mathewhe/aqua_rat huggingface dataset:
Question: If X = 2 + 1/(1+1/(1-1/2))then the value of 4x+7/3
(A) 12 2/3
(B) 15 2/3
(C) 18 2/3
(D) 11 2/3
(E) 17 2/3
Rationale: X = 2 + 1/(1+1/(1-1/2))
= 2 + 1/(1+2)
= 2 + 1/3
X = 7/3 ==> 4X + 7/3 => 4(7/3) + 7/3
=> 28/3 + 7/3
=> 35/3
=> 11 2/3.
Answer is D.
Answer: (D) 11 2/3
Question: A thief goes away with a SANTRO car at a speed of 30 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?
(A) 1 hours
(B) 2 hours
(C) 2/3 hours
(D) 1/3 hours
(E) 2/5 hours
Rationale: -----------30--------------------|
60 30
D = 30
RS = 60 â€“ 30 = 30
T = 30/30 = 1 hours
ANSWER:A
Answer: (A) 1 hours
Question: The ratio of two quantities is 10 : 7. If each of the quantities is increased by 2, their ratio changes to 15:11 then the greatest number is?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 20
Rationale: Let the numbers be 10x and 7x
Then 10x+2 / 7x+2 = 15/11
110x+22 = 105x+30
5x = 8
x = 1.6
Greatest number = 10*1.6 = 16
Answer is D
Answer: (D) 16
Question: The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
(A) 74
(B) 94
(C) 184
(D) 364
(E) 512
Rationale: L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 x 4) + 4 = 364.
Answer: Option D
Answer: (D) 364
Question: If x^2 + 9/x^2 = 22, what is the value of x - 3/x
(A) 36
(B) 25
(C) 9
(D) 5
(E) 4
Rationale: To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (22) - 2*3 = 16
=> t^2 = 16. Thus t=4 or t=-4.
Answer E
Answer: (E) 4
Question: College T has 1000 students. Of the 300 students majoring in one or more of the sciences,150 are majoring in Chemistry and 180 are majoring in Biology. If at least 60 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
(A) 110 to 150
(B) 60 to 150
(C) 30 to 150
(D) 60 to 140
(E) 70 to 130
Rationale: Total = Chemistry + Biology - Both + Neither
300 = 150 + 180 - Both + N
We know that N (Neither) must be at least 30, so set N=30 and solve:
300 = 150 + 180 - Both + 60
300 = 330 - Both
Both = 30
Even if you're not sure whether 150 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,
Both can not be greater than 150, because even if every chemistry major was also a biology major, there are only 130 chemistry majors total. C the solution.
Answer: (C) 30 to 150
Question: A certain class of students is being divided into teams. The class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A) 6
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: Prime factorization of 18 = 2*3^2
Prime factorization of 24 = 2^3 *3
LCM of the given numbers = 2^3 *3^2
=72
Answer E
Answer: (E) 72
Question: Sukhbir is taller than Randhir but not as tall as Ajit. If Manoj is taller than Nitin, who is shorter than Ajit, then who among them is the shortest?
(A) Nitin
(B) Sukhbir
(C) Manoj
(D) Data inadequate
(E) None of these
Rationale: Data Inadequate. As No relation is given among Randhir and Nitin.
ANSWER:D
Answer: (D) Data inadequate
Question: Students are in clubs as follows: Science-20, Drama-30, and Band-12. No student is in all three clubs, but 8 are in both Science and Drama, 6 are in both Science and Band, and 4 are in Drama and Band.
How many different students are in at least one of the three clubs?
(A) 36
(B) 38
(C) 42
(D) 44
(E) 48
Rationale: Total students = S + D + B - (sum of 2-group overlaps) + (all three)
Total students = 20 + 30 + 12 - (6 + 8 + 4) + 0 = 44 students.answer is D
Answer: (D) 44
Question: Find the odd man out.
8, 20, 14, 21, 16, 28, 32
(A) 16
(B) 21
(C) 8
(D) 28
(E) 14
Rationale: Explanation:
Each of the numbers except 21 is a even numbers.
