mathewhe/aqua_rat huggingface dataset:
Question: Take a marker and start from a corner of a cube. How many edges you can trace if you dont move the marker twice anywhere and never remove it? (You can move the marker only on the corner and edges)
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: we can trace 9 edeges
ANSWER:C
Answer: (C) 9
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs 14400
(B) Rs 26400
(C) Rs 12000
(D) Rs 12500
(E) Rs 13000
Rationale: Ratio of the investment
=21000:17500=210:175 = 42:35 = 6:5
26400*6/11=2400*6 =14400
ANSWER A
Answer: (A) Rs 14400
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 3/3%
(C) 33 1/3%
(D) 32 1/3%
(E) 33 5/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: Two cups X and Y contain coffee and water combined in the ratio 8:5 and 5:2 correspondingly. What is the ratio in these 2 combinations be combined to get a new combination has coffee and a water in the ratio of 9:4?
(A) 2:5
(B) 2:3
(C) 2:7
(D) 2:9
(E) None of these
Rationale: Explanation :
i) : If C.P. of coffee be Re.1
Given ratio of combination in X= 8:5
Coffee in 1 cup combination in X = (8/13)cups
C.P of 1 cup combination in X= Rs. 8/13
Therefore, The ratio of Combination in Y = 5:2
Coffee in 1 cup combination in Y – (5/7) cups
C.P of 1 cup combination in B = Rs. 5/7
Ratio of new combination = 9:4
milk in 1 cup combination = 9/13
C.P of 1 cup combination = Rs/ 9/13 (Mean price)
ii) : By the rule of allegation,
i. C.P of 1 cup of combination in X =8/13
ii. C.P of 1 cup of combination in Y = 5/7
iii. Mean price (p) = 9/13
iv. d – m = 9/13 – 5-7 = 2/91
v. m – c = 9/13 – 8/13 = 1/13
Needed ratio = 2/91 : 1/13 = 2:7
Answer : C
Answer: (C) 2:7
Question: A seller uses 840gm in place of 1kg to sell his goods. Find his actual % profit or loss, when he sells his article his article on 4% gain on cost price?
(A) 23 17/21%
(B) 25%
(C) 27 25/37%
(D) 30%
(E) 32%
Rationale: Selling price of 840gm = 100+4 = $104
Profit = 104-84 = $20
% of profit = 20*100/84 = 23 17/21 %
Answer is A
Answer: (A) 23 17/21%
Question: Write 840,000,000,000 in scientific notation.
(A) 8.4 * 10^11
(B) 800.900 * 10^11
(C) 8.900 * 10^11
(D) 80.9000* 10^11
(E) 08.900 * 10^11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
840,000,000,000 = 8.4* 100,000,000,000 = 8.4 * 10 11**
correct answer A
Answer: (A) 8.4 * 10^11
Question: The product of all the prime numbers less than 20 is closest to which of the following powers of 20 ?
(A)  10^9
(B)  10^8
(C)  10^7
(D)  10^6
(E)  10^5
Rationale: 2*3*5*7*11*13*17*19
2*19*3*17*5*13*7*11
38*51*65*77
By approximation
40*50*70*70
2000*4900
By approximation
2000*5000
10,000,000
C
Answer: (C)  10^7
Question: Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 300 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1.5 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Say, if speed is 60, 300/40 = 7.5 hrs and 300/50 = 6 hrs (a reduction of 1.5 hr -> Correct answer)
Answer (B)
Answer: (B) 40
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent W of the cost would the gross profit on the item have been if it had been sold without the discount?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 75%
Rationale: Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.
Selling Price (Discounted Price) = 100%of MP - 20%MP
= 80% of MP. ---------------- (1)
Profit made by selling at discounted price = 20% of CP -------------- (2)
Apply the formula:
Profit W= Selling Price - Original Cost Price
=> 20% of CP = 80% of MP - 100% CP
=> MP = 120CP/80 = 3/2 (CP)
Now if Product is sold without any discount, then,
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= 3/2 CP - CP
= 1/2 CP
=50%of CP
Thus, Answer should beC.
