mathewhe/aqua_rat huggingface dataset:
Question: Sunday
Monday
Tuesday
Wednesday
Thursday
What day comes three days after the day which comes two days after the day which comes immediately after the day which comes two days after Monday?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
(E) Thursday
Rationale: C
Tuesday
Answer: (C) Tuesday
Question: A fill pipe can fill 1/2 of cistern in 15 minutes. In how many minutes, it can fill 1/2 of the cistern?
(A) 1 min
(B) 5 min
(C) 10 min
(D) 15 min
(E) 20 min
Rationale: Required time = 15*2*1/2 = 15 minutes
Answer is D
Answer: (D) 15 min
Question: 10^185 - 10^10 = Which of the following best approximates the value of the expression above?
(A) 10^180
(B) 10^185
(C) 10^179
(D) 10^170
(E) 10^160
Rationale: 10^185 - 10^10 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^185 is correct. Note that we need approximate value of the given expression and as 10^(185) is much larger number than 10^(10) then 10^(10) is pretty much negligible in this case: 10^(185)-10^(10)=~10^(185).
Answer : B
Answer: (B) 10^185
Question: Replace the ? with the appropriate number
1 , 4 , 5 , 6 , 7 , 9 , 11 ?
(A) 488
(B) 123
(C) 234
(D) 100
(E) 589
Rationale: D
list of consecutive numbers that does not contain a 'T' in the spelling
Answer: (D) 100
Question: jim and Beth each drove from Smallville to Crown City by different routes. jim drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than jim to complete the trip. How many miles per hour was Beth's average speed on this trip?
(A)  24
(B)  30
(C)  48
(D)  54
(E)  75
Rationale: Speed = Distance/Time
Distance for jim = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for jim +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by jim + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer.
Answer: (B)  30
Question: The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 144 metres, what is its area?
(A) 1320 sq.metres
(B) 1260 sq.metres
(C) 1280 sq.metres
(D) 1380 sq.metres
(E) None of these
Rationale: Let the length and breadth be 7x and 5x respectively.
Then, P = 2(7x + 5x) = 144 ⇒ x = 6
Area = 7 × 6 × 5 × 6 = 1260 sq.m.
Answer B
Answer: (B) 1260 sq.metres
Question: If f is a function defined for all k by f(k) = k^(2/3)/16, what is f(8 k) in terms of f(k)?
(A) 1/8 f(k)
(B) 5/8 f(k)
(C) 4 f(k)
(D) 10 f(k)
(E) 32 f(k)
Rationale: f(k) = (k^(2/3)) /16
f(8 k) = (8 k)^( 2/3)/16 = 4 k^(2/3)/16 = 4 * (k^(2/3)/16) =4 f(k).
So answer is C.
Answer: (C) 4 f(k)
Question: A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
(A) 270 m
(B) 245 m
(C) 235 m
(D) 220 m
(E) 240 m
Rationale: Explanation:
Assume the length of the bridge = x meter
Total distance covered = 135+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (135+x)/30 m/s
=> 45 Ã— (10/36) = (135+x)/30
=> 45 Ã— 10 Ã— 30 /36 = 135+x
=> 45 Ã— 10 Ã— 10 / 12 = 135+x
=> 15 Ã— 10 Ã— 10 / 4 = 135+x
=> 15 Ã— 25 = 135+x = 375
=> x = 375-135 =240
Answer: Option E
Answer: (E) 240 m
Question: Cathy's Catering business is catering a party. She is delivering food that is 1/6 sandwiches, 1/4 salads, 1/6 chips, 1/8 deserts, 1/8 snacks, and the rest drinks. If Cathy dropped the deserts on the way to the party and decides to stop and buy more snacks to make up for it, by doubling the snacks, what proportion of the food is snacks now?
(A) 5/29
(B) 1/8
(C) 5/16
(D) 1/2
(E) 1/4
Rationale: Sandwiches = 1/6 = 4/24
Salads = 1/4 = 6/24
Chips = 1/6 = 4/24
Deserts = 1/8 = 3/24
Snacks = 1/8 = 3/24
Drinks = 1 - (20/24) = 4/24
Now: Deserts = 0/24
If Snacks doubled => (2)(3/24) = 6/24; then, total = 24
and 6 is now snacks => proportion = 6/24.
Answer: E
Answer: (E) 1/4
Question: A number when divided by 100 leaves 11 as a remainder. What will be the remainder if the number is divided by 11?
(A) 11
(B) 1
(C) 2
(D) 3
(E) 21
Rationale: Let 100+11=111
111 divided evenly by eleven leaves a remainder of one.