Answer: B) 21
Answer: (B) 21
Question: Find the odd man out. 21, 28, 35, 42, 49, 51, 56
(A) 21
(B) 28
(C) 35
(D) 42
(E) 51
Rationale: All numbers except 51 are multiples of 7
Answer is E
Answer: (E) 51
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
(A) 3:4
(B) 3:5
(C) 4:5
(D) 16:15
(E) 12:13
Rationale: For an income of $1 in 9% stock at 96, investment =$(96/9)=32/3
For an income of $1 in 12% stock at 120, investment =$(120/12)
=$10
Ratio of investment=32/3:10
=16:15
Option D
Answer: (D) 16:15
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 4720 votes were polled, then how many valid votes did B get?
(A) 1534
(B) 2999
(C) 2834
(D) 2777
(E) 2991
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 4720
32.5k = 32.5k/100k * 4720 = 1534
The number of valid votes polled in favour of B is 1534.
Answer: A
Answer: (A) 1534
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 22
(B) 28
(C) 29
(D) 20
(E) 21
Rationale: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
Answer: D
Answer: (D) 20
Question: A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ?
(A) Rs.8600
(B) Rs.8620
(C) Rs.8820
(D) Rs. 8840
(E) Rs. 8940
Rationale: Amount = 8000 *1+(5/100)2
= 8000 *21/20 * 21/20
= Rs.8820
ANSWER:C
Answer: (C) Rs.8820
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $211?
(A) 1,108
(B) 2,100
(C) 2,108
(D) 2,124
(E) 2,180
Rationale: I think it should be E.
I can buy 8 250-pack for Rs 22.95*8 = $183.60
Now, I can buy 9 20-pack for 3.05*9 = $15.25
Now, I am left with only $1.15. I cannot but anything with this.
Hence Total Hotdogs = 250*8 + 20*9 = 2180
Answer: (E) 2,180
Question: Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 5 kg of fresh grapes?
(A) 2 kg
(B) 2.4 kg
(C) 2.5 kg
(D) 10 kg
(E) 0.625
Rationale: The weight of non-water in 5 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 5âˆ—0.1=xâˆ—0.8--> x=0.625
Answer: E.
Answer: (E) 0.625
Question: Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%.
(A) 429.3
(B) 270
(C) 177
(D) 166
(E) 111
Rationale: Explanation:
Cost of each share = (20 + 2.5% of 20) = Rs.20.5
Therefore, number of shares = 8800/20.5 = 429.3
ANSWER:A
Answer: (A) 429.3
Question: A fast food restaurant sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this restaurant?
(A) 23
(B) 33
(C) 43
(D) 53
(E) 63
Rationale: 43.
After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
Answer: (C) 43
Question: A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.50. If the company’s latest order required a truck with at least 384,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?
(A) $3,000
(B) $1,350
(C) $1,725
(D) $2,050
(E) $2,250
Rationale: Number of boxes= Total volume/volume of one box= 384,000/ (8*10*12)= 400
One box costs 7.50, so 400 box will cost= 400*7.5= 3000
A is the answer
Answer: (A) $3,000
Question: Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?
(A) 435
(B) 456
(C) 467
(D) 489
(E) 512
Rationale: Let suppose total number of students in class are X.
Then from the question we can conclude it that,
X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512
E
Answer: (E) 512
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
(A) 60%
(B) 50%
(C) 80%
(D) 70%
(E) 53%
Rationale: L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100
= 50%
Answer: B
Answer: (B) 50%
Question: Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
(A) 18 hrs
(B) 16 hrs
(C) 15 hrs
(D) 12 hrs
(E) 10 hrs
Rationale: Explanation:
1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
ANSWER IS B
Answer: (B) 16 hrs
Question: A & B started one company. They invest Rs. 1,00,000/- each. They deposit the money to Bank. Bank give 1% interest per month. After 2 years B left from company and asked A to return the money with interest. A says it will take time to release the FD and he assure B to give the money withinterest @0.5%. B Agreed this. What is the profit of A?
(A) 48000
(B) 12000
(C) 36000
(D) 24000
(E) 30000
Rationale: Total Investment : 100000/-*2=200000/-
Interest rate @ 1%= 200000*1%*12*2= 48000/-
Total : 248000/-
Interest to B : 100000/-*0.5%*12*2 = 12000/-
Paid to B : 100000/- + 12000/- = 112000/-
profit of A : 36000/-
Answer is C
Answer: (C) 36000
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses T at the restaurant? (Assume that all boxes are filled to capacity.)