Answer: (C) 50%
Question: The expression 10^12−120 is divisible by all of the following integers EXCEPT
(A) 7
(B) 3
(C) 4
(D) 8
(E) 11
Rationale: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (A) is correct.
Answer: (A) 7
Question: The public library has exactly 2 floors. It has 1/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
(A) 1/4
(B) 5/14
(C) 5/9
(D) 9/14
(E) 18/23
Rationale: Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (1/3)*x
no of books per shelf on 2nd floor = (5/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (1/3)*x*(5/6)*y = (5/18)*xy
fraction of library books on first floor = (xy)/(xy + (5/18)*xy)
=1 / (1+(5/18))
=18/23
So E
Answer: (E) 18/23
Question: Seller selling an apple for Rs.19, a Seller loses 1/6th of what it costs him. The CP of the apple is?
(A) 10
(B) 12
(C) 20
(D) 18
(E) 21
Rationale: SP=19Loss=CP20Loss=CP−SP=CP−19⇒CP20=CP−19⇒19 CP20=19⇒CP20=1⇒CP=20
C
Answer: (C) 20
Question: Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ?
(A) 1
(B) 10
(C) 30
(D) 20
(E) 21
Rationale: This is a solution from Beatthegmat:
even numbers:
(60-2)/2 + 1 = 30 even integers.
(60+2)/2 = 31 is the average of the even set.
sum = avg*(#of elements) = 31*30 = 930 = a
odd numbers:
(59-1)/2 + 1 = 30 odd integers.
(59+1)/2 = 30 is the average of the odd set.
sum = avg*(#of elements) = 30*30 = 900 = b
a-b = 930 - 900 = 30. Answer : C
Answer: (C) 30
Question: The value of (1/log3 60 + 1/log4 60 + 1/log5 60) is:
(A) 0
(B) 1
(C) 5
(D) 60
(E) 2
Rationale: log60 3 + log60 4 + log60 5 + log60 (3*4*5)
= log60 60 = 1
ANSWER:B
Answer: (B) 1
Question: Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability W that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?
(A) 8/28
(B) W=9/28
(C) W=10/28
(D) 10/18
(E) 11/18
Rationale: (3c2 *2c1*3c2)/8c5
=(3*2*3)/(8*7*6/3*2)
=18/56
=9/28
B
Answer: (B) W=9/28
Question: Eight years ago, Ajay's age was 4/3 times that of Vijay. Eight years hence, Ajay's age will be 6/5 times that of Vijay. What is the present age of Ajay?
(A) 30 years
(B) 40 years
(C) 32 years
(D) 48 years
(E) None of these
Rationale: Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.
A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)
3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8
V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8
=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8
=> 10 - 20/3 = 10/12 A - 9/12 A
=> 10/3 = A/12 => A = 40.
ANSWER:B
Answer: (B) 40 years
Question: A, B and C start a business each investing 20,000. After 6 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 67,600 was recorded. Find the share of B.
(A) 20,000
(B) 21,200
(C) 21,600
(D) 20,500
(E) None of these
Rationale: Ratio of the capitals of A, B and C
= 20000 Ã— 6 + 15000 Ã— 6 : 20000 Ã— 6 + 16000 Ã—6 : 20000 Ã— 6 + 26000 Ã— 6
= 210000 : 216000 : 250000 = 210 : 216 : 250
Bâ€™s share = (67600 Ã— 216â„676) = 21600
Answer C
Answer: (C) 21,600
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 45 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 372$
(C) 420$
(D) 450$
(E) 480$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 45 ) = 21 + 351 => 372
Hence answer will be (B) 372
Answer: (B) 372$
Question: The point A and point B is 30 miles apart, the point B and point C is 25 miles apart. A car travels from point A to point B in 30 min and point B to point C in 40 min. What is the average speed of the car?
