mathewhe/aqua_rat huggingface dataset:
Question: A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream,it takes 5 hours.What is the speed of the boat in still water ?
(A) 4 km/hr
(B) 6 km/hr
(C) 7 km/hr
(D) Data inadequate
(E) None of these
Rationale: Solution
Rate downstream =(20/2) kmph = 10 kmph, Rate upstream =(20/5) = 4 kmph.
∴ Speed in still water =1/2(10+4) kmph = 7 kmph. Answer C
Answer: (C) 7 km/hr
Question: The editor of an anthology of short stories will select authors from a pool of 11 authors, of which 4 are female. If the anthology is to include the work of 7 authors of which at least 2 are female, in how many ways can the editor select the authors?
(A) 301
(B) 312
(C) 323
(D) 334
(E) 345
Rationale: 11C7 = 330
The number of ways to select 7 males is 7C7 = 1
The number of ways to select 6 males and 1 female is 7C6*4C1 = 28
330 - 1 - 28 = 301
The answer is A.
Answer: (A) 301
Question: Tough and Tricky questions: Arithmetic.
(14^2 + 14^2)/7^2 =
(A) 4
(B) 58
(C) 29
(D) 8
(E) 116
Rationale: Ans is 8
my approach was:
(14^2 + 14^2)/29^2 =14(14+14)/7*7
=14*28/7*7=2*4=8
D
Answer: (D) 8
Question: Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr?
(A) 4864
(B) 4854
(C) 4844
(D) 4868
(E) 4866
Rationale: p=1000000, r=4% annual , t=3 yr
SI = p*r*t/100 = 1000000*4*3/100 = 120000
CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864
difference = CI - SI = 124864 - 120000 = 4864
ANSWER:A
Answer: (A) 4864
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 787
(C) 288
(D) 212
(E) 233
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: (A) 432
Question: Find the curved surface area, if the radius of a cone is 21 m and slant height is 15 m?
(A) 660
(B) 770
(C) 880
(D) 900
(E) 990
Rationale: Cone curved surface area = Ï€rl
22/7 Ã— 21 Ã— 15 = 66 Ã— 15 = 990 m(power2)
Answer is E.
Answer: (E) 990
Question: A train is 360 meter long is running at a speed of 54 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 27 seconds
(B) 33 seconds
(C) 40 seconds
(D) 11 seconds
(E) 12 seconds
Rationale: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/15) = 33 seconds
Answer:B
Answer: (B) 33 seconds
Question: Find the value of (70+ 28/100) × 100
(A) 7028
(B) 4028
(C) 3128
(D) 3256
(E) 5264
Rationale: (7000 +28)/100 * 100 = 7028
Answer : A
Answer: (A) 7028
Question: A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
(A) 48m3
(B) 94m3
(C) 44m3
(D) 04m3
(E) 14m3
Rationale: Volume=πr2hVolume=(227∗1∗1∗14)m3=44m3
Answer:C
Answer: (C) 44m3
Question: What is the smallest five digit number that is divisible by 15, 32, 45, and 54?
(A) 11260
(B) 11860
(C) 12360
(D) 12960
(E) 13560
Rationale: 15 = 3 * 5
32 = 2^5
45 = 3^2 * 5
54 = 2 * 3^3
LCM = 2^5 * 3^3 * 5 = 4320
The smallest five-digit number that is a multiple of 4320 is 3*4320 = 12,960
The answer is D.
Answer: (D) 12960
Question: Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog?
(A) 16.5 kmph
(B) 16.6 kmph
(C) 16.4 kmph
(D) 16.9 kmph
(E) 16.2 kmph
Rationale: In an average speed of 22 kmph horse got dog in 6 hours
So distance=speed*time
distance=22*6=132km
Dog takes 8 hours to travel 132 km. So the speed if dog is
speed=distance/time
speed=132/8=16.5 kmph
Answer: 16.5 kmph
Answer A
Answer: (A) 16.5 kmph
Question: A & B can make paintings in 6 days, B & C can can make those paintings in 10 days. If A, B & C together can finish the work in 4 days, then A & C together will do it in ________ days.
