mathewhe/aqua_rat huggingface dataset:
Question: A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21, and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box?
(A) 7/72
(B) 1/6
(C) 7/36
(D) 5/28
(E) 21/36
Rationale: Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.
(1,2) (2,3) (3,5) (5,8) (8,13) . There are 5 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome.
So No: of desired outcomes = 5
Probability = 5/28
Answer :D
Answer: (D) 5/28
Question: A man can do a piece of work in 15 days and his son do the same work in 12 days, both are working together for 5 days after that son left the job. then in how many days a man alone complete the remaining work?
(A) 2.58 DAYS
(B) 2.33 DAYS
(C) 5.69 DAYS
(D) 8.85 DAYS
(E) 2.36 DAYS
Rationale: First take LCM of (15,12) = 60; Total work =60; A man one day work = 60/15 =4; son's one day work =60/12 = 5; One day work of both man+son= 4+5 = 9; Total work completed in 5 days = 5*5=25; remaining work is = 60 - 25 = 35; remaining work completed by a man in = 35/15= 2.33 days. Answer =B
Answer: (B) 2.33 DAYS
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 11
(B) 12
(C) 15
(D) 10
(E) 27
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer: D
Answer: (D) 10
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
(A) 200
(B) 250
(C) 260
(D) 270
(E) None
Rationale: Sol.
Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 26 sec.
Let the length of the train be x metres.
Then, x + 250 / 26 = 20 ⇔ x + 250 = 520 ⇔ x = 270.
Answer D
Answer: (D) 270
Question: Find the HCF of 2.1, 1.05 and 0.63
(A) 0.44
(B) 0.64
(C) 0.21
(D) None of above
(E) 0.56
Rationale: Explanation:
To solve this question quickly, first remove decimal by multiplying each term with 100,
Then terms become 210, 105, 63
Then HCF of above terms is 21,
So Answer is 0.21
Option C
Answer: (C) 0.21
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is
(A) 1/4
(B) 1/10
(C) 7/15
(D) 8/15
(E) 1/15
Rationale: A's 1 day's work =1/15
B's 1 day's work =1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60,
(A + B)'s 4 day's work =(7/60x 4)=7/15.
Therefore, Remaining work =(1-7/15) = 8/15
Answer: Option D
Answer: (D) 8/15
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1234
(B) 1345
(C) 1350
(D) 1356
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: Michael cashed a check for $1,270 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
(A)  $830
(B)  $800
(C)  $770
(D)  $730
(E)  $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1270 - 470 = 800.
Answer B
Answer: (B)  $800
Question: A man can row upstream at 32 kmph and downstream at 48 kmph, and then find the speed of the man in still water?
(A) 22
(B) 37
(C) 30
(D) 27
(E) 40
Rationale: US = 32
DS = 48
M = (48 + 32)/2 = 40
Answer:E
Answer: (E) 40
Question: In a garden, there are 10 rows and 14 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
(A) 20 m
(B) 22 m
(C) 24 m
(D) 26 m
(E) 28 m
Rationale: Explanation:
Each row contains 14 plants.
There are 13 gapes between the two corner trees (13 x 2) metres and 1 metre on each side is left.
Therefore Length = (26 + 2) m = 28 m.
Answer: E
Answer: (E) 28 m
Question: The surface of a cube is 384sq cm. Find its volume?
(A) 8cc
(B) 9cc
(C) 512cc
(D) 4cc
(E) 6cc
Rationale: 6a2 = 384 = 6*64
a = 8 => a3 = 512cc
Answer: C
Answer: (C) 512cc
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $45,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,000
(B) $11,200
(C) $12,000
(D) $13,600
(E) $13,200
Rationale: 1 machine of type B will cost: 20% down payment of 45,000 = 9,000plusremaining sum (50,000-9,000=41,000) with 40% of finance charges 41,000*1.4=57,400 --> 9,000+57,400=66,400;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,400 - 52,800 = 13,600.
