mathewhe/aqua_rat huggingface dataset:
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference would have been how much?
(A) 40/3
(B) 40
(C) 120
(D) 360
(E) 420
Rationale: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference = (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D
Answer: (D) 360
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $9.95 each. One day, she bought 20 t-shirts. How much money did she spend?
(A) $150
(B) $248.75
(C) $199
(D) $171.6
(E) $190
Rationale: $9.95*20=$199. Answer is C.
Answer: (C) $199
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 2 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 4.8 km
(C) 3.4 km
(D) 4.4 km
(E) 5.6 km
Rationale: Explanation:
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph
Let the required distance be x km
Total time taken = 2 hour
â‡’ x/6+x/4=2
â‡’2x+3x=24
â‡’5x=24
â‡’x=4.8 km
Answer: Option B
Answer: (B) 4.8 km
Question: A van takes 5 hours to cover a distance of 600 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?
(A) 80
(B) 84
(C) 88
(D) 92
(E) 96
Rationale: (3/2)*5 = 7.5 hours
600 / 7.5 = 80 kph
The answer is A.
Answer: (A) 80
Question: The sum of the ages of 5 children born at the intervals of 3 year each is 50 year. what is the age of the eldest child ?
(A) 16 year
(B) 8 year
(C) 10 year
(D) None of these
(E) 9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 â‡” 5 x = 20 â‡” x= 4.
âˆ´ Age of the eldest child = x+12 = 4 +12 =16 years. Answer A
Answer: (A) 16 year
Question: A batsman makes a score of 110 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
(A) 40
(B) 50
(C) 60
(D) 45
(E) 56
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+110 = 11x
x = 110-50 = 60
Answer is C
Answer: (C) 60
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(A) 47200
(B) 48000
(C) 42000
(D) 50400
(E) 65400
Rationale: Explanation:
The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
Number of ways to arrange these letters
=7!2!=7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—12Ã—1=2520=7!2!=7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—12Ã—1=2520
In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves =5!3!=5Ã—4Ã—3Ã—2Ã—13Ã—2Ã—1=20=5!3!=5Ã—4Ã—3Ã—2Ã—13Ã—2Ã—1=20
Hence, required number of ways
=2520Ã—20=50400=2520Ã—20=50400
ANSWER IS D
Answer: (D) 50400
Question: In a factory, there are 80% technicians and 20% non-technicians. If the 80% of the technicians and 20% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 62%
(B) 68%
(C) 52%
(D) 22%
(E) 42%
Rationale: Total = 100
T= 80 NT= 20
80*(20/100)=24 80*(20/100)=24
16 + 16 = 32 => 100 - 32 = 68%
Answer:B
Answer: (B) 68%
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,80,000 as total savings, how much has he saved in Public Provident Fund?
(A) 81000
(B) 85000
(C) 75000
(D) 72000
(E) 77000
Rationale: Let savings in National Savings Certificate = x
and savings in Public Provident Fund = (180000 - x)
1/3x=1/2(180000−x)
⇒2x=3(180000−x)
⇒2x=540000−3x
⇒5x=540000
⇒x=540000/5=108000
Savings in Public Provident Fund = (180000 - 108000) = 72000
Answer is D.
Answer: (D) 72000
Question: The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then
(A) None of these
(B) x = y + z
(C) 2x = y + z
(D) x = 2y + 2z
(E) x = y + 2z
Rationale: Explanation:
Average of 6 numbers = x
=> Sum of 6 numbers = 6x
Average of the 3 numbers = y
=> Sum of these 3 numbers = 3y
Average of the remaining 3 numbers = z
=> Sum of the remaining 3 numbers = 3z
Now we know that 6x = 3y + 3z
=> 2x = y + z
Answer: Option C
Answer: (C) 2x = y + z
Question: In how many ways 2 students can be chosen from the class of 20 students?
(A) 190
(B) 180
(C) 240
(D) 390
(E) None
Rationale: Solution: Number of ways = 20C2 = 20!/(2! 18!)
= 20*19/2
= 190.
Answer: Option A
Answer: (A) 190
Question: 1939392 * 625
(A) 1212120010
(B) 1212120000
(C) 1212120011
(D) 1212121010
(E) 1212121000
Rationale: Explanation:
Trick: when multiplying with
5n
5n
then put n zeros to the right of multiplicand and divide the number with
2n
2n
So using this we can solve this question in much less
time.
