mathewhe/aqua_rat huggingface dataset:
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
(A) 22 degrees
(B) 64 degrees
(C) 77 degrees
(D) 26 degrees
(E) 18 degrees
Rationale: Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 8 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 8 or x = 8.
Temperature on the 5th day = 8x = 64 degrees.
Answer: B
Answer: (B) 64 degrees
Question: Mr. Kela purchased two steel factories, one in india and other one in Malaysia for total Rs. 72
crores. Later on he sold the india factory at 16% profit and malaysian factory at 24% profit.
Thus he gained a total profit of 19%. The selling price of Indian factory is:
(A) 52.2 crores
(B) 56 crores
(C) 55.5 crores
(D) 59.3 crores
(E) None of these
Rationale: Explanation :
If price(in crore) of Indian factory=x and Malaysian factory=72-x, then
=> x*(116/100) + (72-x)*(124/100) = 72*(119/100)
=> 1.16x+89.28-1.24x = 85.68
=> x = 45
So selling price of an Indian factory = 45*(116/100) = 52.2
Hence (A) is correct answer.
Answer : A
Answer: (A) 52.2 crores
Question: There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
(A) Rs. 450
(B) Rs. 320
(C) Rs. 550
(D) Rs. 420
(E) None
Rationale: Solution:
Let the original average expenditure be Rs.x then, 42(x - 1) - 35x = 42.
=> 7x = 84
=> x = 12
Therefore original expenditure,
= Rs.(35 × 12)=Rs.420.
Answer: Option D
Answer: (D) Rs. 420
Question: A container 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 3 times. Find how much spirit is left in the resulting mixture finally?
(A) 6(257/525) gallons
(B) 6(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)^3 / 20^3
Left QTY = 20 (16/20)^3
Left QTY = 20 ( 4/5 )^3
Left QTY = 10.24
Answer is E
Answer: (E) None of these
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c+a=b+a+1
II. abc is an even integer
III. (a+b+c)/3 is an integer
(A) I
(B) II
(C) I and II
(D) II and III
(E) all are true
Rationale: 1. c+a=b+a+1 --> a, b, c are consequitive positive integers and a<b<c then c+a=b+a+1. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.
Answer: E.
Answer: (E) all are true
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
(A) 756
(B) 730
(C) 250
(D) 600
(E) 350
Rationale: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= 7C3*6C2 + 7C4*6C1 + 7C5=>756
ANSWER A
Answer: (A) 756
Question: Two trains 150 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.16 sec
(B) 18.8 sec
(C) 14.8 sec
(D) 10.8 sec
(E) 11.16 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 150 + 160 = 310 m.
Required time = 310 * 9/250 = 279/25 = 11.16 sec.
Answer: E
Answer: (E) 11.16 sec
Question: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 32 liters of Fuchsia to change it to Mauve paint?
(A) 9
(B) 13
(C) 15
(D) 16
(E) 18
Rationale: in 32 liters, Red = 5/8 * 32 = 20 and Blue = 12
so, 20/(12+x) = 4/5
or, x = 13 (Answer B)
Answer: (B) 13
Question: (1000)7÷(10)18=?
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) None of these
Rationale: Explanation:
=(103)7/(10)18
=(10)21/(10)18=10(3)=1000
Option C
Answer: (C) 1000
Question: What is the principal sum?
I. The sum amounts to Rs. 690 at S.I.
II. Total year is 8 years.
III. The rate of interest is 5% p.a.
(A) I and III only
(B) II and III only
(C) I and II only
(D) Any two of the three
(E) All I, II and III
Rationale: Explanation:
Clearly, all the three statements are needed to solve this question
Answer: E
Answer: (E) All I, II and III
Question: If 'a' and 'b' are non-zero numbers such that their sum is seven times the product, what is the value of 1/a + 1/b?
(A) 6
(B) 7
(C) 8
(D) 14
(E) 21
Rationale: a+b = 7ab
1/a + 1/b = (b + a)/(ab) = 7.
The answer is B.
Answer: (B) 7
Question: The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is:
(A) 1/289
(B) 289/290
(C) 290/289
(D) 289
(E) 300
Rationale: Explanation:
Let the numbers be a and b. Then,
ab = 17, a = 1 and b = 17
So, 1/a2 + 1/b2 = (a2 + b2)/a2 b2
= (12 + 172)/(1 * 17)2 = 290/289
ANSWER IS C
Answer: (C) 290/289
Question: The average of five consecutive even numbers A, B, C, D and E is 20. What percent of E is D?
(A) 90.1
(B) 91.7
(C) 97.1
(D) 101.1
(E) 107.1
Rationale: Explanation :
In such a case the middle number (C) is the average
∴ C = 20 and D = 22 and E = 24
Required percentage = 22/24 x 100 = 91.7
Answer : Option B
Answer: (B) 91.7
Question: Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have?