Correct answer is B.
Answer: (B) 1
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
(A) 220
(B) 230
(C) 960
(D) 780
(E) 400
Rationale: C
C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
Answer: (C) 960
Question: At a certain college there are twice as many history majors as English majors and three times as many history majors as mathematics majors. What is the ratio of the number of english majors to the number of mathematics majors?
(A) 6 to 1
(B) 2 to 3
(C) 3 to 2
(D) 1 to 5
(E) 1 to 6
Rationale: This is how I translated the question:
At a certain college there are twice as many english majors as history majors
H = 2E
and three times as many english majors as mathematics majors.
H = 3M
What is the ratio of the number of history majors to the number of mathematics majors?
What is E:M?
Just set E equal to each other to get the ratio in terms of E and M.
2E = 3M
E/M = 3/2
The answer is 3:2
Answer : C
Answer: (C) 3 to 2
Question: Choose the missing terms out of the given alternatives.
AZ, BY, CX, DW, EV ?
(A) EF
(B) GH
(C) ED
(D) FU
(E) KN
Rationale: D
FU
The first letter moves one step forward. The second letter moves one step backward.
Answer: (D) FU
Question: If 2|2 –a| = 5, what is the sum of all the possible values for a ?
(A) 1/2
(B) 2
(C) 5/2
(D) 4
(E) 5
Rationale: if a<2, then 2-a=5/2; a=-1/2
if a>2 , then a-2=5/2; a=9/2
9/2-1/2=8/2=4=D
Answer: (D) 4
Question: Carol and Blake invested 12000 and 24000, respectively in a business. Carol manages the business and for this he receives 9% of the profit while the rest is divided in proportion to their capitals. Find the share of Carol in a profit of 4000.
(A) 2573.3
(B) 1573.3
(C) 1565.3
(D) 2473.3
(E) 6573.3
Rationale: The Carol gets for managing
= 9% of Rs. 4000 = 360
Remaining profit = 4000 â€“ 360 = 3640
This is to be divided in the ratio 12000 :24000=12: 24=1:2.
Share of Carol = 1/3 of 3640 = 1213.3
â‡’ Total share of Carol = 360 + 1213.3 = 1573.3.
Answer B
Answer: (B) 1573.3
Question: 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
(A) Friday
(B) Saturday
(C) Wednesday
(D) Sunday
(E) None of these
Rationale: Explanation :
Number of days from 6th March, 2004 to 5th March 2005 = 365 days
(Though Feb 2004 has 29 days as it is a leap year, it will not come in the required period)
365 days = 1 odd day
Given that 6th March, 2005 is Monday
Hence 6th March, 2004 = (Monday - 1 odd day) = Sunday
Answer : Option D
Answer: (D) Sunday
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
(A) 375
(B) 475
(C) 575
(D) 675
(E) 775
Rationale: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
correct answer D
Answer: (D) 675
Question: Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is
(A) 360
(B) 240
(C) 2520
(D) 480
(E) None of these
Rationale: Solution
Order of vowels of fixed
âˆ´ required number of ways are 7!/2!.
Answer C
Answer: (C) 2520
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
(A) 22
(B) 77
(C) 26
(D) 41
(E) 66
Rationale: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.
Answer: D
Answer: (D) 41
Question: A shopkeeper sold an article at $1200 and gained a 20% profit. What was the cost price?
(A) $1000
(B) $1020
(C) $1040
(D) $1060
(E) $1080
Rationale: Let x be the cost price.
1.2x = 1200
x = 1200/1.2 = 1000
The answer is A.
Answer: (A) $1000
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
(A) 1/8
(B) 1/4
(C) 1/5
(D) 1/9
(E) 1/1
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Answer: (C) 1/5
Question: A and B invests Rs.8000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:99
(B) 82:31
(C) 8:15
(D) 34:89
(E) 35:21
Rationale: A : B
(8000*4)+(4000*8) : (12000*6)+(9000*6)
64000 : 120000
8 : 15
Answer:C
Answer: (C) 8:15
Question: How many different possible arrangements S can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
(A) 360
(B) 720
(C) 900
(D) 1800
(E) 5040
Rationale: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans S= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Answer: (C) 900
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 48 years, was replaced by a new person. Find the age of the new person?
(A) 18
(B) 56
(C) 12
(D) 17
(E) 14
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 48 + Q
=> Q = 18
Answer:A
Answer: (A) 18
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/96
(B) 33/91
(C) 33/93
(D) 13/91
(E) 33/99
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91.Answer: B
Answer: (B) 33/91
Question: Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756
(A) 16
(B) 33
(C) 105
(D) 424
(E) 2124
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
3th term should 34 instead of 33.