(A) 4 (2/7) days
(B) 1/ 8 days
(C) 2 (2/5) days
(D) 6 (3/ 8) days
(E) 1/ 9 days
Rationale: EXPLANATION:
Hint:
We are given that, A,B, & C together complete the work in 4 days.
We can write, (A+B+C) 's 1 day work =	1/4
Similarly, (A+B) 's 1 day work = 1/6 days & (B+C)'s 1 day work =	1/10
Since the work is divided in combination and we are asked to find out the combined work of (A + C), so we can find out,
(A + C)'s 1 day work = [2 (A+B+C)'s 1 day work] – [(A+ B) 's 1 day work + (B+C)'s 1 day work]
=[2*1/4]-[(1/6)+(1/10)]
=	1/2	–	16/60	=	1/2	–	4/15	=	7/30
Hence, A & C together can complete the work in 30 /7 days = 4(2/7)days.
ANSWER IS A
Answer: (A) 4 (2/7) days
Question: a = 4^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 2 different values and answer is C....
Answer: (C) Two
Question: the average distance between the sun and a certain planet is approximatly 2.6 10^9 inches. which of the following is the closest to the average distence between sun and the planet in kelometers? (1 km is approx 3.9 x 10^4 inches)
(A) 7 x (10)^5
(B) 7 x (10)^7
(C) 6.7 x (10)^4
(D) 7 x (10)^8
(E) 7 x (10)^12
Rationale: No need to solve entire problem.
Distance in KM = 26*(10)^9/39*(10)^4 which is -260*(10)^8/39*(10)^4 = 6.7 x(10)^4
Answer : C
Answer: (C) 6.7 x (10)^4
Question: If W is the set of all the integers between 59 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 27
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Multiples of 2 from 59 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 58=[99/2]-[58/2]=49-29=20
Multiples of 3 from 59 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 58=[99/3]-[58/3]=33-169=14
Multiples of2 and 3 bothi.e.6 from 59 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 58=[99/6]-[58/6]=16-9=7
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 20 + 14 - 7 = 27
Answer Option A
Answer: (A) 27
Question: Which of the following equations has a solution in common with x^2 + 5x + 4 = 0?
(A) 2x^2 + 5x +4 = 0
(B) x^2 - 3x - 4 = 0
(C) 2x^2 - 14 1/2x + 7/2 = 0
(D) x^2 + 4x - 21 = 0
(E) none of the above
Rationale: Given : x^2 + 5x + 4 = 0 => (x+1) (x+4) = 0 => -1 and -4 are the roots..
A. 2x^2 + 4x + 3/2 = 0 => (x+1/2) (2x+3)
B. x^2 - 3x - 4 = 0 => (x-7) (2x-1/2)
C. 2x^2 - 14 1/2x + 7/2 = 0 => (x-7) (x-3)
D. x^2 + 4x - 21 = 0 => (x+7) (x-3)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "B" is correct answer... because it shares the one root (part of the solution), -1, from the (x+1) portion of its simplification.
Answer: (B) x^2 - 3x - 4 = 0
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
(A) 5
(B) 3
(C) 4
(D) 7
(E) 9
Rationale: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.
Answer: B
Answer: (B) 3
Question: A train running at the speed of 52 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 130 m
(B) 786 m
(C) 566 m
(D) 546 m
(E) 440 m
Rationale: Speed = 52 * 5/18 = 130/9 m/sec
Length of the train = speed * time = 130/9 * 9
= 130 m
Answer: A
Answer: (A) 130 m
Question: Approximately how many revolutions will be made by a car tire with a 14-inch diameter if the car travels 1 mile?
