mathewhe/aqua_rat huggingface dataset:
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 48/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
(A)  $20000
(B)  $15000
(C)  $12000
(D)  $10000
(E)  $9000
Rationale: Since investment doubles in 48/r years, then for r=8 it'll double in 48/8=~6 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*3=$15,000 .
Answer: B.
Answer: (B)  $15000
Question: My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate cost Re 1. The cost of apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if number of chocolates, biscuits and apples brought were all integers?
(A) Rs 34
(B) Rs 33
(C) Rs 8
(D) None of the above
(E) Cannot be determined
Rationale: Explanation :
Let the person buy c chocolates, 2c buiscuits. Therefore, apples is >3c.
In any case, total cost will be
=>cost of chocolates + cost of biscuits + cost of apples.
=> (c*1) + [2c*0.5] + (2*something greater than 3c).
Thus, Total cost=>
=> 2c + (2* something greater than 3c).
Here, the total cost is an even number. Thus ans should be an even number.
Taking c=1, the total minimum cost we get is 10.
Thus the only other option that satisfies the constraints is 34.
Answer : A
Answer: (A) Rs 34
Question: A company hired a printer to produce a total of x + 2 envelopes. The job consisted of two types of envelopes, 3¢ envelopes and 7¢ envelopes. If the company requested 2 more 3¢ envelopes than 7¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 2 envelopes ?
(A) (9x-5)/2
(B) (7x+4)/2
(C) 5x+6
(D) 6x+5
(E) 4x+13
Rationale: we can take
X+2 = 10
X= 8
So 3c envelopes will be 6
and 7c envelopes will be 4
So total cost will be 46
Then that is our target
Plug x =8 in answer choices
Only c works
Correct Answer : C
Answer: (C) 5x+6
Question: In a school of 400 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) 41
(B) 63
(C) 72
(D) 63
(E) 50
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
400 * 18/100 = 72
ANSWER:C
Answer: (C) 72
Question: A man can row his boat with the stream at 14 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 3 kmph
(C) 8 kmph
(D) 7 kmph
(E) 5 kmph
Rationale: DS = 14
US = 4
S = ?
S = (14 - 4)/2 = 5 kmph
Answer: E
Answer: (E) 5 kmph
Question: In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?
(A) $9 x 10^4
(B) $9.90 x 10^6
(C) $1.00 x 10^7
(D) $1.05 x 10^7
(E) $9.90 x 10^7
Rationale: The max product of any two balls can be 9 * 10 = 9900 = 9 * 10
If we multiply it by $1000 the max amount will be 9 * 10^4.
A
Answer: (A) $9 x 10^4
Question: If A : B = 4 : 3 and B : C = 5 : 9 then A : B : C is :
(A) 20 : 35 : 63
(B) 20 : 15 : 27
(C) 30 : 35 : 65
(D) 25 :34: 68
(E) None of these
Rationale: Expl : A : B = 4 : 3
B : C = 5 :9 = 5*3/5 : 9 *3/5 = 3 : 27/5
A : B : C = 4 : 3 : 27/5 = 20 : 15 : 27
Answer: B
Answer: (B) 20 : 15 : 27
Question: A third of Arun’s marks in mathematics exeeds a half of his marks in english by 80.if he got 240 marks In two subjects together how many marks did he got inh english?
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: M=mathematics marks
E=english marks
M+E=240-(1eqution)
M=E+E/2-(2 equation)
put 2nd equation in 1st equation
E+E/2+E=240
3E/2=240
3E=240*2
3E=180
E=180/3
E=160
ANSWER:C
Answer: (C) 160
Question: There are 3 mixtures when mixed in the ratio of 3:4:5 price was 240.When mixed with 6:4:9 price was 340.what's the price when mixed in 5:6:8 ration price is_________
(A) 346
(B) 356
(C) 366
(D) 376
(E) 386
Rationale: 3x+4x+5x=240
x=20
6x+4x+9x=340
x=17.89
5*20+6*20+8*20=380-4=376
ANSWER:D
Answer: (D) 376
Question: The number 81 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?
(A) 2
(B) 5
(C) 8
(D) 7
(E) 9
Rationale: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-1, +/-4 and +/-8, so the difference could be 7,9, or 12. Since only one of them is among the choices, then it must be the correct answer.
Answer: D.
Answer: (D) 7
Question: E is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can E be?
(A) 300,000
(B) 349,999
(C) 350,000
(D) 399,999
(E) 400,000
Rationale: E 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
Answer: (B) 349,999
Question: Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 80 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following?
