mathewhe/aqua_rat huggingface dataset:
Question: What is the area of a right angle triangle with base = 12 and height = 14 ?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: Since the area of a right angle triangle is 1/2 * base * height
Area = 1/2 * 12 * 14
= 84
Ans: E
Answer: (E) 84
Question: Of the three-digit integers greater than 600, how many have distinct digits ?
(A)  90
(B)  82
(C)  80
(D)  45
(E) 288
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 600 to 999 = 299 (3-digit numbers greater than 600);
A. all digits are distinct = 4*9*8=288
Answer: E
Answer: (E) 288
Question: a/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 2, 3, or 6. What is the largest possible value of the expression?
(A) 2/18
(B) 6/3
(C) 30/2
(D) 18/2
(E) 6/18
Rationale: a/(b/c)
= (a*c)/b
The expression will have the largest value when numerator (a*c) is the largest.
=(6*3)/2
=18/2
Answer D
Answer: (D) 18/2
Question: A certain quantity of 45% concentration solution is replaced with 15% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
(A) 1:3
(B) 1:2
(C) 2:3
(D) 2:1
(E) 3:1
Rationale: 15% - - - - - - - - - 35% - - - - - - 45%
From 15 to 35 =20
From 35 to 45 = 10
So the ratio is 20/10 = 2 to 1
B it is
Answer: (B) 1:2
Question: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
(A) 5
(B) 7
(C) 4
(D) 8
(E) 6
Rationale: Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20)
so there will be 6 significant digits to the right of the decimal point.
Answer is E.
Answer: (E) 6
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 8:3. The sum of numbers is:
(A) 22
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be 8x and 3x.
Then, their L.C.M = 24x. So, 24x = 48 or x = 2.
The numbers are 16 and 6.
Hence, required sum = (16 + 6) = 22.
ANSWER:A
Answer: (A) 22
Question: Triangle STV has sides ST = TV = 25, and SV = 14. What is the area?
(A) 144
(B) 168
(C) 176
(D) 190
(E) 206
Rationale: Let the base B of the triangle be SV = 14. Then we need to find the height H.
H^2 = 25^2 - 7^2 = 576 and then H = 24.
The area is (1/2)*B*H = 7*24 = 168
The answer is B.
Answer: (B) 168
Question: Christine selects an item at a 25% off ticket price sale. The item is ticket priced at $25. How much should Christine expect to pay at the register?
(A) 22.5
(B) 20.0
(C) 18.75
(D) 12.5
(E) 10.0
Rationale: R.P.=$25.00
Sale%=25
S.P.=R.P.*(1-(Sale%/100))=25*(1-(25/100))=18.75
ANSWER:C
Answer: (C) 18.75
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
(A) 529 sq m
(B) 240 sq m
(C) 260 sq m
(D) 480 sq m
(E) 580 sq m
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
ANSWER:D
Answer: (D) 480 sq m
Question: A person has to cover a distance of 10km in 1hour. If he covers one half of the distance in half of the total time; to cover the remaining distance in the remaining time, his speed must be?
(A) 5km/hr
(B) 8km/hr
(C) 10km/hr
(D) 12km/hr
(E) 15km/hr
Rationale: Remaining distance = 5km
Remaining time = 1/2 * 60 = 30min = 1/2 hour
Required speed = 5*2 = 10km/hr
Answer is C
Answer: (C) 10km/hr
Question: If integer k is equal to the sum of all even multiples of 25 between 295 and 615, what is the greatest prime factor of k?
(A) 5
(B) 7
(C) 11
(D) 13
(E) 17
Rationale: if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600.
using arithmetic progression to find n : 600 = 300 + (n - 1) 50
300+ 50 = 50n
350 = 50n => n = 7
the sum would be: 11* mean
mean = [600 + 300] / 2 = 450
7*450 = 4950
B
Answer: (B) 7
Question: A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.
(A) 4360
(B) 4460
(C) 4560
(D) 4660
(E) 4760
Rationale: Let the sum be Rs.P.then
P(1+R/100)3=6690 …(i) P(1+R/100)6=10035…(ii)
On dividing,we get (1+R/100)3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is Rs.4460. answer : B
Answer: (B) 4460
Question: In the Land of Oz only one or two-letter words are used. The local language has 69 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
(A) 65
(B) 66
(C) 67
(D) 131
(E) 138
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 69 letters is 69;
The number of 2 letter words (XX) that can be made from 69 letters is 69*69, since each X can take 69 values.
Total: 69+69*69.
Similarly:
The number of 1 letter words (X) that can be made from 68 letters is 68;
The number of 2 letter words (XX) that can be made from 68 letters is 68*68, since each X can take 68 values.