1939392×5(4)=1939392000016=1212120000
Option B
Answer: (B) 1212120000
Question: In how many different number of ways 4 man and 3 woman can sit on a bench such that girls always sit together.
(A) 700
(B) 720
(C) 730
(D) 750
(E) 770
Rationale: Option 'B'
Answer: (B) 720
Question: Two employees X and Y are paid a total of Rs. 440 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.150
(B) s.200
(C) s.250
(D) s.350
(E) s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 440
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 440
â‡’ y[12/10 + 1] = 440
â‡’ 22y/10 = 440
â‡’ 22y = 4400
â‡’ y = 4400/22 = 400/2 = Rs.200
B)
Answer: (B) s.200
Question: Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case
(A) 4
(B) 7
(C) 9
(D) 13
(E) 15
Rationale: Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
ANSWER IS A
Answer: (A) 4
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 6
(B) 5
(C) 7
(D) 8
(E) 2
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer:C
Answer: (C) 7
Question: A cube of side one meter length is cut into small cubes of side 20 cm each. How many such small cubes can be obtained?
(A) 2878
(B) 2778
(C) 1000
(D) 120
(E) 125
Rationale: Along one edge, the number of small cubes that can be cut
= 100/20 = 5
Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 5 * 5 * 5 = 125
Answer: E
Answer: (E) 125
Question: A man sold 18 toys for Rs. 25200, gaining thereby the cost price of 3 toy find the cost price of a toy
(A) s. 600
(B) s. 800
(C) s.500
(D) s.900
(E) s. 1200
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 25200.
Gain = SP â€“ CP
3X = 25200 â€“ 18X
21X = 25200
X = Rs. 1200.
ANSWER : OPTION E
Answer: (E) s. 1200
Question: If in a certain sequence of consecutive multiples of 50, the median is 625, and the greatest term is 850, how many terms that are smaller than 625 are there in the sequence?
(A) 5
(B) 7
(C) 8
(D) 12
(E) 13
Rationale: Since the median is 625 we know there must be a even number of integers because 50 is not a multiple of 625.
So the list around 625 must go. 600 (625) 650 700 750 800 850
Since we know there are 5 numbers greater than 625 then there must be 5 numbers less then 625.
A
Answer: (A) 5
Question: 23,8,34,81,33,...
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: 23 : 2^3=8
34 : 3^4=81
33 : 3^3=27
ANSWER:D
Answer: (D) 27
Question: If 2ab - 3c = 2a(b - c), which of the following must be true?
(A)  a=3/2 and c=0
(B)  a=1/2 and b=2
(C)  b=1 and c=0
(D)  a=1 or b=0
(E)  a=1/2 or c=0
Rationale: 2ab-3c = 2a (b-c)
2ab - 3c = 2ab - 2ac
3c= 2ac
2ac-3c = 0
c(2a-3) = 0
Either c = 0; or a = 3/2
A is the answer
Answer: (A)  a=3/2 and c=0
Question: Anita has 360 apples. There are 60 students are studying in her class. She would like to give each student the same amount of apples, how much should she give to each student?
(A) 12
(B) 6
(C) 9
(D) 15
(E) 7
Rationale: 360/60 = 6
The answer is B.
Answer: (B) 6
Question: Find the length of the wire required to go 11 times round a square field containing 27889 m2.
(A) 7348
(B) 3388
(C) 2667
(D) 8766
(E) 66711
Rationale: a2 = 27889 => a = 167
4a = 668
668 * 11 = 7348
Answer: A
Answer: (A) 7348
Question: Mary received a 20% raise each month for three consecutive months. What was her salary after the three raises if her starting salary was $1,000 per month?
(A) $1,348
(B) $1,500
(C) $1,631
(D) $1,728
(E) $1,863
Rationale: 1000 * 1.2 * 1.2 * 1.2 = 1000 * 1.728 = 1728
Answer: D
Answer: (D) $1,728
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
(A)  5
(B)  9
(C)  10
(D)  12
(E)  15
Rationale: This is an inverse proportional problem......
5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10
So, 10-5 = 5
Answer A
Answer: (A)  5
Question: A can do a work in 9 days and B can do the same work in 18 days. If they work together, in how many days will they complete the work?