(A) 45
(B) 50
(C) 60
(D) 72
(E) 80
Rationale: AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 80
y - 80 + (y/4) = 80
5y/4 =160
y = 128
2x/3 = 128 - 80 = 48
x = 144/2 = 72
Answer: D
Answer: (D) 72
Question: From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x)
(A) 10
(B) 14
(C) 15
(D) 16
(E) 30
Rationale: Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations
E
Answer: (E) 30
Question: An urn contains g green marbles and b blue marbles. If 2 green marbles and 5 blue marbles are added, and then one marble is selected at random from the urn, what is the probability that a blue marble will be drawn?
(A) b/(b+g)
(B) (b+5)/(g+3)
(C) (b+5)/(b+g+7)
(D) (b+5)/(b+g+3)
(E) b/(b+g+5)
Rationale: no of fav outcomes i.e. blue MArbles = b+5
Total no of outcomes i.e. total Marbles = (b+5)+(g+2)= b+g+7
probability = (b+5) /(b+g+7)
Answer C
Answer: (C) (b+5)/(b+g+7)
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}?
(A) {6, 12}
(B) {6, 15}
(C) {21,28}
(D) {9, 15}
(E) {15, 24}
Rationale: p/q= d=p/q+7
d= .75 q
d= .6(q+7)
we get d = 21 and q = 28. Answer = C.
Answer: (C) {21,28}
Question: Of the 50 electronics components that a factory must
manufacture, 70 percent would be most e¢ ciently manufactured
by Machine A and the remaining 30 percent would be most
e¢ ciently manufactured by Machine B, though either machine
could manufacture any of the 50 components. If 36 percent of
the components were manufactured by Machine A and the
remainder were manufactured by Machine B, what is the
highest possible number of components that were
manufactured by the machine that would manufacture them
the most efficiently?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: # components A and B could manufacture efficiently:
A: 50*70% = 35
B: 50*30% = 15
# components A and B effectively manufacture:
A: 50*36% = 18
B: 50*64% = 32
Max. # components efficiently manufactured:
18 (from A) and 15 (from B) = 33
ANSWER:D
Answer: (D) 33
Question: It is known that no more than 5 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
(A) 35
(B) 105
(C) 60
(D) 210
(E) 420
Rationale: The question states that there are no more than 5 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4 or 5 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 5).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5), i.e., 60.
Answer (C)
Answer: (C) 60
Question: Company A has 13 employees, 6 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift?
(A) 81
(B) 231
(C) 336
(D) 350
(E) 406
Rationale: Looks easy: -- 6C4*5C1 + 6C5 -- 81 (A).
Answer: (A) 81
Question: A is 30% more efficient than B. How much time will they working together take to complete a job which A alone could have done in 23 days?
(A) 11
(B) 13
(C) 20 3/17
(D) 14
(E) None of these
Rationale: Explanation:
Ratio of times taken by A and B= 100:130 =10:13
suppose B takes x days to work the 10:13::23:x =>x=23 x 13/10 = 299/10
A’s one day work = 1/23 and B’s is 10/299
Then A+B ‘s work = 1/23 + 10/299 = 23/299 =1/13 => 13 days
Answer: Option B
Answer: (B) 13
Question: How many bricks each measuring 21cm x 10cm x 8cm, will be needed to build a wall 9m x 5m x 18.5m
(A) 4955
(B) 4899
(C) 4650
(D) 7200
(E) None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (900 x 500 x 18.5) / (21 x 10 x 8) = 4955
Answer: A
Answer: (A) 4955
Question: John has taken four (4) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 88. What will he need to average on his final two tests to achieve this grade?
(A) 100
(B) 90
(C) 92
(D) 94
(E) 97
Rationale: 88-82=6*4=24 points
2*88=176
176+24=200 points to be scored in the 2 tests.
Avg of 2 tests = 200/2=100
Answer: A
Traditional Method:
Total scored till now 82*4=328
Total score to avg 88 in 6 tests = 88*6=528
Total to be scored on 2 tests = 528-328=200
Avg on 2 tests = 200/2 = 100
Answer A
Answer: (A) 100
Question: If shares of two persons in profits are Rs.300 and Rs.500 then ratio of their capitals is
(A) 3:4
(B) 3:5
(C) 4:3
(D) 1:3
(E) 1:5
Rationale: total profit =1000
ratio=300/500
=3:5
ANSWER:B
Answer: (B) 3:5
Question: A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes ?
(A) 32 rolls
(B) 54 rolls
(C) 108 rolls
(D) 120 rolls
(E) 140 rolls
Rationale: Explanation:
Number of cuts made to cut a roll into 10 pieces = 9.
Therefore Required number of rolls = (45 x 24)/9 = 120.