(A) 96
(B) 240
(C) T=256
(D) T=384
(E) T=480
Rationale: Most Test Takers would recognize the system of equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: (E) T=480
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $400 before any discount?
(A)  $230.00
(B)  $224.00
(C)  $263.80
(D)  $282.00
(E)  $210.00
Rationale: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $400 would be.....
($400)(.7)(.8) =
($400)(.56)=224
Final Answer:
B
Answer: (B)  $224.00
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 20 hrs and a machine of type S does the same job in 30 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Type R completes 1/20 of the job each hour.
Type S completes 1/30 of the job each hour.
Together R and S complete 1/20 +1/30 = 1/12 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/12) = 1 job completed
n = 6
The answer is C.
Answer: (C) 6
Question: A letter lock consists of three rings each marked with nine different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
(A) 176
(B) 178
(C) 728
(D) 789
(E) 770
Rationale: Since each ring consists of nine different letters, the total number of attempts possible with the three rings is
= 9 * 9 * 9= 729. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 729 - 1 = 728.
Answer: C
Answer: (C) 728
Question: How many words can be formed using the letters of the word “COMPANY”?
(A) 1224
(B) 2434
(C) 3243
(D) 3435
(E) 5040
Rationale: There are ‘7’ different letters of the word “COMPANY”
Number of Permutations taking all the letters at a time = 7P7
7!= 5040
E
Answer: (E) 5040
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
(A) 6 months
(B) 8 months
(C) 9 months
(D) 10 months
(E) 15 months
Rationale: TD=Amt*R*T/(100+RT)
given TD=160,Amt=1760,R=12,T=?
by substituting the values we get,
160=(1760*12T)/(100+12T)
160(100+12T)=1760*12T
100+12T=(1760*12T)/160
100+12T=132T
120T=100
t=100/120=5/6yrs i.e (5/6)*12=10months
ANSWER:D
Answer: (D) 10 months
Question: On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor.
(A) 170
(B) 179
(C) 37
(D) 67
(E) 32
Rationale: Divisor = (Dividend – Remainder/Quotient)
=(15968-37)/89 =179
ANSWER B 179
Answer: (B) 179
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 6*+2 and 6*+6, inclusive ?
(A) 1
(B) None of the above
(C) 2
(D) 3
(E) 4
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6* + 2 = 6! + 2 and 6* + 6 = 6! + 6.
Now, notice that we can factor out 2 our of 6! + 2 so it cannot be a prime number, we can factor out 3 our of 6! + 3 so it cannot be a prime number, we can factor out 4 our of 6! + 4 so it cannot be a prime number, ... The same way for all numbers between 6! + 2 and 6! +7, inclusive. Which means that there are no primes in this range.
Answer: B
Answer: (B) None of the above
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
(A) 90 sec
(B) 75 sec
(C) 85 sec
(D) 80 sec
(E) None of these
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5) = 90 sec.
ANSWER:A
Answer: (A) 90 sec
Question: Two cars cover the same distance at the speed of 32 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 73
(B) 38
(C) 64
(D) 83
(E) 93
Rationale: Explanation:
32(x + 1) = 64x
X = 1
32 * 2 = 64 km
Answer: Option C
Answer: (C) 64
Question: The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg. What is the weight of the new person?
(A) 75 kg
(B) 85 kg
(C) 95 kg
(D) 65 kg
(E) 105 kg
Rationale: The total weight increase = (8 x 2.5) kg = 20 kg
weight of new person = (85 + 20) kg = 105 kg
The answer is E.
Answer: (E) 105 kg
Question: A Steel company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R =1/24
Rate of machine S =1/12
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/24 +x/12 =1/2
3x/24=1/2
x=24/6=4
So no of machine R is 4
Answer B
Answer: (B) 4
Question: Of the integers between 200 and 799, inclusive, how many do not have digit 2 and 7?
(A)  256
(B)  326
(C)  410
(D)  426
(E)  520
Rationale: Options for the first digit 6-2(2 and 5)=4;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 4*8*8=256.
Answer: A.