(A) 5
(B) 10
(C) 30
(D) 40
(E) 50
Rationale: Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)*100% = 60%
Now by Alligation Rule:
A . ......... B
20% . . . 80%
. . 60% . .
(80-60) . (60-20)
=20 : =40
Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration)
So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%)
So as per above ration Qty B mixed will be 50 gallons.
Qty of water in mixture B = 20% of 50 = 10 gallons.
ANSWER:B
Answer: (B) 10
Question: A jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
(A) 3.6 sec
(B) 18 sec
(C) 35 sec
(D) 72 sec
(E) None of these
Rationale: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (230 + 120) m = 350 m.
∴ Time taken = (350⁄10) sec = 35 sec.
Answer C
Answer: (C) 35 sec
Question: The simple interest on Rs. 8 for 12 months at the rate of 5 paise per rupeeper month is
(A) 1.2
(B) 4.8
(C) 4.4
(D) 3.21
(E) None
Rationale: Sol.
S.I. = Rs. [8 * 5/100 * 12] = Rs. 4.8
Answer B
Answer: (B) 4.8
Question: Two commodities have cost per kg is 4.75Rs & 3.20Rswere mixed in a certain
ratio so as to make cost price of mixture as 17.75 Rs. Find the ratio
(A) 14.55:13
(B) 15.55:13
(C) 16.55:13
(D) 17.55:13
(E) 18.55:13
Rationale: mixture17.75-3.20=14.55
mixture 17.75-4.75=13
14.55:13
ANSWER:A
Answer: (A) 14.55:13
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1800. What is their H.C.F.?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x
60x = 1800
x = 30
The numbers are (3 x 30), (4 x 30) and (5 x 30).
The H.C.F. is 30.
The answer is C.
Answer: (C) 30
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure q in inches of the width of the foil covered prism?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 = 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =q=10
Ans E.
Answer: (E) 10
Question: Two cars start at the same time from opposite ends of a highway that is 175 miles long. One car is riding at 25 mph and the second car is riding at 45 mph. How long after they begin will they meet?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 45+25 = 70 mph
Total distance to be covered = 175 miles.
Time taken would be: 175 miles/70 mph = 2.5 hours
B is the answer.
Answer: (B) 2.5
Question: Find the highest value of 'a' so that 365a16 is divisible by 8.
(A) 9
(B) 8
(C) 0
(D) 2
(E) 1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a16' is divisible by 8.
.: highest value of a is '8'.
Answer: Option B
Answer: (B) 8
Question: A certain machine produces 780 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 4 days?
(A) 7,000
(B) 24,000
(C) 74,880
(D) 100,000
(E) 168,000
Rationale: Since 7 days consist of 24*4 hours the total is 96 hours.
Since every hour the machine produces 780 units of product P the total product during 96 hours is 96*780=74,880.
Correct Option : D
Answer: (D) 100,000
Question: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent Q of the interns report no feelings of tiredness during their shifts?
(A) 6
(B) 14
(C) 19
(D) 20
(E) 81
Rationale: < 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired Q= 5 + 14 = 19.
Answer: C.
Answer: (C) 19
Question: ABCD is a square where AB =âˆš4008. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD.
(A) 3008
(B) 2004
(C) 1008
(D) 2016
(E) 3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
4008/2= 2004 .
correct answer B
Answer: (B) 2004
Question: If x, y, and z are positive integers such that x^2 + y^2 + z^2 = , which of the following could be the values of x, y, and z?
I)x=10 y=20 z=30
II)x=5 y=30 z=13
III)x=20 y=-30 z=10
(A) I only
(B) II only
(C) III only
(D) I​ and II
(E) I and III
Rationale: The x,y and z are easiest number,so it is easy to find the squares of the values.
Here III) option gives y=-30..(30^2) and(-30^2) are equal.
Answer is option E
Answer: (E) I and III
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 30
(B) 40
(C) 70
(D) 80
(E) 60
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 40% of 50% i.e 20%. so he completed 50 +20 =70 % of total trip
C
Answer: (C) 70
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.7
(B) 16.5
(C) 12.3
(D) 12.5
(E) 12.1
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Answer: (D) 12.5
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 26.4 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 100-26,4=73,6. There are only two numbers below 73,6. The answer is B
Answer: (B) two
Question: What is the remainder when (55)(57) is divided by 8?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 7
Rationale: (55)(57) = (56-1)(56+1) = 56^2 - 1 which is 1 less than a multiple of 8.
Then the remainder will be 7.
The answer is E.
Answer: (E) 7
Question: If 40 sheep eat 40 bags of grass in 40 days. In how many days one sheep will eat one bag of grass?
(A) 1
(B) 20
(C) 40
(D) 80
(E) 70
Rationale: Explanation :
Let the required number of days be x.
