mathewhe/aqua_rat huggingface dataset:
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 186 cms. What was the ratio of men to women?
(A)  5:2
(B)  5:1
(C)  5:3
(D)  4:1
(E)  3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 186cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 186M)/(W+M) = 180
170W + 186M = 180W + 180M
6M = 10W
3M = 5W
M/W = 5/3
The ratio of men to women is 5 to 3.
C
Answer: (C)  5:3
Question: Find the one which does not belong to that group ?
(A) 117
(B) 121
(C) 727
(D) 188
(E) 122
Rationale: Explanation:
343 = 73, 121 = 112, 1331 = 113, 2197 = 133 and 125 = 53.
343, 1331, 2197 and 125 are perfect cubes, but not 121.
Answer: B
Answer: (B) 121
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
(A) 2388
(B) 2380
(C) 2385
(D) 2383
(E) 2381
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer:B
Answer: (B) 2380
Question: A cylinder has a diameter of 20 meters and a height of 15 meters. If it is filled to capacity with oil and the content is poured into smaller cylinders of 4 meter radius and 10 meter height, how many smaller cylinders will be filled to capacity?
(A) 11
(B) 5
(C) 2
(D) 2
(E) 3
Rationale: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
larger cylinder volume=1570.8
smaller cylinder volume=502.65
therefore the number of cylinders B that can be filled to capacity=1570.8/502.65=3.1
Answer is E only 3 smaller cylinders can be filled to capacity.
Answer: (E) 3
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets did Irwin score?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored 2 11-point baskets in my opinion.
Answer C
Answer: (C) 2
Question: I had Rs. 10,000 with me. Out of this, money I lent some money to A for 2 years at 15% simple interest. I lent the remaining money to B for an equal number of years at 18% simple interest. After 2 years, I found that A had given me Rs. 360 more as interest as compared to(b) the amount of money which I had lent to B must have been
(A) 2,000
(B) 3,000
(C) 4,000
(D) 5,000
(E) 6,000
Rationale: Explanation:
Total amount = Rs. 10,000
Let money lent A =Rs. x and money lent to B = Rs. (10,000 x)
x = Rs. 6,000. So the amount of money lent to B = Rs. 4,000
Answer: C
Answer: (C) 4,000
Question: A man can row his boat with the stream at 16 km/h and against the stream in 12 km/h. The man's rate is?
(A) 8 kmph
(B) 9 kmph
(C) 2 kmph
(D) 4 kmph
(E) 1 kmph
Rationale: DS = 16
US = 14
S = ?
S = (16 - 2)/2 = 2 kmph
Answer:C
Answer: (C) 2 kmph
Question: Which of the following integers is a divisor of(15!+10)?
(A) 15
(B) 4
(C) 3
(D) 10
(E) 9
Rationale: When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 10) = 10 (1*2*3*4*5*..*9*11*12*13*14*15 + 1) We obtain this by taking 10 common.
Hence 10 is definitely a divisor of (15! + 10).
Ans D
Answer: (D) 10
Question: The cost of producing x tools by a company is given by
C(x) = 1800 x + 5500 (in $)
a) What is the cost of 100 tools?
(A) 185500 $
(B) 185800 $
(C) 185900 $
(D) 186500 $
(E) 182500 $
Rationale: Solution
C(100) = 1800*100 + 5500 = 185500 $
Answer A
Answer: (A) 185500 $
Question: The mean of 30 values was 180. It was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
(A) 151
(B) 149
(C) 152
(D) 148
(E) 180.67
Rationale: Corrected mean = 180×30−135+155/30
= 5400−135+155/30
=5420/30=180.67
Answer E
Answer: (E) 180.67
Question: If x and y are integers, what is the least positive number of 24x+21y?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: 24x+21y = 3(8x+7y) which will be a minimum positive number when 8x+7y = 1.
