) 10 (10 + 1) ( 2 x 10 + 1)
= (1/6) x 10 x 11 x 21
= 385
ANSWER: C
Answer: (C) 385
Question: 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
(A) 4 days
(B) 6 days
(C) 2 days
(D) 8 days
(E) 10 DAYS
Rationale: Explanation :
Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
Answer : Option A
Answer: (A) 4 days
Question: C and D are tying water balloons for a party. 5 out of every 8 balloons that C ties does not pop, and 2 out of every 3 balloons that D ties does not pop. If they each tie 120 balloons, what fraction of the 240-pack will pop?
(A) 85/240
(B) 70/240
(C) 155/240
(D) 140/240
(E) 60/240
Rationale: Ratio of A's balloons that do not pop: 5/8
Ratio of B's balloons that do not pop: 2/3
Ratio of A and B's balloons that do not pop: 5/8+2/3=31/24
Total number of A's and B's balloons that do not pop: 120x(31/24)=155/240
Fraction of balloons that pop: 1-155/240=85/240
Answer is A
Answer: (A) 85/240
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?
(A) 229
(B) 240
(C) 288
(D) 277
(E) 320
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Length of the train = 20 * 20 = 400 m.
Let the length of the platform be x m . Then,
(x + 400)/36 = 20 => x = 320 m.
Answer: E
Answer: (E) 320
Question: 20 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 32
(B) 87
(C) 40
(D) 99
(E) 77
Rationale: 3W = 2M
20M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
20 * 21 * 8 = 14 * x * 6
x = 40
Answer: C
Answer: (C) 40
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 27
(B) 50
(C) 27
(D) 29
(E) 12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: (B) 50
Question: A bag contains 3 white balls, 3 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 0.25
(B) 0.15
(C) 0.35
(D) 0.45
(E) 0.4
Rationale: Each ball has an equal probability of being the third ball drawn.
P(3rd ball is red) = 4/10 = 0.4
The answer is E.
Answer: (E) 0.4
Question: An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference V between the highest and the lowest incentive received by the 5 salesmen in the month?
(A) $4000
(B) $5000
(C) $9000
(D) $11,000
(E) $13,000
Rationale: Break down the question in to steps:
Step #1: incentives received by 5 salesmen -->abcde
Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de
Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000
Step #4: What is the difference between the highest and the lowest incentive:
- The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.
- The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.
- Therefore the first two numbers( ab) must equal 4, 000
- There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b
if a = 1,000 b = 3,000 --> difference V between the highest and the lowest incentive = 12,000 - 1,000 =11, 000
no other options for a or b to fit the criteria
Final List:1,0003,0007,00012,00012,000
Answer D
Answer: (D) $11,000
Question: If a is an even integer and b is an even integer and a > b which of the following must be an odd integer :
(A) a/b
(B) ab
(C) 2a+b
(D) 2(a+b)
(E) none of these
Rationale: a= even = e.g 4
b= even = e.g 2
A. even/even for example 4/2 = 2 ==> even
B. even * even = 4 * 2 = 8 == >even
C. 2*even + even = even + even ===> even
D. 2(even + even) = 2(even) ===> even
Hence E it is.
Answer: (E) none of these
Question: A farm is made up of brown and white goats. the number of male brown goats is 35% less than the total number of brown goats. The total number of female goats is 20 times more than the number of female brown goats. If the total population of male goats is half the population of the female goats, what percentage of male goats are brown?
(A) 30.1
(B) 20.5
(C) 15.2
(D) 10.2
(E) 28.6
Rationale: Since we are dealing in percentage let us pick 100 as the number of brown male goats.
That means that the total number of brown goats is= 135 (number of male brown goats is 35% less than the total number of brown goats),
therefore the number of brown female goats is 35.
The total number of female goats is 15x the number of brown female goats= 35*20=700 female goats.
Male goats total population is half the population of the female goats = 700/2=350
Therefore percentage of male horses goats that are brown= 100/350*100=28.6
Correct option is E
Answer: (E) 28.6
Question: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of T?
(A)  7
(B)  8
(C)  9
(D)  10
(E)  11
Rationale: A simple and elegant solution.
As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1
39-15 = 24
24 divide by 3 is 8.
Meaning mean of the n terms is 15+8 = 39-16 = 23
Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.
T*23 +39 = 25*(T+1)
T = 7
Ans. (A)
Answer: (A)  7
Question: A circular well with a diameter of 2 metres , is dug to a depth of 8 metres. What is the volume of the earth dug out?
(A) 32 m3
(B) 25.1 m3
(C) 40 m3
(D) 44 m3
(E) None
Rationale: Solution
Volume	= πr2h
‹=› (22 /7 ×1×1×8)m3
‹=›25.1 m3.
Answer B
Answer: (B) 25.1 m3
Question: 0.0002152/0.000205 x 12.05=?
(A) 19.64
(B) 14.64
(C) 12.6
(D) 15.64
(E) 13.64
Rationale: Explanation :
? = 0.0002152/0.000205 x 12.05 = 12.6
Answer : Option C
Answer: (C) 12.6
Question: In how many ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?
(A) 4586
(B) 5896
(C) 2415
(D) 1771
(E) 1881
Rationale: In order that two books on Hindi are never together, we must place all these books as under:
H E H E H E H….. H E H
Where H denotes the position of Hindi book and E that of English book.