B
Answer: (B) 33
Question: A shopkeeper sold two radio sets for 792 each, gaining 10% on one, and losing 10% on the other. Then he
(A) neither gains nor loses
(B) gains 1%
(C) loses 1%
(D) gains 5%
(E) None of these
Rationale: Sol.(c) When selling price of two articles is same and
% gain = % loss
then there will be always loss.
and overall % loss = (10)2⁄100% = 1%. Answer C
Answer: (C) loses 1%
Question: If x and y are numbers such that (x+5)(y-5)=0, what is the smallest possible value of x^2 + y^2
(A) 0
(B) 4
(C) 9
(D) 25
(E) 16
Rationale: From (x+5)(y-5)=0 it follows that either x=-5 or y=5. Thus either x^2=25 or y^2=25.
Now, if x^2=8125, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 25 + 0 = 25.
Similarly if y^2=25, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 25 = 25.
Answer: D.
Answer: (D) 25
Question: In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?
(A) 4323
(B) 2797
(C) 4320
(D) 2997
(E) 0811
Rationale: Explanation:
There are in all 8 letters in the given word of which 3 are vowels. As the vowels should always be together, considering the 3 vowels as one letter, there are in all 6
letters which can be arranged in 6! ways = 720
Also the 3 vowels can be arranged in 3! ways = 6
Total number of arrangements = 720*6 = 4320
ANSWER:C
Answer: (C) 4320
Question: if(x-10)(y-5)(z-2)=1000 then what is the least value of x+y+z? if x,y,z are all integer no.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: (x-10)(y-5)(z-2)=1000
put x=0
y=-5
z=12
then
(0-10)(-5-5)(12-2)=1000
(-10)(-10)(10)=1000
1000=1000
ANSWER:A
Answer: (A) 7
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many S different victory circles are possible?
(A) 24
(B) 52
(C) 96
(D) 144
(E) 648
Rationale: Possible scenarios are:
1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total: 24+12+12+4=52
Answer: B.
Answer: (B) 52
Question: Jim and Reneeh will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneeh have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?
(A) 5/6
(B) 2/3
(C) 1/2
(D) 5/12
(E) 1/3
Rationale: 1/3
probability of jim winning is basically the sum of three probabilities:
probability of jim picking rock and reneeh picking scissors = 1/3*1/3 = 1/9
probability of jim picking scissors and reneeh picking paper = 1/3*1/3=1/9
probability of jim picking paper and reneeh picking rock = 1/3*1/3=1/9
1/9 + 1/9 + 1/9 = 3/9 = 1/3=E
Answer: (E) 1/3
Question: In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?
(A) 10
(B) 48
(C) 37
(D) 97
(E) 12
Rationale: 3X + 4y = 240
by substitute through options 48 is correct
Answer: B
Answer: (B) 48
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
(A) 36
(B) 232
(C) 216
(D) 455
(E) 363
Rationale: number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
Answer: C
Answer: (C) 216
Question: A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
(A) 15
(B) 16
(C) 19
(D) 20
(E) 36
Rationale: This would be the generic strategy:
Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 19
ANSWER:C
Answer: (C) 19
Question: Bruce purchased 7kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)985
(B) B)1050
(C) C)1055
(D) D)1065
(E) E)1075
Rationale: Cost of 7 kg grapes = 70 × 7 = 490.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 490 + 495 = 985
A
Answer: (A) A)985
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer p?
(A) (2p-1)/(p^3- p)
(B) (2p-1)/(p^4- p)
(C) (2p-1)/(p^2- p)
(D) (2p-1)/(p^2- 2p)
(E) (2p-4)/(p^2- 3p)
Rationale: Let two consecutive positive integers be p and p-1 (Greater integer is p)
So,
(1/p) + [1/(p-1)]
= (2p-1)/p(p-1)
=(2p-1)/(p^2- p)
Answer : C
Answer: (C) (2p-1)/(p^2- p)
Question: Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 20 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
(A) 3:5
(B) 9:25
(C) 5:2
(D) 25:9
(E) Cannot be determined from the information provided
Rationale: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*10/Speed B
Since the times are same,
50pi/Speed A = 20pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/2
Correct Option: C
Answer: (C) 5:2
Question: If the price of a certain computer increased 30 percent from d dollars to 351 dollars, then 3d =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 710
Rationale: Before Price increase Price = d
After 30% Price increase Price = d+(30/100)*D = 1.3d = 351 (Given)
i.e. d = 351/1.3 = $270
i.e. 3d = 3*270 = 710
Answer: option E
Answer: (E) 710
Question: The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife?