8(1) + 7(-1) = 1
Then 3(8x+7y) can have a minimum positive value of 3.
The answer is A.
Answer: (A) 3
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 1, 2, and 4 if each digit can be used only once in each number?
(A) 1210
(B) 1221
(C) 1332
(D) 1443
(E) 1554
Rationale: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(111) + 2(222) + 2(444) = 1554
The answer is E.
Answer: (E) 1554
Question: Find the greatest number that will divide 40, 60 and 120 so as to leave the same remainder in each case.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Required number = H.C.F. of (60 - 40), (120 - 60) and (120-40)
= H.C.F. of 20, 60 and 80 = 2.
ANSWER :A
Answer: (A) 2
Question: A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 26
(D) 30
(E) 32
Rationale: The committee could have
0 men and 3 women = 4 possibilities ( 4c3 )
1 man and 2 women = 12 possibilities ( no couple should be in the team : 4 * 3c2 )
2 men and 1 woman = 12 possibilities ( no couple should be in the team : 4c2 *2c1 )
3 men and 0 women = 4 possibilities ( 4c3 )
Therefore 4+12+12+4=32
Answer E 32
Answer: (E) 32
Question: find out how many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?
(A) 4
(B) 5
(C) 9
(D) 10
(E) 11
Rationale: Number of positive multiples of 5 less than 60 = 11
5*1=5
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5*7=35
5*8=40
5*9=45
5*10=50
5*11=55
Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50
Answer B
Answer: (B) 5
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 580 pounds after processing, how many pounds did it weigh before processing?
(A)  191
(B)  355
(C)  737
(D)  892
(E)  1,560
Rationale: Let weight of side of beef before processing = x
(65/100)*x = 580
=> x = (580 * 100)/65 = 892
Answer D
Answer: (D)  892
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $78.2 after it went on sale for 15% off, what is the difference between the original price and the final price?
(A) $0.00
(B) $5.75
(C) $3.40
(D) $5.00
(E) $6.80
Rationale: 0.85*{Original Price} = $78.2 --> {Original Price} = $92.
{Final Price} = $78.2*1.25 = $97.75.
The difference = $97.75 - $92 = $5.75
Answer: B.
Answer: (B) $5.75
Question: The area of a triangle is with base 4m and height 5m?
(A) 10
(B) 20
(C) 30
(D) 15
(E) 11
Rationale: The area of a triangle=1/2*bh
=1/2 * 4 * 5 = 10 m^2
ANSWER:A
Answer: (A) 10
Question: Three coworkers P , J , R meet for Dinner. P had 5 sandwiches, J had 3 and R had none. Both PJ share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PJ, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
(A) a) 5$
(B) b) 3 $
(C) c) 7 $
(D) d) 4 $
(E) e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
J:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: (C) c) 7 $
Question: A certain league has two divisions. The respective divisions had 7 and 9 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
(A)  30
(B)  31
(C)  34
(D)  36
(E)  38
Rationale: Overall, there can be 31 minuses. Tus, it is B.
Answer: (B)  31
Question: Jill is dividing her eight-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
(A) 10
(B) 35
(C) 126
(D) 252
(E) 630
Rationale: With 8 players, the process of figuring out how many groups of 4 can be formed is pretty straight-forward....
8C4 = 8!/(4!4!) = 70 possible groups of 4
Once forming that first group of 4, the remaining 4 players would all be placed on the second team by default.
The 'twist' is that the two teams of 4 canshow upin either order:
B
Answer: (B) 35
Question: Ram can do a piece of work in 8 days which Shyam can finish in 12 days. If they work at it on alternate days with Ram beginning, in how many days, the work will be finished?