Since there are 22 books on English, the number of places marked E are 23.
Now, 20 places out of 23 can be chosen in 23C20 = 23C3 = 23*22*21
3*2*1
= 1771 ways.
Hence the number of ways = 1771 ways
ANSWER:D
Answer: (D) 1771
Question: A math teacher has 24 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
(A) 7
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 24 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 24 - 17 = 7
Answer (A)
Answer: (A) 7
Question: Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 54 meter head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A)  15 seconds
(B)  18 seconds
(C)  25 seconds
(D)  27 seconds
(E)  45 seconds
Rationale: used pluging in method
say t is the time for cristina to catch up with Nicky, the equation will be as under:
for Nicky=N=3*t+54
for Cristina=C=5*t
@t=27, N=135 C=135 right answer
ans:D
Answer: (D)  27 seconds
Question: Shop Offered 30% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?
(A) 500
(B) 800
(C) 600
(D) 700
(E) 750
Rationale: SP* (70/100) = 560
SP= 8 * 100 => CP = 800
Answer:B
Answer: (B) 800
Question: Dimitri weighs x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of 3y-y pounds. Which of the following represents Allen’s weight?
(A) y - x/2
(B) 2x - y/2
(C) (y - x)/2
(D) y - 2x
(E) 2x - y
Rationale: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs X pounds more than Allen weighs and that they weight a combined TOTAL of 3Y-2Y or Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Answer: (C) (y - x)/2
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) Rs. 3900
(B) Rs. 3990
(C) Rs. 4000
(D) Rs. 4100
(E) Rs. 4200
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
A
Answer: (A) Rs. 3900
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies E and Y . The ratio of p to V in smothie E is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie E?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: The ratio of p to V in smothie E is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Answer: (D) 20
Question: If x > 4 and y < -4, then which of the following must be true ?
(A) x/y > 1
(B) x/y < -1
(C) x/y < 0
(D) x + y > 0
(E) xy > 0
Rationale: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
E should be the answer.
Answer: (E) xy > 0
Question: Jane and Ashley take 20 days and 10 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
(A) 12 Days
(B) 15 Days
(C) 16 Days
(D) 18 Days
(E) 20 Days
Rationale: Let us assume that the work is laying 40 bricks.
Jane = 2 bricks per day
Ashley = 4 brick per day
Together = 6 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 32
Last 4 days Jane works alone,
No. of bricks = 8
Remaining bricks = 40 - 40 = 0
So together, they would take 0/6 = 0
Total no. of days = 8 + 4 + 0 = 12
Answer is A
Answer: (A) 12 Days
Question: Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 50,000 after completion of one year. What will be Madhu's share of profit?
(A) Rs. 27,000
(B) Rs. 24,000
(C) Rs. 25,000
(D) Rs. 36,000
(E) None of these
Rationale: 30,000 *12=45,000*8
1:1
Madhu's share=1/2*50,000
i.e. Rs. 25,000
ANSWER:C
Answer: (C) Rs. 25,000
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) 9:32
(B) 9:31
(C) 9:33
(D) 9:39
(E) 9:12
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: (B) 9:31
Question: In how many different number of ways 4 man and 2 woman can sit on a bench?
(A) 600
(B) 620
(C) 640
(D) 660
(E) 720
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
E)
Answer: (E) 720
Question: A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $3.00, what total number of pens and pencils did the customer purchase?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Answer: Algebraically, the question looks like this: 3.0 = 0.35x + 0.25y
There are six possible numbers of pens that fit that requirement:
1 pen: $0.35
2 pens: $0.70
3 pens: $1.05
4 pens: $1.40
5 pens: $1.75 balance 1.25
5 pencils cost $1.25
That's 5 pens and 5 pencils Choice (C) is correct.
Answer: (C) 10
Question: A 240 meter long train crosses a man standing on the platform in 4 sec. What is the speed of the train?
(A) 176 kmph
(B) 108 kmph
(C) 216 kmph
(D) 134 kmph
(E) 161 kmph
Rationale: S = 240/4 * 18/5
= 216 kmph
Answer: C
Answer: (C) 216 kmph
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) 59028
(B) 27777
(C) 29999
(D) 59000
(E) 27772
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000.Answer:D
Answer: (D) 59000
Question: If f(x) = 6x^4 - 4x^3 - 3x^2 + 6x , then f(-1) =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: f(-1) = 6(-1)^4 - 4(-1)^3 - 3(-1)^2 + 6(-1) = 6+4-3-6 = 1
The answer is D.
Answer: (D) 1
Question: You enter a weight loss challenge game and manage to lose 11% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?
(A) 13%
(B) 9.22%
(C) 9%
(D) 14%
(E) 12%
Rationale: (100%-11%)*(100%+2%) = 0.89*1.02 = 9.22%
The weigh in records your weight loss at 9.22%!
The Answer is B
Answer: (B) 9.22%
Question: Find the arithmetic mean A of all roots of the following equation- see an attachment.
(A) 2
(B) 1
(C) 0.5
(D) -1/3
(E) 0.3
Rationale: Arithmetic mean A your answer C and E are same, can you correct one of them please. thanks.C
Answer: (C) 0.5