Less sheep, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
Sheep 1 : 40 :: 40 : x
Bags 40 : 1
1 x 40 x x = 40 x 1 x 40
x = 40.
Answer : C
Answer: (C) 40
Question: Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
(A) 10 Kmph
(B) 15 Kmph
(C) 25 Kmph
(D) 27 Kmph
(E) 30 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distence of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
B
Answer: (B) 15 Kmph
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 850
(B) 860
(C) 890
(D) 900
(E) 950
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Option B
Answer: (B) 860
Question: If (1/5)^m * (1/4)^4 = 1/(16*(10)^4), then m =
(A) 3
(B) 2
(C) 1
(D) 4
(E) 8
Rationale: (1/5)^m (1/4)^4 = 1/{16(10)^4}
16(10)^4/4^4 = 5^m
[16(2^4)(5^4)]/[2^8] = 5^m
5^4 = 5^m
m=4
D
Answer: (D) 4
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 4x km.
(A) 25kmph
(B) 30kmph
(C) 32kmph
(D) 40kmph
(E) 42kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 4x/(x/8)
= 32 kmph
Answer:C
Answer: (C) 32kmph
Question: Suzy has a lot of skeins of yarn, she has blue, yellow, and red yarn. She has twice as much blue yarn as yellow yarn, and she has twice as much yellow yarn as she has red yarn. If she has X skeins of yarn, how many of the skeins are red, in terms of X?
(A) X/8
(B) X/7
(C) X/6
(D) X/5
(E) X/4
Rationale: Since the total number of skeins is X, then X = Blue + Yellow + Red
Because there are twice as many Blue as Yellow, then Blue = 2*Yellow
Thus X = 2*Yellow + Yellow + Red, which simplifies to X = 3*Yellow + Red
Because there are twice as many Yellow as Red, then Yellow = 2*Red
Thus X = 3*(2*Red) + Red, which simplifies to X = 7*Red
Therefore Red = X/7
Answer: B
Answer: (B) X/7
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 15 kmph
(B) 11 kmph
(C) 16 kmph
(D) 18 kmph
(E) 19 kmph
Rationale: Speed of the boat in still water = (50+80)/2 = 65 kmph. Speed of the stream = (80-50)/2 = 15 kmph.Answer: A
Answer: (A) 15 kmph
Question: The ratio, by volume, of bleach(B) to detergent(D) to water in a certain solution is 2 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
(A) 60
(B) 50
(C) 40
(D) 80
(E) 70
Rationale: B:D:W = 2:40:100
Bnew / Dnew = (1/3)*(2/40) = (1/60)
Dnew / Wnew = (1/2)*(40/100) = (1/5)
Wnew = 300
Dnew = Wnew/5 = 300/5 = 60
So, answer will be
A
Answer: (A) 60
Question: If m<0, which of the following represents a positive number?
(A) -d|d|
(B) d/ |d|
(C) |d|d
(D) |d|/d
(E) d|d|
Rationale: Answer : A
Answer: (A) -d|d|
Question: Find the simple interest on $10000 at 7% per annum for 12 months?
(A) $410
(B) $500
(C) $650
(D) $700
(E) $1000
Rationale: P = $10000
R = 7%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*7*1/100 = $700
Answer is D
Answer: (D) $700
Question: In how many ways can the letters D, G, G, I, T be arranged so that the two I's are not next to each other?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 128
Rationale: 1 D
2 I
1 G
1 T
Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60
Consider 2 Is as 1 entity and thus the number of arrangements for (GG)DIT = 4! = 24
Total allowed cases = 60-24 =36
A is the correct answer.
Answer: (A) 36
Question: A positive integer x has 60 divisors and 7x has 80 divisors. What is the greatest integer y such that 7y7y divides n?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Total number of factors of x = 60 = (p+1)*(q+1)*(r+1)... = 2^2 * 3 * 5
Now note that 7x has only one 7 more than x. The number of all other prime factors stays the same.
Total number of factors of 7x = 80 = (p+2)*(q+1)*(r+1)... = 2^4 * 5
Here, the 3 of previous expression has disappeared so it must have converted to 4. Does it make sense? Let's see:
Total number of factors of x = 60 = 2^2 * 3 * 5 = (3+1)*(2+1)*(4+1)
Total number of factors of 7x = 80 = 2^2 * 4 * 5 = (3+1)*(3+1)*(4+1)
The powers of other factors stay the same. Only the power of 7 increases by 1. So initially, in x, the power of 7 must have been 2. Hence the maximum value of y must be 2.
Answer (C)
Answer: (C) 2
Question: A third of Arunâ€™s marks in mathematics exceed a half of his marks in English by 10.If he got 230 marks in two subjects together how many marks did he got in English?