(A) 9 1/3
(B) 9 1/2
(C) 9 1/4
(D) 10 1/3
(E) 11 1/3
Rationale: (ram+shyam)'s 2 days work = (1/8+1/12) = 5/24
work done in 4 pair of days = (5/24)*4 = 5/6; remaining work = 1-(5/6) = 1/6
work done by ram on 9th day = 1/8; Remaining work = (1/6)-(1/8)= 1/24
On 10th day it is shyam's turn
1/12 work is done by shyam in 1 day
1/24 work is done by shyam in 12*(1/24) = 1/2
total time = (9 + 1/2) day
ANSWER:B
Answer: (B) 9 1/2
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.8 cm when a man gets on it. The mass of man is
(A) 12 kg
(B) 60 kg
(C) 108 kg
(D) 96 kg
(E) None
Rationale: Solution
Volume of water displaced	= (3 x 2 x 0.018)m3
= 0.108m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.108×1000) kg
= 108 kg.
Answer C
Answer: (C) 108 kg
Question: John has on his shelf four books of poetry, four novels, and three 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) 12/55
(C) 3/10
(D) 7/20
(E) 8/45
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 4/11*3/10 + 3/11*4/10 = 12/55.
Answer: B.
Answer: (B) 12/55
Question: What is the sum of all 5 digit numbers which can be formed with the digits 0,1,2,3,4 without repetation?
(A) 2599980
(B) 235500
(C) 923580
(D) 765432
(E) 765434
Rationale: 10(11111)*4! - 10(1111)3! = 2599980
ANSWER:A
Answer: (A) 2599980
Question: The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P?
(A) 0.54
(B) 0.77
(C) 0.82
(D) 0.97
(E) 1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P
Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P
If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD
Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD
So, if these elements lie within 2 and 3 PDs of mean, m=0
we can find which one of these values of PD satisfies each value within Q
Only PD = 0.77 does
Answer : B
Answer: (B) 0.77
Question: A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long?
(A) 76 sec
(B) 89 sec
(C) 87 sec
(D) 95 sec
(E) 16 sec
Rationale: Speed = 360/30 = 12 m/sec.
Required time = (360 + 780)/12
= 95 sec.
Answer:D
Answer: (D) 95 sec
Question: The following questions are based on the information given below:
1)A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
2)Two sides measuring 5 cm x 4 cm are coloured in red.
3)Two faces measuring 4 cm x 3 cm are coloured in blue.
4)Two faces measuring 5 cm x 3 cm are coloured in green.
5)Now the block is divided into small cubes of side 1 cm each.
How many small cubes will have will have three faces coloured ?
(A) 14
(B) 8
(C) 10
(D) 12
(E) 16
Rationale: Such cubes are related to the corners of the cuboid and in the cuboid there are 8 corners.
Hence, the required number of small cubes is 8.
Answer :B
Answer: (B) 8
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 40 days as before. How many of them left?
(A) 100
(B) 0
(C) 200
(D) 400
(E) 500
Rationale: 2000 ---- 50
2000 ---- 40
x ----- 40
x*40 = 2000*40
x=2000
2000
-------
0
ANSWER:B
Answer: (B) 0
Question: If the order of the letter in the English alphabet is reversed which letter will be the seventh to right of the twelfth letter from the right?
(A) E
(B) V
(C) F
(D) U
(E) T
Rationale: Lkjihgfedcba
So ans wiil be
E
ANSWER:A
Answer: (A) E
Question: The proportion of copper and zinc in the brass is 3:7. How much zinc will there be in 100 kg of brass?
(A) 70
(B) 50
(C) 40
(D) 270
(E) 170
Rationale: 7/10 * 100 = 70
ANSWER:A
Answer: (A) 70
Question: A meal cost $ 36.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
(A) 40-42
(B) 39-41
(C) 38-40
(D) 37-39
(E) 36-37
Rationale: 10%(36.5) = 3.65
15%(36.5) = 5.475
total amount could have been 36.5+3.65 and 36.5+5.475
=> could have been between 40.15 and 41.975
=> approximately between 40 and 42
Answer is A.