Answer: D
Answer: (D) 120 rolls
Question: Rama bought goods at a discount of 20% of list price.He marks them at a price as search he can give discount of 20% on a marked price and still makes the profit of 20% on selling price.What percent of list price is the marked price
(A) 100%
(B) 175%
(C) 125%
(D) 180%
(E) 160%
Rationale: If marked price is Rs 100/-
Selling price = Rs 80/-
Profit = 80*0.2= Rs 16
CP= Rs 64
List price = 64*100/80 = Rs 80
so marked price is 100*100/80 = 125%
ANSWER:C
Answer: (C) 125%
Question: if 3rd december 1999 is sunday what day is 3rd january 2000
(A) wednesday
(B) thursday
(C) friday
(D) saturday
(E) sunday
Rationale: There is difference of 31 days from 3rd Dec 1999 to 3rd Jan 2000..
31/7 left with 3 odd days..
that is wednesday
ANSWER:A
Answer: (A) wednesday
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked five 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 320
(D) 350
(E) 400
Rationale: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 5 days -> 80*5=400.
This matches answer choice E.
Answer: (E) 400
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
(A) 165
(B) 187
(C) 277
(D) 266
(E) 261
Rationale: Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2)
= 165 ways
Answer: A
Answer: (A) 165
Question: The avearge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 47. Then find the average for the last four matches?
(A) 33.25
(B) 33.5
(C) 34.25
(D) 35
(E) 26.75
Rationale: Solution
Required average	=(38.9 x 10)-(47 x 6)/ 4
= 107 / 4.
= 26.75
Answer E
Answer: (E) 26.75
Question: Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1200
(A) 30
(B) 120
(C) 210
(D) 300
(E) 700
Rationale: 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.
100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.
Then we want to know what is the largest possible GCF of x and 2100.
Well 1200 = 3 * 4 * 10 * 10
We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.
We know x has one factor of 3, but not two factors --- that takes the 3.
We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other
No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.
3*4*10 = 120
If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 1200.
B
Answer: (B) 120
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.238 less than the sum lent. What was the sum lent?
(A) 228
(B) 350
(C) 289
(D) 500
(E) 821
Rationale: P - 238 = (P*4*8)/100
P = 350
Answer: B
Answer: (B) 350
Question: Two trains, 250 metres and 150 metres long respectively, are running on parallel lines. If they are running in the same directions, the faster train crosses the slower train in 40 seconds. If they are moving in the opposite direction they pass each other in eight seconds. What is the speed of the slower train?
(A) 108 kmph
(B) 82 kmph
(C) 92 kmph
(D) 72 kmph
(E) 62 kmph
Rationale: Let the speed of faster train be f and slower train be y.
Time taken to cross each other traveling in the same direction = 250 +150/ (x-y) = 40………(1)
Time taken to cross each other traveling in the opposite direction = 250+150 /(x+y) = 8 …….(2)
From (1) and (2) f= 30 m/s and s = 20 m/s
Speed of slower train = 20 * 18/5 = 72 kmph
ANSWER:D
Answer: (D) 72 kmph
Question: The arithmetic mean of the 11 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 5?
(A) 2 + s + a
(B) 22 + a
(C) 2s
(D) 2a + 2
(E) 1 + a
Rationale: (11s+55)/11=s+5=a
(9s+54)/9=s+6=1+a
E
Answer: (E) 1 + a
Question: If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?
(A) Rs. 850
(B) Rs. 900
(C) Rs. 980
(D) Rs. 990
(E) Rs. 1000
Rationale: Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mterest u — 12 : wzo — x
Therefore, by u xglurmula.
_umxx
’ Rx’: (
, _ma>< 1nzn—xv
\4Ve|\a\e,Jc— 5“
:> ~(:51DD—S*(or6x:51UU
or, J: : w 350
. The sum of money burrowed : Rs. 850
A)
Answer: (A) Rs. 850
Question: The greatest number of four digits which is divisible by 10, 20, 30 and 60 is:
(A) 9200
(B) 9300
(C) 9400
(D) 9600
(E) 9900
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 20, 30 and 60 is 300.
On dividing 9999 by 300, the remainder is 99.
Required number (9999 - 99) = 9900.
ANSWER :E
Answer: (E) 9900
Question: A man is walking along a numbered path. He repeats the following process of taking 10 steps forward and N steps backward. What should N be in order to guarantee at least one number along the path will be stepped on exactly 5 times. This includes a forward and backward step adding to the total. A tile must be stepped onto to count and not simply stepped off
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Assuming the man's overall direction is headed forward is forward from no answers being greater than 10
Actions:
1: 10 steps
2: 10 - N steps
3: 20 - N steps
4: 20 - 2N steps
5: 30 - 2N steps
6: 30 - 3N steps
All answers less than or equal to 5 are out since by the 4th action the number tile will be 10. Following the procedure, N=5 will making every tile less than 10 have 3 or fewer steps.
