RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
A.63/280
B.1/280
C.3/56
D.3/35
Answer: A.63/280
Explanation: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280.
Answer: A
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
A.7
B.6
C.2
D.8
Answer: B.6
Explanation: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Question: A sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :
A.400
B.500
C.600
D.700
Answer: C.600
Explanation: SI of 5 year = (1020-720)=300
so, SI of 1 year=300/5=60
so, SI of 2 year=60*2=120
so, sum is =(720-120)=600
ANSWER:C
Question: Jack and Jill are marathon runners. Jack can finish a marathon (43 km) in 4.5 hours and Jill can run a marathon in 4.3 hours.What is the ratio of their average running speed? (Jack: Jill)
A.14/15
B.43/45
C.4/5
D.5/4
Answer: B.43/45
Explanation: Average Speed of Jack =Distance/ Time
= 43 /(9/2) = 86/9
Average Speed of Jill = 43/(4.2) = 10
Ratio of Average speed of Jack to Jill = (86/9)/10 = 86/90 = 43/45
Answer B
Question: The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 7350 for a computer table, then what was the cost price of the computer table?
A.Rs.6289
B.Rs.6298
C.Rs.6681
D.Rs.6725
Answer: C.Rs.6681
Explanation: CP = SP * (100/(100 + profit%))
= 7350(100/110) = Rs.6681.
Answer: C
Question: Find the number of zero’s in 173! (173 Factorial)?
A.38
B.39
C.40
D.41
Answer: D.41
Explanation: no of zeroes in 173! is
173/5=34(quotient)
34/5=6(quotient)
6/5=1(quotient)
34+6+1=41
ans 41 zeroes
ANSWER:D
Question: A small water pump would take 4 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
A.1/6
B.4/9
C.1/4
D.5/9
Answer: B.4/9
Explanation: Rate of the small pump is 1/4 tank/hour
Rate of the larger pump is 1/(1/2) or 2 tank/hour;
Combined rate of the two pumps is 1/4+2=9/4 tank/hour, together they will fill the empty tank in 1/(9/4)) = 4/9 hours (time=job/rate).
Answer: B
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 8.
A.161
B.152
C.154
D.158
Answer: A.161
Explanation: D = d * Q + R
D = 17 * 9 + 8
D = 153 + 8
D = 161
ANSWER A
Question: If the day before yesterday was Wednesday, what day will be the day after tomorrow?
A.Sunday
B.Monday
C.Tuesday
D.Friday
Answer: A.Sunday
Explanation: Explanation:
Day before yesterday was Wednesday
=>Yesterday was a Thursday
=>Today is a Friday
=>Tomorrow is a Saturday
=>The day after tomorrow will be a Sunday
Answer: Option A
Question: If x, y, and z are positive integers, and 3x = 5y = 6z, then the least possible value of x + y + z is
A.21
B.28
C.37
D.42
Answer: A.21
Explanation: Take LCM of 3,5 and 6 = 30
Now 3x = 30 => x =10
5y = 30 => y = 6
6z = 30 => z =5
10+6+5 = 21.
Option A.
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A.10/21
B.1/21
C.9/11
D.7/11
Answer: A.10/21
Explanation: Total number of balls = 2 + 3 + 2 = 7
n(S) =Total number of ways 7 = 7C2
let E = event of drawing 2 balls, none of them is blue
n(E) = no of ways of drawing 2 balls, none of them is blue
=No of ways of drawing 2 balls from the total= 5C2
5*4/7*6 = 10/21
ANSWER A
Question: Out of 10 students in a class, 4 are from Maharashtra, 3 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
A.1/3
B.4/9
C.5/6
D.3/7
Answer: C.5/6
Explanation: Total possible ways of selecting 4students out of 10= 10C4 = (10*9*8*7)/(4*3*2*1) =210
The number of ways of selecting a 4 students in which no student belongs to Karnataka = 7C4
Number of ways of selecting atleast one student from Karnataka = 15C4-7C4 = 175
Probability = 175/210 = 5/6
Answer is C
Question: The product of face value of 3 and local value of 6 in the numeral 78934064 is
A.18
B.24
C.180
D.240
Answer: C.180
Explanation: (Face value of 3) x (Local value of 6) = (3 x 60) = 180
C
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.1000
B.2882
C.2799
D.2778
Answer: A.1000
Explanation: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Question: Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
A.3/140
B.1/28
C.7/40
D.3/35
Answer: C.7/40
Explanation: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.