Answer: (A) 40-42
Question: If a square mirror has a 20-inch diagonal, what is the approximate perimeter Q of the mirror, in inches?
(A)  40
(B)  60
(C)  80
(D)  100
(E)  120
Rationale: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter Q must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
Answer: (B)  60
Question: The cost price of a radio is Rs.2550 and it was sold for Rs.2130, find the loss %?
(A) 18
(B) 10
(C) 15
(D) 66
(E) 41
Rationale: 2550 ---- 400
100 ---- ? => 15%
Answer: C
Answer: (C) 15
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 60%
(B) 50%
(C) 25%
(D) 15%
(E) 10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 50 - {both} + 40
{both} = 15%.
Answer: D.
Answer: (D) 15%
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
(A) 3
(B) 2
(C) 1
(D) 0
(E) None of these
Rationale: Let n=4q+3.
2n=8q+6=4(2q+1)+2
Thus, when 2n is divided by 4, the remainder is 2.
Correct Option: B
Answer: (B) 2
Question: The area of a rectangular plot is 21 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
(A) 10 metres
(B) 5 metres
(C) 11 metres
(D) Data inadequate
(E) None of these
Rationale: L × B = 21 × B
∴ L = 21 m
and L – B = 10
∴ B = 21 – 10 = 11 m
Answer C
Answer: (C) 11 metres
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 29
(B) 38
(C) 39
(D) 37
(E) 75
Rationale: Average = (76 + 65 + 82 + 67 + 85)/5
= 375/5
= 75.
Answer: E
Answer: (E) 75
Question: Find the remainder when 6^50 is divided by 215
(A) 36
(B) 99
(C) 27
(D) 99
(E) 17
Rationale: Ans: 650=(63)16.62=21616.62650=(63)16.62=21616.62
So this expression gives a remainder of 36
Answer:A
Answer: (A) 36
Question: complete the numerical series with the correct number
5+2+2=101018
9+3+4=273660
8+2+3=162438
5+2+5=102533
7+5+5= ?
(A) 468645
(B) 454586
(C) 454585
(D) 454386
(E) 353565
Rationale: 7+5+5= 353565
Answer : E
Answer: (E) 353565
Question: Lionel left his house and walked towards Walt's house, 48 miles away. Four hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: In the first 4 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=4*3=12 miles. So, the distance between him and Walt was 48-12=36 miles when Walt left his house. Now, their combined rate to cover this distance was 3+6=9 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=36/9=4 hours. Total time that Lionel was walking is 4+4=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles.
Answer: D.
Answer: (D) 24
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.80 less, he could have gained 25%. What is the cost price?
(A) 372
(B) 375
(C) 278
(D) 400
(E) 288
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
80 ----- ? => 375
Answer:D
Answer: (D) 400
Question: Which of the following is not a prime number ?
(A) 743
(B) 740
(C) 751
(D) 757
(E) 853
Rationale: Clearly, 740 is not a prime number.
Answer : B
Answer: (B) 740
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 7 ounces of corn syrup, how many ounces of water does it contain?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 105
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 7*180/12 = 105 ounces of water
E
Answer: (E) 105
Question: a1, a5, a13 (terms of AP) are in GP and a6 + a15 =63. Find a23
(A) 181/3
(B) 182/3
(C) 183/3
(D) 184/3
(E) 182/5
Rationale: a1
a5= a1+ 4d
a13= a1+12d
Now a5/a1 = a13/a5---->>a1=4d........(1)
Given a6 + a15=63
----> a1+5d + a1+14d=63
---->2a1+ 19d = 63
---->8d+ 19d=63 from (1)
----> d=63/27= 7/3
so a=4d=4*7/3=28/3 from (1)
a23= a1+ 22d =28/3 +22*7/3
=182/3
ANSWER:B
Answer: (B) 182/3
Question: A, B, C together started a business. A invested Rs.2000 for 5 months B invested Rs.8000 for 6 months and C Rs.14000 for 3 months. If they get a total profit of Rs.2500. Find the share of A?