N=6 will allow the 4th action to be 8 making it the first number readily breach single digits for the starting action. This is an important thing to notice since hitting tiles reached by the first action will allow the greatest amount of countable steps.
Steps by the end of the 5th action
7: 3 steps
8: 3 steps (stepped off from)
9:5 steps
10: 4 steps
11: 3 steps
12: 3 steps
By the 6th action, the steps will be at 12 an won't making it back to any tile 1-10. Since this is repeating, inferring that after every 6 actions the process is a renewable position making tile 9 the only tile with 5 steps other than every other tile after that limiting it to 5 steps.
E is correct
Answer: (E) 6
Question: In the third grade of Windblown School there are 102 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
(A) 0.
(B) 6.
(C) 8.
(D) 10.
(E) 12.
Rationale: Total = 102
failed in math = 102/3=34
failed in literature=108/6=17
the least failed in both can be 0
while max can be 17
Answer A
Answer: (A) 0.
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many R digits does this integer consists of?
(A) 150
(B) 339
(C) 342
(D) 359
(E) 362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer R= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: (C) 342
Question: Sales price is $81, gross profit is 170% of cost, what is the value of gross profit?
(A) 32
(B) 33
(C) 39
(D) 40
(E) 51
Rationale: Cost + Profit = Sales
Cost + (170/100)Cost = 81
Cost = 30
Profit = 81 - 30 = 51
Answer (E)
Answer: (E) 51
Question: Integers 3n+4 and 8n+9 are divisible by an integer p. If p is not equal to 1, then p equals to?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: If p divides 3n+4, then p divides 24n+32.
If p divides 8n+9, then p divides 24n+27.
Then p must equal 5.
The answer is C.
Answer: (C) 5
Question: Calculate the average of first 18 even numbers is?
(A) 21
(B) 29
(C) 19
(D) 14
(E) 10
Rationale: Explanation:
Sum of 10 even numbers = 18 * 19 = 342
Average = 342/18 = 19
Answer: Option C
Answer: (C) 19
Question: find next in series 31,29,31,30,31,?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: leave the number 31 in the series,then note that 29,30,31
hence 31 is the result
ANSWER:B
Answer: (B) 31
Question: When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II.18.18
III. 17.17
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I and III only
Rationale: Problem statement was difficult to parse. but some how I managed to understand what we can do.
1) x/y = 15 + 0.15
2) x/y = 18 + 0.18
3) x/y = 17 + 0.17
w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)
therefore :
1) y*0.15=60 -- we can get y an integer.
2) y*0.18=60 -- we can't get y an integer.
3) y*0.17=60 -- we can't get y an integer.
Therefore 1 are possible answers.
Ans A
Answer: (A)  I only
Question: A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 9%. What is the value of x?
(A) 57.5 litres
(B) 56.67 litres
(C) 57.67 litres
(D) 56.5 litres
(E) 50 litres
Rationale: Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
36%(1-X/100)^2 = 9% * 100%
(1-x/100)^2=9/36------>(1-x/100)^2=(3/6)^2
100-X=300/6
x=50
Ans E
Answer: (E) 50 litres
Question: The number of new words that can be formed by rearranging the letters of the word 'NUMBERS' is
(A) 2880
(B) 7670
(C) 1192
(D) 5039
(E) 1120
Rationale: Explanation:
Number of words which can be formed = 7! - 1 = 5040- 1 = 5039.
Answer: D
Answer: (D) 5039
Question: Vindy paddles her kayak upstream at w kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?
(A) wnp
(B) wn/p
(C) (w + n)/p
(D) wnp/(w + n)
(E) pm/n- pn/m
Rationale: let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/w
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/w)+(d/n)
=d(w+n)/wn
d=wmn/(w+n)=D
Answer: (D) wnp/(w + n)
Question: The sum of the squares of two numbers is 3341 and the diference of their squares is 891. The numbers are :
(A) 35 and 46
(B) 35 and 49
(C) 35 and 42
(D) 35 and 41
(E) 35 and 48
Rationale: Explanation:
Let the numbers be x and y. Then,
Adding (i) and (ii), we get :
Subtracting (ii) from (i), we get :
So, the numbers are 35 and 46
Answer: A
Answer: (A) 35 and 46
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?
(A) $100
(B) $115
(C) $125
(D) $130
(E) $135
Rationale: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit = 725-600 = $125
Ans: "C
Answer: (C) $125
Question: The number 90 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: 7^2+5^2+4^2=49+25+16 = 90
7+5+4 =16
Hence answer is B
Answer: (B) 16
Question: A milk man has 10 liters of milk. If he mixes 5 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) 15%
(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 10 liters of milk.
Therefore, profit percentage = 15 %. Answer: B
Answer: (B) 15%