Answer: D.
Answer: (D) $13,600
Question: Three unbased coins are tossed. the probability of getting at most three T is ?
(A) 1/2
(B) 7/8
(C) 3/4
(D) 1/8
(E) 2/3
Rationale: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {TTT}
P(E)=n(E)/n(S)=1/8
Answer(D)
Answer: (D) 1/8
Question: If 130/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.
Ans is A.
Answer: (A) I only
Question: A clock is started at noon. By 10 minutes past 7, the hour hand has turned through how many degrees?
(A) 205Â°
(B) 210Â°
(C) 215Â°
(D) 220Â°
(E) 225Â°
Rationale: The angle traced by the hour hand in 12 hrs is 360Â°
The angle traced by the hour hand in 1 hour is 30Â°
The angle traced by the hour hand in 10 minutes is 5Â°
The angle traced by the hour hand in 7 hours and 10 minutes is 7*30Â° + 5Â° = 215Â°
The answer is C.
Answer: (C) 215Â°
Question: Find the area of circle whose radius is 14m?
(A) 187
(B) 154
(C) 377
(D) 488
(E) 616
Rationale: 22/7 * 14 * 14
= 616
Answer:E
Answer: (E) 616
Question: A and B invests Rs.8000 and Rs.9000 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) 20:23
(B) 34:43
(C) 32:45
(D) 37:45
(E) 37:35
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
ANSWER:C
Answer: (C) 32:45
Question: The difference between the place value and the face value of 6 in the numeral 856973 is
(A) 973
(B) 6973
(C) 5994
(D) 6084
(E) None of these
Rationale: (Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
Answer: Option C
Answer: (C) 5994
Question: A group of people were given 2 puzzles. 77% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?
(A)  11%, 0%
(B)  77%, 63%
(C)  68%, 57%
(D)  79%, 68%
(E)  89%, 79%
Rationale: To solve this question, we don't need any formulas. Just read the question carefully. If 77% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 77%. From the given options, only D looks good
Answer B
Answer: (B)  77%, 63%
Question: There is an antique clock exhibition. So many clock are piled up with distinct numbers tagged with them. The person managing it hangs different clocks numbers periodically on the main wall. At 9:20 am, he hung the clock number 200; at 11:00 am, he hung the clock number 30; at 4:00 pm, he hung the clock number 240.
Which numbered clock will he hang on the wall when the time is 7:30pm ?
(A) 313
(B) 314
(C) 315
(D) 316
(E) 317
Rationale: Solution:
He will hang clock number 315 at 7:30pm. The person has been hanging the clock number which corresponds with the angle between the hour hand and the minute hand of the clock at that time.
Answer C
Answer: (C) 315
Question: In your classes you counted 124 hands. How many students were at the class?
(A) 62
(B) 61
(C) 85
(D) 86
(E) 88
Rationale: Total number of hands = 124
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 124 by 2
124 ÷ 2 = 62
Therefore, there were 62 students at the class.
ANSWER IS A
Answer: (A) 62
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) 587
(B) 287
(C) 585
(D) 658
(E) 572
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135
=585
Answer:C
Answer: (C) 585
Question: Sachin is 40 years old and Ajith is 60 years old. How many decades ago was the proportion of their ages 3 : 5?
(A) 10
(B) 69
(C) 37
(D) 21
(E) 20
Rationale: A
10
If the ratio was 3 : 5, ‘A’ years ago.
Then, 7A – 6A = 4
A = 4
Then, {( 40 – A)/(60 – A)}= (3/5)
5 (40 – A) = 3(60 – A)
2A = 20
A = 10
Answer: (A) 10
Question: There are 14 students in a class. On the day the test was given, Dan was absent. The other 13 students took the test and their average was 75. The next day, Dan took the test, and with this grade included, the new average was 76. What was Dan's grade on the test?