(A) 270
(B) 266
(C) 209
(D) 298
(E) 277
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: (A) 270
Question: Income and expenditure of a person are in the ratio 9 : 8. If the income of the person is Rs. 36000, then find his savings?
(A) 2000
(B) 3000
(C) 4000
(D) 5000
(E) 6000
Rationale: Let the income and the expenditure of the person be Rs. 9x and Rs. 7x respectively.
Income, 9x = 36000
=> x = 4000
Savings = Income - expenditure
= 9x - 8x = x
So, savings =Rs.4000.
Answer: C
Answer: (C) 4000
Question: A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) Rs. 7500
(B) Rs. 9000
(C) Rs. 9500
(D) Rs. 10,000
(E) None
Rationale: Solution: A : B : C = (20,000 * 24) : (15,000 * 24) : (20,000 * 18) = 4 : 3 : 3.
So B's share = Rs. (25000 * 3/10) = Rs. 7,500.
Answer: Option A
Answer: (A) Rs. 7500
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 650, what is the least possible value of n?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 650 = 2 * 5 * 5 * 13
so the least value forNcan be 13.
D
Answer: (D) 13
Question: Palindromes are words or phrases that read the same in both directions, e.g. EYE
Now consider the word LEVEL, such a word is known as palindromes.
Find the maximum possible number of five letter palindromes.
(A) 17515
(B) 17566
(C) 17576
(D) None
(E) Cannot be determined
Rationale: Explanation :
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways.
=> The first two letters can be chosen in 26*26=676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
=> All the three letters can be chosen in 676*26=17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Answer : C
Answer: (C) 17576
Question: -2, 5, 24, 61, ?
(A) 228
(B) 278
(C) 299
(D) 122
(E) 271
Rationale: ANSWER: D
Answer: (D) 122
Question: what is the next term of this series6,10,9,15,12,20,15,25...?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 18
Rationale: 3&2=6;
5*2=10;
3*3=9
3*5=15
3*4=12
5*4=20
3*5=15
5*5=25
3*6=18
ANSWER:E
Answer: (E) 18
Question: Helen went to the stationers and bought things worth Euro 22, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) uro 19.70
(B) uro 15.70
(C) uro 13.70
(D) uro 18.70
(E) uro 16.70
Rationale: E
Euro 16.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [22 - (5 + 0.30)] = Euro 16.70
Answer: (E) uro 16.70
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
(A) 140
(B) 120
(C) 125
(D) 130
(E) 190
Rationale: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
ANSWER A
Answer: (A) 140
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 64√8 cm2
(B) 64√1 cm2
(C) 68√3 cm2
(D) 64√3 cm2
(E) 24√3 cm2
Rationale: Area of an equilateral triangle
= √3/4 S2
If S = 16, Area of triangle
= √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
Answer: (D) 64√3 cm2
Question: A marketing company devised a methodology of spreading its message through one another. One person can tell it to 3 persons in 4 minutes and these three persons tell the other three persons each in further 4 minutes and the process continues so on. How many minutes will it take to spread the message to 2187 persons.
(A) 48 minutes
(B) 24 minutes
(C) 32 minutes
(D) 28 minutes
(E) 29 minutes
Rationale: according to the given condition 3^1 + 3^2 + 3^3 + ........ = 2187
or 3(3^x - 1)/(3-1) = 2187
or 3(3^x - 1)/2 = 2187
or 3^x - 1 = 2187*2/3 = 4374/3 = 1458
or 3^x = 1459 so x = 6 to 7
so total time taken = (6to7)*4 = 24 to 28 min
but if we take only the last step persons then 3^x = 2187 so x = 7
so time = 7*4 = 28 min
ANSWER:D
Answer: (D) 28 minutes
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 7000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
(A) 100000
(B) 100500
(C) 147000
(D) Data inadequate
(E) None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 7000) From the question,
(x - 7000) × 126⁄100 = 6⁄5x ⇒ x = 147000
Answer C
Answer: (C) 147000
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: A. 13 (cannot be weighed)
B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 11(can be weighed by keeping weights of 10 and 1 kg)
E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
A
Answer: (A) 13
Question: The average monthly salary of 10 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
(A) Rs.3601
(B) Rs.3618
(C) Rs.2700
(D) Rs.3619
(E) Rs.3610
Rationale: Manager's monthly salary
= Rs. (1700 * 11 - 1600 * 10)
= Rs. 2700 Answer:C
Answer: (C) Rs.2700