(A) 120
(B) 180
(C) 1,231
(D) 1,433
(E) 1,440
Rationale: Diameter of car tire = 14 inches
Radius of car tire = 7 inches = 7*2.54 cm = 17.78 cm
Circumference of the car tire = 2*pi * 17.78 = 2 *3.14 *17.78= 111.66 cm
Distance traveled by car = 1 mile = 1 *1.6 km = 1.6 km = 1600 m = 1.6 * 10^5 cm
Number of revolutions =Distance traveled / Circumference of tire = 1.6*10^5 / 111.66 = 1432.92
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer D
Answer: (D) 1,433
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
(A) 29798
(B) 27908
(C) 78902
(D) 25000
(E) 27991
Rationale: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
25 = 1/100 * x => x
= 25000
Answer: D
Answer: (D) 25000
Question: In X game of billiards, X can give Y 20 points in 60 and he can give Z 50 points in 60. How many points can Y give Z in X game of 100?
(A) 30
(B) 20
(C) 25
(D) 40
(E) 75
Rationale: X scores 60 while Y score 40 and Z scores 10.
The number of points that Z scores when Y scores 100 = (100 * 50)/40 = 25.
In X game of 100 points, Y gives (100 - 25) = 75 points to C.
E
Answer: (E) 75
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 1
Rationale: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio.
Total ratio = 35
For 6 : (300/35)*6 = 51.4
Similarly , we will get for others as 60 , 68.57 , 77.14
Hence , there are 5 subject where he secured more that 50 %.
The answer is 5.
D
Answer: (D) 5
Question: 20, 19, 17, ?, 10, 5
(A) 15
(B) 14
(C) 13
(D) 12
(E) 11
Rationale: The Pattern is - 1, - 2, -3, ...
Answer : B.
Answer: (B) 14
Question: .05% of seeds in a packet do not germinate. How many seeds must be in the packet for 6 seeds not to germinate?
(A) 10000
(B) 11000
(C) 12000
(D) 14000
(E) 6000
Rationale: Let the number of total seeds be x
Then, .05% of x=6
(5/100)*(1/100)*x=6
x=12000
Answer is C
Answer: (C) 12000
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 15
(B) 10
(C) 81
(D) 71
(E) 12
Rationale: 4/12 + x/15 = 1
x = 10
Answer: B
Answer: (B) 10
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 9 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $10,395
(C) $10,791
(D) $11,500
(E) $12,705
Rationale: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10791. So the answer is (C).
Answer: (C) $10,791
Question: The average age of 25 students in a class is 12years. If teacher's age is also included then average increases 1year then find the teacher's age?
(A) 40
(B) 35
(C) 29
(D) 38
(E) 42
Rationale: Total age of 25 students = 25*12 = 300
Total age of 26 persons = 26*13 = 338
Age of teacher = 338-300 = 38years
Answer is D
Answer: (D) 38
Question: A house wife saved $4 in buying an item on sale. If she spent $29 for the item, approximately how much percent she saved in the transaction?
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) 12%
Rationale: Actual price = 29+4 = $33
Saving = 4/33* 100 = 12% approximately
Answer is E
Answer: (E) 12%
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 13 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
(A)  4
(B)  6
(C)  7.2
(D)  7.8
(E)  9
Rationale: Answer is A.
x/x+36=1/5
x=9
13-9=4
Answer: (A)  4
Question: In a certain production lot, 40 percent of the toys are red and the remaining toys are green. Half of toys are small and half are large. If 10 percent of the toys are red and small, and 40 toys are green and large. How many of the toys are red and large?
(A) 40
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 40% toys are red.
50% toys are small - 50% are large
Red and small - 10%
Red and large must be 30% (since there are total 40% red toys)
But 50% toys are large. If 30% are red and large, the rest 20% large toys must be green. So large and green toys are 20%.
These 20% large and green toys are actually 40 so total number of toys must be 200.
Since red and large toys are 30%, they must be 60.
ANSWER:B
Answer: (B) 60
Question: Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.
(A) 81
(B) 91
(C) 99
(D) 108
(E) 111
Rationale: AB² = AC² - BC²
= 15² - 12²
= 225 - 144
= 81
ANSWER :OPTION A
Answer: (A) 81
Question: During a two-week period, the price of an ounce of silver increased by 8 percent by the end of the first week and then decreased by 12 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period?