(A) 86
(B) 87
(C) 88
(D) 89
(E) 90
Rationale: 13*75+Dan's grade=14*76
Dan's grade is 14*76-13*75=89.
The answer is D.
Answer: (D) 89
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.73 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 13%
Rationale: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.
3(0.22-x)(15) + 2x(18) = 8.73
9.9 - 45x + 36x = 8.73
9x = 1.17
x = 0.13
The answer is E.
Answer: (E) 13%
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?
(A) 36.7
(B) 36.1
(C) 36.5
(D) 36.9
(E) 36.3
Rationale: Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean = 1825/50
= 36.5
Answer:C
Answer: (C) 36.5
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 96. Find their present ages.
(A) 24,42,54
(B) 8,20,28
(C) 16,28,36
(D) 16,28,46
(E) None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 96
20K = 120
K = 6
Therefore, then present ages are 24,42,54.
ANSWER:A
Answer: (A) 24,42,54
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.21168/- in 3 years at the same rate of interest. Find the rate percentage?
(A) 5%
(B) 7%
(C) 9%
(D) 11%
(E) 20%
Rationale: Explanation:
The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.
S.I = 21168/- - 17640/- = Rs. 3528/-
Rate of interest = (3528/17640) × (100/1) => 20%
Answer: Option E
Answer: (E) 20%
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/38
(C) 21/32
(D) 31/33
(E) 36/32
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32 .Answer: A
Answer: (A) 31/32
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 61?
(A) 68
(B) 69
(C) 144
(D) 68^2
(E) 68·69
Rationale: In order to get the lowest LCM, we have to take the first number as 62 and the next number as its multiple.
So, I can take 62 and 144 as two distinct numbers, such that Lowest LCM = 144.
Answer should be C.
Answer: (C) 144
Question: Clara is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of waffle. The pattern repeats after she leaves the morsel of rye. If Clara drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
(A) waffle − wheat − wheat
(B) wheat − wheat − white
(C) white − waffle − wheat
(D) white − white − white
(E) white − white − waffle
Rationale: In a single round Clara drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: (A) waffle − wheat − wheat
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
Answer: option C
Answer: (C) 6
Question: A store sells chairs and tables. If the price of 3 chairs and 1 table is 60% of the price of 1 chair and 3 tables, and the price of 1 table and 1 chair is $80, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
(A) 68
(B) 84
(C) 72
(D) 60
(E) 64
Rationale: LET C= CHAIR ; T =TABLE
3C+1T = 0.6 (1C + 3T) OR C( 3-0.6) = 1.8T -1T OR 2.4C = 0.8 T THEREFORE C= 0.8/2.4 T = 1/3 T
IC +1T =80 OR 1/3T + 1T =80 THEREFORE T= 80*3/4 = 60
D
Answer: (D) 60
Question: 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 35% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?
(A) 19
(B) 25
(C) 35
(D) 45
(E) 75
Rationale: Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 35% = 63 responded as satisfied, So remaining Satisfied are 120 - 63 = 57
so 57 is what percentage of 300 - 19%
So the answer should be A
Answer: (A) 19
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled?
(A) 600
(B) 700
(C) 800
(D) 850
(E) None of these
Rationale: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 280 (40*6 = 240)
100% -----> 600 (100*6 = 600)
Answer: Option A
Answer: (A) 600
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 35%. Staff are allowed a further 30% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.555D
(B) 0.765D
(C) 0.455D
(D) 0.785D
(E) 0.805D
Rationale: Effective discount = a + b + ab/100 = - 35 - 30 + (-35)(-30)/100 = -54.5
Sale price = D * ( 1 - 54.5/100)
Sale price = .455 * D
Answer (C)
Answer: (C) 0.455D
Question: A sum of money at simple interest amounts to Rs. 800 in 3 years and to Rs. 850 in 4 years. The sum is:
(A) Rs. 670
(B) Rs. 690
(C) Rs. 600
(D) Rs. 625
(E) Rs. 657
Rationale: Explanation:
S.I. for 1 year = Rs. (850 - 800) = Rs. 50.