(A) 6 days
(B) 7 days
(C) 5 days
(D) 3 days
(E) 2 days
Rationale: One day's work of A and B = 1/9 + 1/8 = (2+1)/18 = 1/6 So, the time taken to complete the work is 6 days.
Answer:A
Answer: (A) 6 days
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 15 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter of liquid A was contained by the can initially?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Ci*Vi = Cf*Vf
(7/12)*(V1 - 15) = (7/16)*V1
(V1 - 15)/V1 = 3/4
15 accounts for the difference of 1 on ratio scale so Initial volume = V1 = 4*15 = 60 litres.
7/12 of the initial mixture was liquid A so liquid A was (7/12)*60 = 35 litres.
Answer : B
Answer: (B) 35
Question: The compound interest on Rs. 20,000 at 8% per annum is Rs. 3,328. What is the period (in year)?
(A) 1 year
(B) 4 years
(C) 3 years
(D) 2 years
(E) 5 years
Rationale: Explanation:
Let the period be n years.
Amount after n years = Rs.20000 + Rs.3328 = Rs. 23328
P(1+R/100)T=23328
20000(1 + 8/100)n = 23328
20000(108/100)n = 23328
(108/100)n = 23328/20000 = 11664/10000 = (108/100)2
n = 2 years
Answer: Option D
Answer: (D) 2 years
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
(A) 23
(B) 27
(C) 30
(D) 32
(E) 34
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
B)
Answer: (B) 27
Question: How many 7s are there in the following series which are not immediately following by 3 but immediately preceded by 8?
8 9 8 7 6 2 2 6 3 2 6 9 7 3 2 8 7 2 7 7 8 7 3 7 7 9 4
(A) Nil
(B) One
(C) Two
(D) Three
(E) More than three
Rationale: 876 and 872
ANSWER:C
Answer: (C) Two
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 30 in two years, at the same percent rate per annum?
(A) s. 20
(B) s. 48
(C) s. 42
(D) s. 20
(E) s. 60
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 30
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(30 – 20) / 20] * 100
= 50 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 50% p.a.
SI = (PRT/100)
20 = (X*50*2) / 100
X = Rs. 20
ANSWER: A
Answer: (A) s. 20
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 26 sec
(B) 28 sec
(C) 12 sec
(D) 77 sec
(E) 66 sec
Rationale: D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: C
Answer: (C) 12 sec
Question: If the function Q is defined by the formula Q = 5w/(4m(z^2)), by what factor will Q be multiplied if w is quadrupled, m is doubled, and z is tripled?
(A) 1/9
(B) 2/9
(C) 4/9
(D) 3/9
(E) 2/27
Rationale: We just need to find the factor thats all,
w -> quadrupled -> 4w
m-> doubled -> 2m
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
W is in numerator, and m*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B
Answer: (B) 2/9
Question: Three partners A,B & C invested total Rs. 1,15,000. After one year one olhem gets a profit of Rs.6000, second gets Rs. 10,000 and third gets Rs. 14000 then how much amount did B invested?
(A) Rs.10,000
(B) Rs.40,000
(C) Rs.20,000
(D) Rs.50,000
(E) none
Rationale: 3:5:7 is thr ratio's of their profits
(5/15)*115000
ans is 38333.3
ANSWER:E
Answer: (E) none
Question: (74 + 75 + 76 + 77 + ..... + 149 + 150) = ?
(A) 8624
(B) 8634
(C) 8654
(D) 8644
(E) 8677
Rationale: Explanation:
Sum of first n natural numbers
= (1 + 2 + 3 + ..... + n) = n(n+1)/2
(74 + 75 + 76 + .....+ 150)
=(1 + 2 + .... + 73 + 74 + 75 + .....+ 150) - (1 + 2 + .... + 73)
=(1/2 x 150 x 151) - (1/2 x 73 x 74)
= 11325 - 2701 = 8624
Answer: Option A
Answer: (A) 8624
Question: Rectangular tile each of size 45cm by 50cm must be laid horizontally on a rectangular floor of size 250cm by 180cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 35
(B) 40
(C) 25
(D) 18
(E) 20
Rationale: Area of tile = 45*50 = 2250
Area of floor = 250*180 = 45000
No of tiles = 45000/2250 = 20
So, the no of tile =20
ANSWER:E
Answer: (E) 20
Question: The speeds of three motor bikes are in the ratio 12 : 4 : 6. The ratio between the time taken by them to travel the same distance is :
(A) 1 : 3 : 5
(B) 1 : 4 : 2
(C) 1 : 2 : 2
(D) 1 : 3 : 3
(E) 1 : 3 : 2
Rationale: Ratio of time taken :
1/12 :1/4 : 1/6 = 1 : 3 : 2
ANSWER:E
Answer: (E) 1 : 3 : 2
Question: Vijay bought 160 shirts at the rate of Rs. 245 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) Rs. 258
(B) Rs. 270
(C) Rs. 277.5
(D) Rs. 309
(E) None of these
Rationale: Total CP per shirt = 245 + 1400/160 + 1.75 + 320/160 = Rs. 257.5
SP = CP[(100 + profit%)/100]
= 257.5 * [(100 + 20)/100] = Rs. 309.