(A) 0.93x
(B) 0.95x
(C) 0.97x
(D) 0.99x
(E) 1.01x
Rationale: The price at the end is 0.88(1.08x)=0.9504x which is approximately 0.95x
The answer is B.
Answer: (B) 0.95x
Question: Soja finished 2/3 of a book. She calculated that she finished 100 more pages than she has yet to read. How long is her book?
(A) A)300
(B) B)150
(C) C)130
(D) D)90
(E) E)210
Rationale: Let x be the total number of pages in the book, then she finished 2/3*x pages.
Then she has x−2/3*x=1/3*x pages left.
2/3*x−1/3*x=100
1/3*x=100
x=300
So the book is 300 pages long.
Answer is A.
Answer: (A) A)300
Question: A clock is started at noon. By 10 minutes past 2, the hour hand has turned through how many degrees?
(A) 55Â°
(B) 60Â°
(C) 65Â°
(D) 70Â°
(E) 75Â°
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 2 hours and 10 minutes is 2*30Â° + 5Â° = 65Â°
The answer is C.
Answer: (C) 65Â°
Question: If g is the smallest positive integer such that 3,150 multiplied by g is the square of an integer, then g must be
(A)  2
(B)  5
(C)  6
(D)  7
(E)  14
Rationale: Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by g is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x g = square of an integer
According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, g = 7 x 2 = 14
Answer is E.
Answer: (E)  14
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is?
(A) 11
(B) 66
(C) 88
(D) 10
(E) 27
Rationale: Let the rate be R% p.a. Then,
(5000 * R * 2)/100 + (3000 * R * 4)/100 = 2200
100 R + 120 R = 2200
R = 10%
Answer:D
Answer: (D) 10
Question: A shopkeeper sold 30 articles at the cost price of 35 articles. Then find the profit% or lost%
(A) 12%
(B) 15%
(C) 16.67%
(D) 18%
(E) 22%
Rationale: here 30 articles selling price = 35 articles cost price
so the difference = 35-30 = 5
% of profit = 5*100/30 = 16.67%
correct option is C
Answer: (C) 16.67%
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 30% solution?
(A) A)6.7
(B) B)1.3
(C) C)9.6
(D) D)12.5
(E) E)28.6
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=30/100
100+10x=300+3x
7x = 200
x = 28.6
Answer is E
Answer: (E) E)28.6
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 8 days
(B) 10 days
(C) 15 days
(D) 11 3/7 days
(E) 16 days
Rationale: Explanation:
(x – 5)/15 + x/20 = 1
x = 11 3/7 days
Answer: D
Answer: (D) 11 3/7 days
Question: If n = (33)^43 + (53)^33 what is the units digit of n?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: First of all, the units digit of (33)^53 is the same as that of 3^53 and the units digit of (53)^33 is the same as that of 3^33. So, we need to find the units digit of 3^53 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
3^1=3 (the units digit is 3)
3^2=9 (the units digit is 9)
3^3=27 (the units digit is 7)
3^4=81 (the units digit is 1)
3^5=243 (the units digit is 3 again!)
...
Thus:
The units digit of 3^53 is the same as the units digit of 3^3, so 7 (53 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^53 + (53)^33 is 7 + 7 = 4.
Answer: C.
Answer: (C) 4
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 1 percent, what was the annual interest rate last year?
(A) 1%
(B) 1.1%
(C) 9.1%
(D) 10%
(E) 10.8%
Rationale: let i = interest rate
i(this year) = i(last year) + 0.10i(last year) = 1.1i(last year)
1 = 1.1 x i(last year)
i(last year) = 1/1.1 = 10/11 = 0.90909...
or i(last year) = 0.91%
ANSWER:C
Answer: (C) 9.1%
Question: The average employee age of a certain company which has 80 employees is 38. One employee aged 60 got retired and replaced by a fresher of age 22. What is the new average age of employees?