(A) 34.15
(B) 40.35
(C) 47.14
(D) 50.12
(E) 56.66
Rationale: Average speed=Total distance covered/Total time taken
=55miles/70min
=0.79miles/min
=47.14 miles/hour
Answer: C
Answer: (C) 47.14
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 385 the Other is
(A) 180
(B) 300
(C) 270
(D) 250
(E) 350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/385 = 180
Answer is A.
Answer: (A) 180
Question: If n is a positive integer, which of the following is a possible value of |46 - 5n| ?
(A) 7
(B) 2
(C) 11
(D) 15
(E) 20
Rationale: When 46>5n, then |46- 5n| = 46- 5n = (45-5n) + 1 = {multiple of 5} + 1
When 46<=5n, then |46- 5n| = -(46- 5n) = (5n-45) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.
Answer: C
Answer: (C) 11
Question: The length of a train and that of a platform are equal. If with a speed of 54 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 227
(B) 299
(C) 450
(D) 750
(E) 211
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 15 è x = 15 * 60 / 2 = 450
Answer: C
Answer: (C) 450
Question: Sum of three numbers 286, If the first number be twice then second and third number be one third of the first, then the second number is
(A) A)70
(B) B)71
(C) C)78
(D) D)73
(E) E)74
Rationale: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=286
<=>11x/3=286
=>x=78
Answer: Option C
Answer: (C) C)78
Question: Rony walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:20. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 35 meters. What is Rony's speed in meters per minute?
(A) 108
(B) 175
(C) 198
(D) 216
(E) 252
Rationale: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×35(per block dist)
Speed = 3500mts/20min =175m/min
B is the answer
Answer: (B) 175
Question: Rs.1200 is divided so that 5 times the first share, 10 times the 2nd share and fifteen times third share amount to the same. What is the value of the second share?
(A) s525
(B) s527
(C) s598
(D) s400
(E) s500
Rationale: A+B+C = 1200
5A = 10B = 15C = x
A:B:C = 1/5:1/10:1/15 =3:2:1
2/6 * 1200 =Rs 400
Answer:D
Answer: (D) s400
Question: Mohit sold an article for $12000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 16000
(B) 25000
(C) 10000
(D) 18000
(E) 17000
Rationale: Let the CP be $x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 12000 - 10/100(12000) = 12000 - 1200 = $10800
=> 1.08x = 10800
=> x = 10000
C
Answer: (C) 10000
Question: A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is?
(A) $440
(B) $450
(C) $460
(D) $470
(E) $480
Rationale: avg = sum of observations/number of observations
avg income=(250+400+750+400+500)/5 = 460
Answer is C
Answer: (C) $460
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
(A) 175
(B) 116
(C) 197
(D) 176
(E) 267
Rationale: 25x + 46
= 26(x – 5)
x = 176
Answer:D
Answer: (D) 176
Question: What is the next number of the following sequence.
3, 10, 13, 20, 23, 30,
(A) 28
(B) 29
(C) 30
(D) 33
(E) 36
Rationale: 3
3+7=10
10+3=13
13+7=20
20+3=23
23+7=30
30+3=33
ANSWER:D
Answer: (D) 33
Question: A regular square is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ?
(A) 45 degrees
(B) 54 degrees
(C) 72 degrees
(D) 84 degrees
(E) 108 degrees
Rationale: its a regular square so divide the globe by 4.
= 360/4
= 90
90 would be the angle at O.
Angles at A and B are equivalent, so
90 + 2x = 180
2x = 90
x =45
Angles OAB and OBA will be 45 degrees each.
A
Answer: (A) 45 degrees
Question: 5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
(A) 360
(B) 430
(C) 510
(D) 540
(E) 630
Rationale: we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
5c1*4c1*3c1*3!=360
ANSWER:A
Answer: (A) 360
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his first child?
(A) 12
(B) 24
(C) 30
(D) 48
(E) 120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and C1 are always together.