Answer: C.
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability T that a + b is prime?
A. 0
B. 1/12
C. 5/12
D. 7/18
Answer: C. 5/12
Explanation: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
T=15/36.
Answer: C.
Question: Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?
A.4
B.4 2/3
C.5 1/3
D.6
Answer: A.4
Explanation: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?
a) 4
b) 4 and 2/3
c) 5 and 1/3
d) 6
e) 6 and 1/4
To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.
Answer: A.
Question: In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
A.12540
B.11450
C.11760
D.13250
Answer: C.11760
Explanation: Required number of ways = 8C5*10C5 = 8C3*10C4 = 11760
Answer is C
Question: 66.2 is what percent of 1000?
A.6.62
B.66.2
C.662
D.0.662
Answer: A.6.62
Explanation: We assume that 1000 is 100%
assume 'x' is value we looking for
here,
1000 = 100% and
x% = 66.2
therefore,
100/x = 1000/66.2
100/x = 15.105
x = 6.62
A
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer m?
A.(2m-2)/(m^2- m)
B.(2m-1)/(m^2- m)
C.(2m-1)/(m^4- m)
D.(3m-1)/(m^2- m)
Answer: B.(2m-1)/(m^2- m)
Explanation: Let two consecutive positive integers be m and m-1 (Greater integer is m)
So,
(1/m) + [1/(m-1)]
= (2m-1)/m(m-1)
=(2m-1)/(m^2- m)
Answer : B
Question: How many numbers from 10 to 50 are exactly divisible by 3?
A.13
B.14
C.15
D.17
Answer: A.13
Explanation: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.
13 Numbers.
10/3 = 3 and 50/3 = 16 ==> 16 - 3 = 13. Therefore 13 digits.
A)
Question: A garage has a bin that is used by an "add stuff" worker and a "throw away" worker. Working alone, the "add stuff" worker can fill the bin in 5 hours. Working alone, the "throw away" worker can empty the bin in 15 hours. If it is desired that the bin should be filled, from empty, exactly 6 hours after the "add stuff" worker begins his shift at 9:30am, then at what time should the "throw away" worker begin his own shift?
A.10:00am
B.10:45am
C.12:00pm
D.12:30pm
Answer: D.12:30pm
Explanation: In 6 hours the "add stuff" worker can fill the bin equal to 6*1/5 = 6/5 of the bin. So, 1/5 more than necessary, which should be compensated by the "Throw away" worker. To get rid of 1/5 of the inventory the "throw away"worker needs 15/5 = 3 hours.
Therefore, the "throw away" worker should begin his shift at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Question: The ratio of flour to water to sugar in a recipe is 7:2:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 2 cups of water, how much sugar is required?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: The ratio of flour to water is 14:2.
The ratio of flour to sugar is 3.5:1=14:4.
The new ratio of flour to water to sugar is 14:2:4
If we need 2 cups of water, then we need 4 cups of sugar.
The answer is C.
Question: All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.
How many small cubes will be formed having only one face coloured ?
A.54
B.8
C.16
D.24
Answer: A.54
Explanation: no.of small cubes will have only one face painted=(X-2)2*6
Here x=side of the small cube=5
therfore(X-2)2*6=54
ANSWER:A
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
A.14009
B.14409
C.14006
D.14000
Answer: D.14000
Explanation: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Question: A cab driver 5days income was $400, $250, $650, $400 , $500. Then his average income is?
A.$400
B.$420
C.$440
D.$460
Answer: C.$440
Explanation: avg = sum of observations/number of observations
avg income=(400+250+650+400+500)/5 = 440
Answer is C
Question: A train 50 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
A.3 sec.
B.7 sec.
C.9 sec.
D.11 sec.