ANSWER:D
Answer: (D) Rs. 309
Question: John has on his shelf one books of poetry, seven novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) 14/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 7/10*2/9 + 2/10*7/9 = 14/45.
Answer: E.
Answer: (E) 14/45
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?
(A) 76
(B) 55
(C) 14
(D) 33
(E) 99
Rationale: Part filled in 2 hours = 2/6 = 1/3.
Remaining part = 1 - 1/3 = 2/3
(A + B)'s 1 hour work = 2/21
C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]
= (1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.Answer:C
Answer: (C) 14
Question: A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight.
(A) 19.81%
(B) 20%
(C) 37.5%
(D) 25%
(E) 42.86%
Rationale: There is a one step calculation method too. It requires more thought but is faster.
The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up.
While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70.
But he also sells at 9.09% less i.e. gives a discount of 1/11.
(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 10/7 * 10/11 = (1 + p%)
profit % = 42.86%E
Answer: (E) 42.86%
Question: The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.
(A) 40
(B) 29
(C) 28
(D) 27
(E) 12
Rationale: Explanation:
Let the breadth of the wall be x metres.
Then, Height = 5x metres and Length = 40x metres.
x * 5x * 40x = 12.8
=>\inline \fn_jvn x^3=\frac{12.8}{200}=\frac{128}{2000}=\frac{64}{1000}
=>\inline \fn_jvn x=\frac{4}{10}m
=>\inline \fn_jvn x=\frac{4}{10}\times 100=40cm
Answer: A) 40cm
Answer: (A) 40
Question: There are 5,280 feet in 1 mile and 10 inches in one foot. How many inches are in a mile?
(A) 5,280 - 12
(B) 5,280/12
(C) 12(5,280)
(D) 12^2(5,280)
(E) 10*5,280
Rationale: 1 feet = 10 inches
1 mile = 5280 feet
1 mile = 5280*10 inches
Ans: E
Answer: (E) 10*5,280
Question: What is the remainder when 5990990900032 is divided by 32 ?
(A) 16
(B) 8
(C) 0
(D) 2
(E) 3
Rationale: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!
divisibility rule for 4- last two digits must be divisible by 4
divisibility rule for 8- last three digits must be divisible by 8
similarly, divisibility rule for 32 - last five digits must be divisible by 32
Hence, Ans C
Answer: (C) 0
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 25%
(B) 25%
(C) 29%
(D) 55%
(E) 45%
Rationale: 800 --- 200
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: if integer N has p factors ; how many factors will 8N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;
8N = 48 => No. of factors = 10; (p+6)
Case 2:
Let N = 7 => 3^2 (prime factorization) => p = 2;
8N = 56 => no of factors = 8; (4p)
For different N different results are observed. So, shouldn't E be the right answer?
Answer: (E) Cannot be determined
Question: Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 9 even numbers. His mother immediately worked out the answer. How much had he scored in Math?
(A) 80
(B) 90
(C) 30
(D) 70
(E) 60
Rationale: B
90
Sum = (n x n) + n
Hence, 9 x 9 = 81 + 9 = 90
Answer: (B) 90
Question: A, B and C start a business, each investing Rs. 30,000/-. After 4 months A withdrew Rs. 10,000/-, B Rs. 6,000/- and C invested Rs 8000/- more. At the end of the year, a total profit of Rs. 69,000/-was recorded. What is the share of B?