Total: 68+68*68.
The difference is (69+69*69)-(68+68*68)=138.
Answer: E.
Answer: (E) 138
Question: Two pipes A and B can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 18 hours
(B) 15 hours
(C) 10 hours
(D) 12 hours
(E) 8 hours
Rationale: Part filled by A in 1 hour = 1/30
Part filled by B in 1 hour = 1/45
Part filled by (A+B) in 1 hour = 1/30 + 1/45 = 5/90 = 1/18
Both the pipes together fill the tank in 18 hours
Answer is A
Answer: (A) 18 hours
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
(A) r / (r + b + w)
(B) (r + b + w)
(C) r * (r + b + w)
(D) (r + b + w)/r
(E) None
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Answer: (A) r / (r + b + w)
Question: The sum of two numbers is 56, and one of them is 12 more than the other. What are the two numbers?
(A) 36-48
(B) 22-34
(C) 60-24
(D) 42-42
(E) 21-63
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 56:
word problem = 56
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 56 âˆ’ 12
= 44.
x = 44/2
= 22.
This is the first number. Therefore the other number is
x + 12 = 22 + 12 = 34.
The sum of 22 + 34 is 56.
B
Answer: (B) 22-34
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $200 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $245 as interest. What was the value of his total savings before investing in these two bonds?
(A) 4000
(B) 3500
(C) 2500
(D) 3000
(E) 2000
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $100, thus 0.2x = $100 --> x = $1,000.
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,000 = $2,000
Answer E
Answer: (E) 2000
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
(A) 876 km
(B) 224 km
(C) 657 km
(D) 176 km
(E) 168 km
Rationale: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: B
Answer: (B) 224 km
Question: Find the sum of first 20 natural numbers
(A) 470
(B) 210
(C) 465
(D) 463
(E) 485
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)/2
=20(20+1)/2=20(21)/2=210
Answer: Option B
Answer: (B) 210
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-3, 1), (1, 1), (1, -2) and (-3, -2)?
(A) 12
(B) 24
(C) 20
(D) 30
(E) 36
Rationale: Length of side 1= 3+1=4
Length of side 2= 2+1= 3
Area of rectangle= 4*3= 12
A is the answer
Answer: (A) 12
Question: If 6^k = 4, then 6^(2k+3) =
(A) 2925
(B) 3456
(C) 4581
(D) 3683
(E) 1308
Rationale: 6^k=4
6^2k=4^2
6^2k=16
6^(2k+3)
=6^2k*6^3
=16*216
=3456
Answer: B
Answer: (B) 3456
Question: Magnabulk Corp sells boxes holding y magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
(A) 100by/m
(B) m/(by)
(C) by/(100m)
(D) 100m/(by)
(E) by/m
Rationale: We're given some facts to work with:
1) Magnabulk Corp sells boxes holding Y magnets each.
2) The boxes are shipped in crates, each holding B boxes.
3) Magnabulk charges M DOLLARS for each crate
We're asked for the price charged per magnet, in CENTS....
IF....
Y = 2
B = 3
M = 12
(2 magnets per crate)(3 crates) = 6 magnets
$12 for 6 magnets = $2 per magnet = 200 cents per magnet
So we're looking for an answer that equals 200 when Y=2, B=3 and M=12. There's only one answer that matches...
Answer is D
Answer: (D) 100m/(by)
Question: If x and y are integers and 2x–y= 11, then 4x+ y CANNOT be
(A) –5
(B) 1
(C) 13
(D) 17
(E) 55
Rationale: 2x-y=11
2x=11+y
4x=22+2y
now we need to check the value of 4x+4 => 22+2y+y=22+3y
hence 22+3y=value(in the options)
so y=value-22/3
so checking the options only D is unfit
ANSWER:D
Answer: (D) 17
Question: In how many ways can seven different rings be worn on four fingers of one hand?
(A) 10
(B) 12
(C) 35
(D) 16
(E) 18
Rationale: Required number of ways = ways of selecting 4 objects out of 7 given objects
= 7C4 = 7*6*5*4/24= 35
Answer C
Answer: (C) 35
Question: The ages of two person differ by 12 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
(A) 30, 10
(B) 25, 5
(C) 29, 9
(D) 50, 30
(E) 20, 8
Rationale: Let their ages be x and (x + 12) years.
Then, 5(x - 5) = (x + 12 - 5)
=> 4x = 32
=>x =8
Their present ages are 20 years and 8 year.
ANSWER:E
Answer: (E) 20, 8
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 14 households had a both a car and a bike and 44 had a car, how many had bike only?