S.I. for 3 years = Rs.(50 x 3) = Rs. 150.
Principal = Rs. (800 - 150) = Rs. 600.
Answer: Option C
Answer: (C) Rs. 600
Question: The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item?
(A) 17%
(B) 21%
(C) 24%
(D) 29%
(E) 42%
Rationale: The price decreased by 23.99 - 16.99 = $7.
$7 is a bit more than 29% of original price of $24.
Answer: D.
Answer: (D) 29%
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 7232
(B) 828
(C) 12
(D) 83
(E) 29
Rationale: Explanation:
T = 9/45 * 60 = 12
Answer: Option C
Answer: (C) 12
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 56%
(B) 57%
(C) 60%
(D) 61%
(E) 65%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = 11628	x 100	% = 57%.
20400
Option B
Answer: (B) 57%
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 9800
(C) 8000
(D) 7500
(E) 8600
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
ANSWER A
Answer: (A) 9680
Question: If the radius of a circle is increased by 40% then the area is increased by:
(A) 44%
(B) 120%
(C) 96%
(D) 40%
(E) None of the above
Rationale: initially A=pi*r2
now R2=140/100r
then area=Pi*(140R/100)2
area=196R/100
that is area increases from 100 to 196=increase in area=96%
ANSWER:C
Answer: (C) 96%
Question: What is the unit digit in {(6374)^1793 x (625)^317 x (341^491)}?
(A) 5
(B) 1
(C) 0
(D) 7
(E) 2
Rationale: Unit digit in (6374)^1793 = Unit digit in (4)^1793
Unit digit in [(4^2)^896 x 4]
= Unit digit in (6 x 4) = 4.
Unit digit in (625)^317 = Unit digit in (5)^317 = 5.
Unit digit in (341)^491 = Unit digit in (1)^491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Answer C)0.
Answer: (C) 0
Question: A scooter costs 10,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
(A) 10,000
(B) 12,500
(C) 12,800
(D) 12,000
(E) 5,120
Rationale: After first year, the value of the scooter = 8,000
After second year, the value of scooter = 6,400
After third year, the value of scooter = 5,120
Answer E
Answer: (E) 5,120
Question: The regular price per can of a certain brand of soda is $0.30. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?
(A) $16.32
(B) $18.36
(C) $21.60
(D) $24.48
(E) $28.80
Rationale: The discounted price of one can of soda is (0.85)($0.30), or $0.255.
Therefore, the price of 72 cans of soda at the discounted price would be (72)($0.255) = 18.36
Answer: B.
Answer: (B) $18.36
Question: If a fast song has 160 beats per minute, and a slow song has 90 beats per minute, how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1,020 beats?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: We can determine quickly that total number should range between 1,020/160<= N <= 1,020/90 , so ans should be between 6 and 12.
Now solving the expression 160A+90B = 1,020
decreasing 1,020 by multiples of 160 and checking divisibility of that number by 9, we get
fast song plays for 3 minutes and slow somg plays for 6 minutes, 3*160 + 6*90 = 1,020
Hence total number of minutes stream of music plays is 3 + 6 = 9 minutes
Ans D
Answer: (D) 9
Question: Find the 25th term of an arithmetic progression whose first term is 5 and the common difference is 7.
(A) 145
(B) 38
(C) 173
(D) 156
(E) 189
Rationale: n th term of A.P = a +(n-1) *d
= 5+(25-1)*7 , = 5 + 168 = 173.
ANSWER:C
Answer: (C) 173
Question: Select the one which is different from other Four alternatives.
(A) 988
(B) 1140
(C) 1064
(D) 1197
(E) 1352
Rationale: E
(A) 988 ÷ 19 = 52
(B) 1352 ÷ 19 = 71.15
(C) 1064 ÷ 19 = 56
(D) 1197 ÷ 19 = 63
(E) 1140 ÷ 19 = 60
Answer: (E) 1352
Question: What is the greatest prime factor of 6^8−3^8 ?