(A) 35.5
(B) 36.2
(C) 36.8
(D) 37.5
(E) 38.2
Rationale: Sum of ages of employees before replacement= 80x38=3040
Sum of ages of employees after replacement=(80x38)+22-60=3002
The new average age=3002/80=37.5
Answer: D
Answer: (D) 37.5
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) Rs:1000
(B) Rs:1067
(C) Rs:1278
(D) Rs:1028
(E) Rs:1027
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? =>
Rs:1000
Answer: A
Answer: (A) Rs:1000
Question: A committee of 4 people is to be selected from 8 people. How many different committees are possible?
(A) 28
(B) 40
(C) 56
(D) 420
(E) 336
Rationale: Because the order does not matter in selecting 4 people for the committee, this is a combination question.
The number of ways to select 4 people from 8 = 8C4 = 8!/4!*4! = 420. Hence D.
Answer: (D) 420
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
(A) 6
(B) 9
(C) 5
(D) 1
(E) 2
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5
For Rs. 6/5, toffees sold = 6. For re. 1.
Toffees sold = 6 * 5/6 = 5
AnswerC
Answer: (C) 5
Question: A, B, and C working alone can finish constructing a house in 6, 9, and 18 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
(A) 11:45 am
(B) 11:55 am
(C) 12:10 pm
(D) 12:25 pm
(E) 12:40 pm
Rationale: A completes 1/6 of the job each hour.
B completes 1/9 of the work each hour.
C completes 1/18 of the work each hour.
A completes 1/6 of the work in the first hour.
Working together, A and B complete another 5/18 for a total of 8/18.
Working together, A, B, and C can complete 6/18 of the work each hour.
To complete 10/18, the time required is (10/18) / (6/18) = 10/6 hours.
The work will be completed at 12:00 plus 4*60/6 minutes which is 12:40 pm.
The answer is E.
Answer: (E) 12:40 pm
Question: If k^3 = m^3, which of the following must be true?
(A) k = m
(B) k = -m
(C) k = |m|
(D) k = -|m|
(E) |k| = |m|
Rationale: Solution:
We are given that k^3 = m^3, and we can start by simplifying the equation by taking the square root of both sides.
3√k^3 = 3√m^3
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
3√k^3 = 3√m^3 is |k| = |m|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: E
Answer: (E) |k| = |m|
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
(A) 676
(B) 833
(C) 1023
(D) 839
(E) 1035
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C
Answer: (C) 1023
Question: 7122,6521,8332,4743,9911,387?
find the value of the question tag.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 7+1+2+2=12
6+5+2+1=14
so
9+9+1+1=20
3+8+7+x=22
so x=4
ANSWER:D
Answer: (D) 4
Question: The average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.
(A) 68
(B) 80
(C) 78
(D) 60
(E) 87
Rationale: Clearly 13th result=(sum of 25 results)-(sum of 24 results)
=(18*25)-(14*12)+(17*12)
=450-(168+204)
=450-372
=78.
Answer is C.
Answer: (C) 78
Question: Evaluate: 13 + sqrt(- 4 + 5Ã—3Ã·3) =?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: According to order of operations, inner brackets first where 5x3Ã·3 is first calculated since it has a multiplication and a division.
5Ã—3Ã·3 = 15Ã·3 = 5
Hence
13 + sqrt(- 4 + 5Ã—3Ã·3)= 13 + sqrt(- 4 + 5)
= 13 + sqrt(1) = 13 + 1 = 14
correct answer C)14
Answer: (C) 14
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?
(A) 2
(B) 1
(C) 4
(D) 3
(E) 5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 120,000 m : C is the circumference
C = 5 meters
correct answer E
Answer: (E) 5
Question: How many 5-digit positive integers exist the sum of whose digits are odd?
(A) 36000
(B) 38000
(C) 45000
(D) 90000
(E) None
Rationale: Solution:
There are 9�104 = 90000, 5-digit positive integers.
Out of these 90000 positive integers, the sum of the digits of half of the numbers will add up to an odd number and the remaining half will add up to an even number.
Hence, there are 90000 /2= 45000, 5-digit positive integers whose sum add up to an odd number.
Answer: Option C
Answer: (C) 45000
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:
(A) 86
(B) 90
(C) 92
(D) 94
(E) 95
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86.
A
Answer: (A) 86