(A) Rs. 25000/-
(B) Rs. 21,600/-
(C) Rs. 21,000/-
(D) Rs. 21,200/-
(E) None of these
Rationale: Explanation:
A : B : C = (30000 * 4 + 10000 * 8) : (30000 * 4 + 6000 * 8) : (30000 * 4 + 8000 * 8)
(120000 + 80000) : (120000 + 48000) : (120000 + 64000)
= 200000 : 168000 : 184000
A : B : C = 25 : 21 : 23
B’s Share = Rs. (69000 * 21/69) = 1000 * 21 = Rs. 21,000/-
Answer: Option C
Answer: (C) Rs. 21,000/-
Question: If the cost price of 72 articles is equal to the selling price of 60 articles, then what is the percent profit?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let x be the cost price of one article.
Let y be the selling price of one article.
60y = 72x
y = 1.2x
The answer is C.
Answer: (C) 20%
Question: In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be?
(A) Friday
(B) Tuesday
(C) Monday
(D) Sunday
(E) Saturday
Rationale: From the information given, March 20, 2000 is 366 days after March 20, 1999.
366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday
Answer: A
Answer: (A) Friday
Question: The list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 9.33%
(B) 9.44%
(C) 9.45%
(D) 9.56%
(E) 9.67%
Rationale: 69*(90/100)*((100-x)/100) = 56.16
x = 9.56%
ANSWER:D
Answer: (D) 9.56%
Question: The ratio of the volumes of two cubes is 729 : 2197. What is the ratio of their total surface areas?
(A) 81 : 169
(B) 81 : 122
(C) 81 : 124
(D) 81 : 126
(E) 81 : 129
Rationale: Ratio of the sides = 3√729 : 3√2197 = 9 : 13
Ratio of surface areas = 9^2 : 13^2 = 81 : 169
Answer: Option A
Answer: (A) 81 : 169
Question: Country X taxes each of its citizens an amount equal to 14 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
(A) $40,000
(B) $52,000
(C) $64,000
(D) $66,667
(E) $80,000
Rationale: Equation is correct, so math must be a problem.
0.14*40,000+0.2*(x-40,000)=8,000 --> 5,600+0.2x-8,000=8,000 --> 0.2x=10,400 --> x=52,000.
Answer: B.
Answer: (B) $52,000
Question: What is the smallest positive integer x such that 507+x is the cube of a positive integer?
(A) 15
(B) 5
(C) 50
(D) 2
(E) 4
Rationale: Given 507+x is a perfect cube
so we will take 512 = 8*8*8
507+x = 512
x = 512-507 = 5
correct option is B
Answer: (B) 5
Question: There are two shelves A and B.The number of books in shelf A is 50 more than in shelf B..Then 20 books are removed from each shelf..Then the number of books in shelf A is twice the number of books in shelf..what are the number of books in shelf A originally?
(A) 100
(B) 115
(C) 130
(D) 120
(E) 140
Rationale: consider the books in B is x,then A has x+50,now 20 books are removed from both A&B then A has x+30,B has x-20,now books in A will be twice of books in shelf B
so x+30=2(x-20) solve this eq gives x=70 so initially A has 120 books
ANSWER:D
Answer: (D) 120
Question: Calculate the share of Y , if Rs. 690 is divided among X, Y and Z in the ratio 5 : 7 : 11?
(A) 190
(B) 160
(C) 120
(D) 151
(E) 150
Rationale: 5 + 7 + 11 =23
690/23=30
so Y's share=5*30
=150
ANSWER:E
Answer: (E) 150
Question: If 60 percent of 600 is 50 percent of x, then x=?
(A) 600
(B) 720
(C) 820
(D) 800
(E) 920
Rationale: 0.6 * 600 = 0.5 * x
x = 6/5 * 600 = 720
Answer: (B) 720
Question: One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
(A) 5:4
(B) 5:9
(C) 5:6
(D) 5:1
(E) 5:7
Rationale: 45 * 5/18 = 10
25:20 => 5:4
Answer: A
Answer: (A) 5:4
Question: The current of a stream runs at the rate of 3 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) A)7.24
(B) B)2
(C) C)8.5
(D) D)6.67
(E) E)3
Rationale: S = 3
M = x
DS = x + 3
US = x - 3
6/(x + 3) + 6/(x - 3) = 2
x = 7.24
Answer:A
Answer: (A) A)7.24