Consider F and C1 to be one unit, then we would have total of four units: {FC1}, {M}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and C1 within their unit can be arranged in 2 ways: {FC1} or {C1F}, so total number of arrangements is 4!*2=48.
Answer: D.
Answer: (D) 48
Question: If x < y < z and y-x > 1, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
(A) 6
(B) 3
(C) 8
(D) 9
(E) 10
Rationale: We have:
1) x<y<z
2) y-x>1
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>1, the least value for y-x must be 3, the least value for x must be 2, and, thus, the least possible value for y must be 3 (y-2=1, y=3)
2<3<z, since z is odd, the least possible value for z is 5
z-x=5-2=3
Answer B
Answer: (B) 3
Question: A certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 10,800
(C) c) 10,900
(D) d) 12,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 142k
x = 12,000
Answer : D
Answer: (D) d) 12,000
Question: 2, 6, 12, 20, 30, 42, 56, (...)
(A) 62
(B) 74
(C) 72
(D) 81
(E) 58
Rationale: The pattern is 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8.
Hence, next number is 8×9 = 72
Answer is C
Answer: (C) 72
Question: In what ratio must water be mixed with milk to gain 1623% on selling the mixture at cost price?
(A) 6 : 1
(B) 1 : 6
(C) 1 : 4
(D) 4 : 1
(E) None of these
Rationale: Explanation :
Let CP of 1 litre milk = Rs.1SP of 1 litre mixture = CP of 1 litre milk = Rs.1Gain=1623%=503%CP of 1 litre
mixture = 100(100+Gain%)×SP=100(100+503)×1=100(3503)=300350=67 By the rule of alligation, we
have
CP of 1 litre water CP of 1 litre milk
0 1
CP of 1 litre mixture
6/7
1 - 6/7 = 1/7 6/7 - 0 = 6/7
Quantity of water : Quantity of milk = 1/7 : 6/7 = 1 : 6
Answer : Option B
Answer: (B) 1 : 6
Question: Two mixers and one T.V. cost Rs. 7000, while two T.V.s and a mixer cost Rs, 9800. The value of one T.V. is:
(A) Rs.4000
(B) Rs.4500
(C) Rs.4300
(D) Rs.4200
(E) None of these
Rationale: Explanation :
Let C.P. of a mixer be Rs. x and that of a T.V. be Rs. y.
Then,
2x + y = 7000 and 2y + x = 9800.
Multiplying 2nd equatien by 2 and subtracting first from it, we get
3y = 19600 - 7000 = 12600
or
y = 4200 C.P. of a T.V. = Rs. 4200
Answer : D
Answer: (D) Rs.4200
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 40 percent of the pollutant?
(A)  $500,000
(B)  $100,000
(C)  $50,000
(D)  $10,000
(E)  $5,000
Rationale: To remove 90% of pollutant
C= 100,000(90)/(100-90) = 900,000
To remove 40% of pollutant
C' = 100,000(40)/(100-40) = 400,000
Difference = C - C' = 500,000
Answer - A
Answer: (A)  $500,000
Question: The average age of a class of 12 students is 8 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 30 Years
(B) 31 Years
(C) 21 Years
(D) 34 Years
(E) 49 Years
Rationale: Total age of students is 12X8 = 96 Years
Total age inclusive of teacher = 13X (8+1) = 117
So, Teacher's age is 117-96 = 21 Yrs
There is a shortcut for these type of problems
Teacher's age is 8+(13X1) = 21 Years
C
Answer: (C) 21 Years
Question: A man counted his animals, 80 heads and 280 legs (ducks and goats). how many goats are there?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=240 and divide 2d+4g=240 by 2 we get d+2g=140 -----------> eq2
subtract eq1 from eq2
we get no of goats=60
ANSWER:D
Answer: (D) 60
Question: A fisherman sells 300 fish for Rs. 9000 at a profit of Rs. 6 per fish. Find his cost price for one metre of cloth?