(A) 30
(B) 35
(C) 20
(D) 18
(E) 10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-14+11 --> {Bike}=49 --> # those who have bike only is {Bike}-{Both}=49-14=35.
Answer: B.
Answer: (B) 35
Question: The volume of a box with a square base is 128 cubic cm. The area of the base of the box is 8 inches more than the height. What is the length of the base of the box?
(A) 4 cm
(B) 8 cm
(C) 16 cm
(D) 24 cm
(E) None of the above
Rationale: l x w x h = 64
l x w - 8 = h
l=w
Solving the 3 equations we get Area of Base = 16 square cm and height = 8 cm, which means length = 4 cm and width = 4 cm
Correct Answer: A
Answer: (A) 4 cm
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
(A) 588 apples
(B) 742 apples
(C) 750 apples
(D) 600 apples
(E) 700 apples
Rationale: Suppose originally he had X apples.
Then, (100 - 40)% of X = 420.
60/100 x X = 420
x =(420 x 100)/60= 700.
answer E
Answer: (E) 700 apples
Question: In a certain random experiment, exactly one of the outcomes A, B, and T will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and T will occur twice?
(A) 5/243
(B) 1/12
(C) 10/81
(D) 1/6
(E) 16/81
Rationale: Number of ways in which a group of 2A,2B,2T can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/T; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: (C) 10/81
Question: A squirrel has 13 nuts, then he finds 8 more nuts. Now how many nuts he have?
(A) 5
(B) 9
(C) 21
(D) 11
(E) 16
Rationale: 13+8=21. Answer is C
Answer: (C) 21
Question: If a, p, q, and r are positive integers and (p)×(q)×(r)=a^2, which of the following could be the values of p, q, and r?
(A) 3, 16, 25
(B) 9, 25, 24
(C) 2, 25, 32
(D) 2, 9, 16
(E) 8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*25*32 = 2*5*5*8*4 = 5*5*8*8
ans C
Answer: (C) 2, 25, 32
Question: Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is
(A) 12
(B) 24
(C) 36
(D) 46
(E) 52
Rationale: Let the angles be a, ar, ar 2, ar 3.
Sum of the angles = a ( r 4- 1 ) /r -1 = a ( r 2 + 1 ) ( r + 1 ) = 360
a< 90 , and ar< 90, Therefore, a ( 1 + r ) < 180, or ( r 2 + 1 ) > 2
Therefore, r is not equal to 1. Trying for r = 2 we get a = 24
Therefore, The angles are 24, 48, 96 and 192.
ANSWER:B
Answer: (B) 24
Question: Jack and Christina are standing 270 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 4 feet per second and Christina walks in a straight line toward Jack at a constant speed of 5 feet per second. Lindy runs at a constant speed of 8 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
(A) 150
(B) 180
(C) 210
(D) 240
(E) 270
Rationale: The relative speed of Jack and Christina is 4 + 5 = 9 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 270/7 = 30 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 8*30 = 240 feet.
Answer: D.
Answer: (D) 240
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fell ill for the next five daysreducing the daily avg for the month to 58 sets/day. The average production perday for day last 5days is ?
(A) 36
(B) 39
(C) 48
(D) 50
(E) 53
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: (C) 48
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Q of the sequence?
(A) 360
(B) 365
(C) 369
(D) 374
(E) 383
Rationale: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term Q, t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Answer: (D) 374
Question: At exactly what time past 5:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 7:00
(B) 20 13/17 minutes past 7:00
(C) 21 9/11 minutes past 5:00
(D) 21 9/11 minutes past 7:00
(E) 22 4/9 minutes past 7:00
Rationale: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?
That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 5:00. At 5:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.
So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.
Thus, C is the correct answer.
Answer: (C) 21 9/11 minutes past 5:00
Question: find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.
(A) 214
(B) 216
(C) 114
(D) 116
(E) 118
Rationale: Explanation:
Let the number is x,
=>2/3x−50=1/4x+40
<=>2/3x−1/4x=90
<=>5x/12=90
<=>x=216
Option B
Answer: (B) 216
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 900 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
(A) 8/3
(B) 3/8
(C) 8/5
(D) 4/1
(E) 5/3
Rationale: Distance traveled by Eddy = 900 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 900/3 = 300 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 300/75 = 4/1
Answer D
Answer: (D) 4/1
Question: To furnish a room in a model home an interior decorator is to select 3 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 100 different combinations are possible, how many tables are there in the warehouse?
(A) A)5
(B) B)8
(C) C)10
(D) D)15
(E) E)30
Rationale: Total number of ways to choose 3 chairs from 5= 5C3=10
Total number of combination=100
That means we need get 10 combinations from the selection of tables....