Answer: (A)  256
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: (B) 1
Question: In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area
(A) 600 m2
(B) 540 m2
(C) 680 m2
(D) 574 m2
(E) None of these
Rationale: In a parallelogram.
Area = Diagonal × length of perpendicular on it.
= 30 × 20 = 600 m2
Answer A
Answer: (A) 600 m2
Question: The average of 7 numbers is 24. If each number be multiplied by 5. Find the average of new set of numbers?
(A) 110
(B) 122
(C) 120
(D) 125
(E) 145
Rationale: Explanation:
Average of new numbers = 24 * 5 = 120
Answer: Option C
Answer: (C) 120
Question: In a college election between two rivals, a candidate who got 40% of the total votes polled, was defeated by his rival by 160 votes. The total number of votes polled was
(A) 900
(B) 800
(C) 700
(D) 600
(E) None of these
Rationale: Let total number of votes polled be x.
Then, votes polled by other candidate
= (100 – 40)% of x = 60% of x
Now 60% of x – 40% of x = 160
⇒ 20x⁄100 = 160 ⇒ x = 800 votes
Answer B
Answer: (B) 800
Question: Krishan and Nandan jointly started a business. Krishan invested four times as Nandan did and invested his money for trible time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs.26000, find the Nandan's earning.
(A) 4000
(B) 1000
(C) 5000
(D) 3000
(E) 2000
Rationale: 4:1
3:1
------
12:1
13 ----- Rs.26000
1 ----- ? => Rs.26,000/13=Rs. 2000
Answer: E
Answer: (E) 2000
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $44. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) xy/360
(B) 9xy/40
(C) 40xy/9
(D) 396xy
(E) 396/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 44 / (xy/9) = 396/(xy).
The answer is E.
Answer: (E) 396/(xy)
Question: The ratio of two speeds of two trains is 3 to 4. If each of the trains slows its speed 5 km/ hr, what will be the ratio of these two train speeds ?
(A) 3/4
(B) 8/9
(C) 18/19
(D) 23/24
(E) It cannot be determined from the information given
Rationale: 3/4 = 3x/4x
we need to find out (3x+5)/(4x+5) off course we cannot solve this to arrive at any rational number hence E.
Answer: (E) It cannot be determined from the information given
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
(A) 94
(B) 66
(C) 39
(D) 87
(E) 58
Rationale: A
94
Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
Answer: (A) 94
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 55 percent of the pack would be outfielder cards?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 55% of toatal Ocards
12-X<.55*12
X<12-6.6
X<5.4
X=5
Ans B
Answer: (B) 5
Question: A man can row upstream at 20 kmph and downstream at 80 kmph, and then find the speed of the man in still water?
(A) 32 kmph
(B) 50 kmph
(C) 30 kmph
(D) 45 kmph
(E) 65 kmph
Rationale: US = 20
DS = 80
M = (20 + 80)/2 = 50
Answer:B
Answer: (B) 50 kmph
Question: In an office, 30 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
(A)  480
(B)  48
(C)  50
(D)  144
(E)  160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(30/100)*Workers = x+16 = > x = 48
Answer B
Answer: (B)  48
Question: 9.5 , 9.8 , 9.9 , 9.9 , 9.9 , 10.2 , 10.3 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.296 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
(A) 90.75%
(B) 85.60%
(C) 80%
(D) 75.25%
(E) 62.5%
Rationale: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.296; 10+0.296} = {9.704; 10.296}.
From the 8 listed numbers, 5 are within this range so 5/8=62.5%.
Answer: E.
Answer: (E) 62.5%
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 5
(B) 8
(C) 1
(D) 6
(E) 1.5
Rationale: Explanation:
M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: E
Answer: (E) 1.5
Question: A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days?
(A) 4
(B) 4/5
(C) 7/9
(D) 10
(E) 24/7
Rationale: A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4
A,B,C together will complete the job in 4 days
Answer is A
Answer: (A) 4
Question: The sum and the product of two numbers are 16 and 15 respectively, the difference of the number is?
(A) 14
(B) 6
(C) 7
(D) 8
(E) 2
Rationale: Explanation:
x + y = 16
xy = 15
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 256 - 60 => (x - y) = 14
Answer: A
Answer: (A) 14