(A) 2999
(B) 3000
(C) 2777
(D) 2999
(E) 250
Rationale: 1*5:4*6:7*3
5: 24: 21
5/50 * 2500 = 250
Answer:E
Answer: (E) 250
Question: (800/64) x (1296/36)=?
(A) 420
(B) 460
(C) 500
(D) 540
(E) None of them
Rationale: =800/64 x 1296/36
=12.5 x 36
=450
Answer is E
Answer: (E) None of them
Question: If 3x – 5y = 5 and x/x+y=5/7, then what is the value of x – y?
(A) 9
(B) 6
(C) 4
(D) 3
(E) None of these
Rationale: 3x – 5y = 5...(i)
And xx+y=57xx+y=57
⇒ 7x = 5x+ 5y
⇒ 2x = 5y... (ii)
From (i) and (ii), x = 5 and y = 2
∴ x – y = 3
Answer D
Answer: (D) 3
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $13. If the shop keeper has a order of 200 articles, how much profit he will get?
(A) A)200
(B) B)2000
(C) C)1500
(D) D)600
(E) E)700
Rationale: Total money after selling articles = 200*13 = 2600
cost price = 200*10 = 2000
profit = 600
correct option is D
Answer: (D) D)600
Question: The speed of a boat in still water in 18 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 14 minutes is:
(A) 11.4 km
(B) 10.9 km
(C) 10.4 km
(D) 6.06 km
(E) 12.56 km
Rationale: Explanation:
Speed downstream = (18 + 6) = 24 kmph
Time = 14 minutes = 14/60 hour = 7/30 hour
Distance travelled = Time × speed = (7/30)×26 = 6.06 km
Answer: Option D
Answer: (D) 6.06 km
Question: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must be positive, where k is :
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: straight forward question if you realize that 4 negative numbers when added can NEVER give you a positive sum. This directly eliminates A.
As we are given that x+y+z+w=15 and we need to find what is the least number of variables out of the 4 given (x,y,z,w) that need to be positive to adhere to x+y+z+w=15 ,
Consider any large value for x = 45 and -15,-10 and -5 for y,z,w respectively to give you x+y+z+w=15.
Thus k =1 for 'k' value to be the least.
ANSWER:B
Answer: (B) 1
Question: A rectangular table seats 5 people on each of two sides, with every person directly facing another person across the table. If 10 people choose their seats at random, what is probability that person P directly faces person Q?
(A) 1/10
(B) 1/9
(C) 1/8
(D) 1/7
(E) 1/6
Rationale: Person P will be seated somewhere at the table.
Each of the other 9 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/9.
The answer is B.
Answer: (B) 1/9
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 187.5 m
(B) 127.5 m
(C) 277.5 m
(D) 727.5 m
(E) 777.5 m
Rationale: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
Answer: B
Answer: (B) 127.5 m
Question: In an objective test, a correct answer scores 4 marks, and a wrong answer scores 2 marks. A student scores 480 marks from 150 questions. how many answers are correct?
(A) 90
(B) 80
(C) 70
(D) 60
(E) 50
Rationale: if all ans. right the marks=4*150=600
but score=480
wrong attempt marks=600-480=120
wrong ans.=120/2=60
right ans.=150-60=90.
ANSWER:A
Answer: (A) 90
Question: By using the numbers 1, 2, 5, 7 and 9 only once, how many five digit numbers can be made that are divisible by 25?
(A) 11
(B) 12
(C) 5
(D) 10
(E) 9
Rationale: A number to be divisible by 25 must end with 00, 25, 50, or 75.
So, there are the following cases possible:
179-25 --> the first three digits can be arranged in 3=6 ways.
129-75 --> the first three digits can be arranged in 3=6 ways.
Total = 6 + 6 = 12.
Answer: B.
Answer: (B) 12