(A) 140,90
(B) 180,60
(C) 160,90
(D) 150,80
(E) None of them
Rationale: Let Arunâ€™s marks in mathematics and English be x and y
Then (1/3)x-(1/2)y=10
2x-3y=60â€¦â€¦>(1)
x+y=230â€¦â€¦.>(2)
solving (1) and (2)
x=150
and y=80
Answer is D.
Answer: (D) 150,80
Question: The length of the ribbon was originally 55cm. It was reduced in the ratio 11 : 7. What is its length now?
(A) 6 cm
(B) 12 cm
(C) 35 cm
(D) 44 cm
(E) None of these
Rationale: Explanation :
Length of ribbon originally = 55 cm
Let the original length be 11x and reduced length be 7x.
But 11x = 55 cm
x = 55/11 cm = 5 cm
Therefore, reduced length = 7x cm
= 7 5 cm = 35 cm
Answer : C
Answer: (C) 35 cm
Question: The C.P of 10 pens is equal to the S.P of 14 pens. Find his gain % or loss%?
(A) loss 16 2/8%
(B) loss 28.57%
(C) loss 16 2/3%
(D) loss 18 2/3%
(E) loss 16 25%
Rationale: 10 CP = 14 SP
14 --- 4 CP loss
100 --- ? => 28.57% loss
Answer:B
Answer: (B) loss 28.57%
Question: John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/1 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
(A) 45
(B) 65
(C) 98
(D) 107
(E) 198
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 1 x 60 ) = 60.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 60 x + 20 x + 15 x + 12 x) = 107 x.
For minimum number of pencils x = 1 .
The person should have at least 107 pencils.
D)
Answer: (D) 107
Question: If x and y are odd integers, which of the following must always be a non-integer
(A) x^2 y
(B) -x^2y
(C) y/x
(D) xy/4
(E) x/y
Rationale: as X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/4 will always be non integer.
D
Answer: (D) xy/4
Question: What is the compound interest paid on a sum of Rs.3500 for the period of 2 years at 10% per annum.
(A) 630
(B) 735
(C) 825
(D) 600
(E) None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Total % of interest= 10 + 11=21
Total interest = 21 % 3500 = 3500* (21/100)= 735
Answer B
Answer: (B) 735
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 4860. What was the number of original inhabitants?
(A) 7000
(B) 7200
(C) 7400
(D) 7600
(E) 7800
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 4860
(27/40) * x = 4860
x = 4860 * 40 / 27 = 7200
The answer is B.
Answer: (B) 7200
Question: Which of the following points is symmetric with y=x at (-2,-3)?
(A) (-3,-2)
(B) (-2,1)
(C) (2,1)
(D) (-1,-2)
(E) (-1,2)
Rationale: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(-2,-3) would become (-3,-2).
Answer (A).
Answer: (A) (-3,-2)
Question: Find the odd man out. 12, 24, 34, 48, 64, 84
(A) 34
(B) 48
(C) 24
(D) 12
(E) 64
Rationale: All numbers except 34 are multiples of 4
Answer is A
Answer: (A) 34
Question: In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20 m
(B) 22 m
(C) 32 m
(D) 40 m
(E) 30 m
Rationale: Distance covered by B in 9 sec. =(100/45 x 9) m = 20m
THEREFORE - A beats B by 20 metres.
ANSWER:A
Answer: (A) 20 m
Question: John purchased some shirts and trousers for $800. He paid $400 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 10
Rationale: Given that the total purchase of two items cost 800.
So the average purchase of one item will cost 800/2 = 400.
Its given as total shirt cost 400$ less. Hence Total Shirt cost = 400 - 200 and Total trouser cost = 400 + 200
5 shirts = 200$ ==> One shirt = 40$
One trouser = 40 + 20 = 60$
Total trousers = 600 / 60 =10.
E
Answer: (E) 10
Question: A man spends 1/3rd of his salary on food. he spends 1/4th on rent and 1/5th on cloths. If he is left with 1760, then who much salary does he earn.
(A) 8120
(B) 8123
(C) 8222
(D) 8322
(E) 8422
Rationale: let salary be x
total spent=( x/3 + x/4 +x/5 )= (47/60)*x
left = (x-47x/60)=(13/60)*x
given,(13/60)*x = 1760
x=(1760*60)/13=8123.077=8123(approax)
ANSWER:B
Answer: (B) 8123
Question: A car gets 24 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 12 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
(A) 96
(B) 100
(C) 104
(D) 108
(E) 112
Rationale: Originally, the distance the car could go on a full tank was 12*24=288 miles.
After it has been modified, the car can go 24/0.75=32 miles per gallon.
On a full tank, the car can go 32*12= 384 miles, thus 96 miles more.
The answer is A.
Answer: (A) 96
Question: 62, 60, 55, 53, 48, 46, ?
(A) 15
(B) 23
(C) 41
(D) 25
(E) 28
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : C.
Answer: (C) 41