Screening through the answers.... 5C2=10..... 10*10=100
Answer is 5... A
Answer: (A) A)5
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 22000
(C) 24000
(D) 25000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: Pipe A that can fill a tank in an hour and pipe B that can fill the tank in 15 are opened simultaneously when the tank is empty. Pipe B is shut 15 minutes before the tank overflows. When will the tank overflow?
(A) 40 mins
(B) 35 mins
(C) 30 mins
(D) 32 mins
(E) 36 mins
Rationale: The last 15 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.
The combined rate of two pipes is 1 + 4 = 5 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/5 = 3/20 hours = 15 minutes.
Total time = 15 + 15 = 30 minutes.
Answer: C
Answer: (C) 30 mins
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 1 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
(A) 37/20
(B) 1/2
(C) 1/4
(D) 1
(E) 5/6
Rationale: A+B =6/5 ; A+C =3/2 ,B+C =1 ; ADD THEN 2*(A+B+C) = 6/5+3/2+1 =37/10
A+B+C = 37/20 HRS
A
Answer: (A) 37/20
Question: What is the difference between the place value of 5 in the numeral 15295?
(A) 5005
(B) 495
(C) 4995
(D) 505
(E) 4115
Rationale: Difference between the place values of 5 = 5000-5 = 4995
Answer is C
Answer: (C) 4995
Question: In a certain game, a player begins with a bag containing tiles numbered 1 through 9, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
(A) 5/18
(B) 13/36
(C) 3/8
(D) 5/8
(E) 23/36
Rationale: player begins with containing tiles 1 to 10 and have equal probability of selecting means
Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.
Next , player draws one title , if number is even player stops or otherwise title is odd without replacement
player draws second title.
If second title is even , player stops or title is odd without replacement player draws third title.
in third title , without replacement of first and second title, player draws and stops it.
the sum of tilte probability is odd. here two conditions are possible.
1st condition is
1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.
Here are we are not selecting 1st condition as even stops because sum of tile is odd.
Here 5 odd numbers are there we can select 1out of 5 odd numbers.
without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.
here we are selecting one number out of remaining 9 numbers. so probability is 5/18.
we are selecting 1 even number out of 5.
2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.
Then probability is 5/10*4/9*3/8=1/12.
Finally sum of probability of two conditions is 5/18+1/12
=5/8.
so option D is correct.
Answer: (D) 5/8
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed seven times, what is the probability that the coin turns up tails on at least one of the tosses?
(A) 7/8
(B) 15/16
(C) 31/32
(D) 63/64
(E) 127/128
Rationale: P(7 heads)= 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128.
P(at least one tail)=1-1/128=127/128.
The answer is E.
Answer: (E) 127/128
Question: 5 goats’s and 10 hens are brought for Rs.2500. If the average price of a hen be Rs.50. What is the average price of a goat.
(A) 425
(B) 375
(C) 350
(D) 400
(E) 500
Rationale: Explanation:
Average price of a hen = Rs.50
total price of 10 hens = 10*50 = Rs.500
But total price of 5 goats and 10 hens = Rs. 2500
Total price of 5 goats is = 2500 - 500
= 2000
Average price of a goat = 2000/5
= Rs. 400
Answer: D
Answer: (D) 400
Question: The price of sugar is increased by 4%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
(A) (300/103) %
(B) (400/104) %
(C) (100/107)%
(D) (7/100)%
(E) (100/700)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $104.
We want the spendings to remain at $100.
(New consumption)*104 = 100 --> (New consumption) = 100/104 kg.
Percent decrease = Change/Original *100 = (1 - 100/104)/1*100 = 400/104%.
Answer: B.
Answer: (B) (400/104) %
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?
(A) 20%
(B) 26%
(C) 42%
(D) 29%
(E) 22%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 86
2/3 SP1 = 86
SP1 = 129
100 --- 29 => 29%
Answer: D
Answer: (D) 29%
Question: A reduction of 5% in the price of oil enables a house wife to obtain 10kgs more for Rs.5000, what is the reduced price for kg?
(A) 23
(B) 27
(C) 25
(D) 35
(E) 15
Rationale: 5000*(5/100) = 250 ---- 10
? ---- 1 => Rs.25
Answer:C
Answer: (C) 25
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:6then find the smallest number?
(A) 22/3
(B) 19/3
(C) 20/3
(D) 25/3
(E) 24/3
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 6
6[2x + 10] = 5[3x + 10]
12x + 60 = 15x + 50
15x -12x = 60 - 50
3x = 10, then X=10/3
Then the first number is = 2
2x = 10
Option C
Answer: (C) 20/3