(A) 3
(B) 11
(C) 17
(D) 19
(E) 31
Rationale: 6⁸ − 3⁸ is a DIFFERENCE OF SQUARES. So we can factor it.
6⁸ − 3⁸ = (6⁴ + 3⁴)(6⁴ - 3⁴)
= (6⁴ + 3⁴)(6² + 3²)(6² - 3²)
= (6⁴ + 3⁴)(6² + 3²)(6 + 3)(6 - 3)
= (6⁴ + 3⁴)(45)(9)(3)
= (6⁴ + 3⁴)(3)(3)(5)(3)(3)(3)
Hmmmm, we can see that the correct answer is "hiding" in the first number (6⁴ + 3⁴)
Let's factor out the 3⁴, to get:
6⁴ + 3⁴ = 3⁴(2⁴ + 1)
= 3⁴(16 + 1)
= 3⁴(17)
= (3)(3)(3)(3)(17)
So, 6⁸ − 3⁸ = (3)(3)(3)(3)(17)(3)(3)(5)(3)(3)(3)
So the correct answer is C
Answer: (C) 17
Question: Find LCM of fraction series 4/5, 8/35, 2/15, 6/25 ?
(A) 36/5
(B) 24/5
(C) 16/5
(D) 36/7
(E) 25/2
Rationale: We know that the LCM for fraction can be calculated as:
LCM = (LCM of numerators) / (HCF of denominators)
= (LCM of 4, 8, 2, 6) / (HCF of 5, 35, 15, 25)
= (2 x 2 x 2 x 3) / (5)
= 24 / 5
Ans - B
Answer: (B) 24/5
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 20 m long and 16 1/2 m board?
(A) 66
(B) 18
(C) 16
(D) 10
(E) 15
Rationale: 20 * 33/2 = 5/2 * 2 * x => x
= 66
Answer:A
Answer: (A) 66
Question: In how many different ways can the letters of the word RUMOUR be arranged?
(A) 180
(B) 720
(C) 30
(D) 90
(E) None of these
Rationale: Reqd. number of ways
6!/2!×2!=6×5×4×3/1×2=180
Answer A
Answer: (A) 180
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 1 : 4. If D gets Rs. 6000 more than C, what is B's share?
(A) Rs. 500
(B) Rs. 1000
(C) Rs. 1500
(D) Rs. 4000
(E) NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. x and Rs. 4x respectively.
Then, 4x - x = 3000 ⇔ 3x = 6000 ⇔ x = 2000.
∴ B's share = Rs. 2x= Rs. (2x2000) = Rs. 4000.
Answer D
Answer: (D) Rs. 4000
Question: The perimeter of one face of a cube is 20 cm. Its volume will be:
(A) 125cm3
(B) 400cm3
(C) 250cm3
(D) 625cm3
(E) None of these
Rationale: Explanation:
Edge of cude = 20/4 = 5 cm
Volume = a*a*a = 5*5*5 = 125 cm cube
Option A
Answer: (A) 125cm3
Question: There are 6 physics books and 1 chemistry book on shelf P and 4 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?
(A) 1/42
(B) 1/35
(C) 1/28
(D) 1/21
(E) 1/14
Rationale: P(a chemistry book is moved to shelf Q) = 1/7
P(a chemistry book is then chosen from shelf Q) = 1/5
P(the student takes a chemistry book) = 1/7 * 1/5 = 1/35
The answer is B.
Answer: (B) 1/35
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.154. Find the unknown rate of two blankets?
(A) 420
(B) 550
(C) 490
(D) 450
(E) 457
Rationale: 10 * 154 = 1540
3 * 100 + 5 * 150 = 1050
1540 – 1050 = 490
Answer:C
Answer: (C) 490