(A) 24
(B) 36
(C) 30
(D) 18
(E) 20
Rationale: SP per fish = 9000/300 = Rs. 30 Profit per fish = Rs. 6 CP per metre = 30 - 6= Rs. 24Answer: A
Answer: (A) 24
Question: Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2.5
(B) 3
(C) 3.5
(D) 4
(E) 4.5
Rationale: The part filled by A + B + C in 1 hour
= 1/6 + 1/8 + 1/24
= 8/24 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer is B.
Answer: (B) 3
Question: If x is the reciprocal of a positive integer, then the maximum value of x^y, where y = –x^2, is achieved when x is the reciprocal of
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let's take answer C and try to substitute it in the task:
x=13
y=−(13)^2=−1/9
x^y=1/3−1/9
So x will be equal to ninth square root from 33.
And we can infer that maximum value will be when we take x=1 because then x^y will be equal to 1
Answer is A
Answer: (A) 1
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 9 and 15 is?
(A) 44
(B) 48
(C) 46
(D) 47
(E) 50
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 15 will be divided into 3 parts= 9, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*24*4= 48
B
Answer: (B) 48
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
(A) 5.0 sec
(B) 2.9 sec
(C) 1.3 sec
(D) 2.9 sec
(E) 1.8 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 200/40
= 5.0 sec.
Answer:A
Answer: (A) 5.0 sec
Question: The price of rice falls by 10%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
(A) 5 kg
(B) 15 kg
(C) 25 kg
(D) 30 kg
(E) None
Rationale: Solution: Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 10%, new price for 20 kg rice,
= (100 -10% of 100) = 90
New price of rice = 90/20 = Rs. 4,5 per kg.
Rice can bought now at = 100/4,5 = 22,22 kg.
Answer: Option E
Answer: (E) None
Question: The total marks obtained by a student in Mathematics and Physics is 40 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 26
(C) 27
(D) 28
(E) 30
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 40 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (40 + 20) / 2 = 30.Answer:E
Answer: (E) 30
Question: Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6, then the resultant number contains same all digits (of course in a different place)
(A) 143258
(B) 142876
(C) 142881
(D) 142852
(E) 142857
Rationale: E
142857
Explanation:
142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
Note: Such numbers are called cyclic numbers.
Answer: (E) 142857
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction E of the total distance did he cover while the sun was shining on him?
(A) 1/4
(B) 4/5
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is E=2/14 = 1/7. Answer: E
Answer: (E) 1/7
Question: There are between 90 and 100 cards in a collection of cards. If they are counted out 3 at a time, there is 1 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A) 91
(B) 93
(C) 95
(D) 97
(E) 99
Rationale: The numbers with the form 4n+1 are 93 and 97.
Only 97 has the form 3k+1.
The answer is D.
Answer: (D) 97
Question: A man can row a boat at 25 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 50 km downstream?
(A) 1/2
(B) 4/3
(C) 2/3
(D) 5/3
(E) 1/3
Rationale: Speed downstream = 25 + 5 = 30 kmph.
Time required to cover 50 km downstream = d/s = 50/30
= 5/3 hours.
Answer: D
Answer: (D) 5/3
Question: The Salary of an employee increase consistently by 15% per year. If his present salary is Rs. 24000 then what will his salary be after 3 years ?
(A) Rs. 32497
(B) Rs. 34384
(C) Rs. 35065
(D) Rs. 36501
(E) Rs. 37650
Rationale: Explanation :
Salary = 24000 x 1.15 x 1.15 x 1.15 = 36501
Answer : Option D
Answer: (D) Rs. 36501
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is
(A) 1/26
(B) 1/25
(C) 1/20
(D) 1/21
(E) 1/22
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26.
Answer: A
Answer: (A) 1/26
Question: In how many ways can two members be selected from a group of ten members?
(A) 10C2
(B) 10C8
(C) 10C4
(D) 10C3
(E) 10C1
Rationale: two members can be selected from ten members in
10C6
= 10C2 ways.
Answer: A
Answer: (A) 10C2