Answer: A.3 sec.
Explanation: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 50 m at (50 /3)m/sec	= (112 - 50)kmph
= (50 x 3/50)sec
= 3 sec.
Answer A
Question: 15th august 2010 was which day of the week?
A.Thursday
B.Friday
C.Wednesday
D.Sunday
Answer: D.Sunday
Explanation: ANSWER: Sunday
Explanation:
15th August 2010 can be written as 2009 + days from 1st January 2010 to 15th August 2010.
=> Total number of odd days in 400 years = 0
Hence, total number of odd days in 2000 years = 0 (as 2000 is a perfect multiple of 400)
Odd in days in the period 2001-2009:
7 normal years + 2 leap yeas
=> (7*1) + (2*2) = 11
=> Odd days will be 11- (7*1) = 4
Days from January 1 to August 15 in 2010: 31+28+31+30+31+30+31+15
= 227 days.
= 32 weeks and 3 days, this gives additional 3 odd days.
=> Total odd days= 3+4=7
=> 7 odd days=1 week= 0 odd days
=> 0 odd days= Sunday
Thus, 15th August 2010 was a Sunday.
Answer: D
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?
A.2.5 kmph
B.6.5 kmph
C.1.5 kmph
D.8.5 kmph
Answer: C.1.5 kmph
Explanation: Explanation:
72 --- 9
? ---- 1
=> Down Stream = 8
45 ---- 9
? ---- 1
=> Up Stream = 5
Speed od current S = ?
S = (8 - 5)/2 = 1.5 kmph.
Answer: C
Question: How many different arrangements of A, B, C, D, and E are possible where A is not adjacent to B ?
A.72
B.48
C.32
D.30
Answer: A.72
Explanation: So you have A,B,C,D,E
five possible ways to arrange it = 5! = 120
AB cannot be adjacents
(AB),C,D,E = 4! = 24 x 2(because it can be (AB) or (BA) ) = 48
120 -48- = 72 possible ways
A
Question: Bottle R contains 350 capsules and costs $6.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
A. $0.25
B. $0.12
C. $0.0052
D. $0.003
Answer: C. $0.0052
Explanation: Cost per capsule in R is 6.25/350=0.0178
Cost per capsule in T is 2.99/130=0.023
The difference is 0.0052
The answer is C
Question: 45 litres of mixture is created by mixing Liquid A and Liquid B in the ratio 3:2. How much more Liquid B must be added to make the ratio 9:11?
A.9 Litres
B.10 Litres
C.12 Litres
D.15 Litres
Answer: D.15 Litres
Explanation: In current ratio A = (3/5) * 45 = 27
B is 18
Suppose "b" amount of b is added
new ratio = 27/(b+18) = 9/11
=> b+18 = 33
=> b = 15
So, answer will be D
Question: When 3 fair coins are tossed together, what is the probability of getting 2 tails?
A.1/2
B.1/3
C.1/4
D.3/4
Answer: A.1/2
Explanation: We can get 2 tails in 3C2 ways.
We can get 3 tails in exactly one way.
Also, there are a total out 8 possible outcomes.
Thus, the required probability = (3 + 1)/8 = 1/2
ANSWER:A
Question: A certain galaxy is known to comprise approximately 4 x 10^12 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
A.800
B.1,250
C.80,000
D.12,000
Answer: C.80,000
Explanation: Total no. of stars on galaxy = 4 * 10^12
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 4 * 10^12 / 50 * 10^6
=40 * 10^4 /5
= 80000
therefore answer is C
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
A.12.5
B.12.1
C.12.9
D.12.7
Answer: B.12.1
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Question: Apple Infotech has 4 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of two managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Apple Infotech possibly provide guidance for?
A. 16
B. 20
C. 26
D. 54
Answer: C. 26
Explanation: P(at least 1 S D) = P(Total) - P(0 Senior Director)
=9C2 - 5C2
= 26
Question: Rebecca's annual income is $15, and Jimmy's annual income is $18. By how much must Rebecca's annual income increase so that it constitutes 50% of Rebecca and Jimmy's combined income?
A.7
B.8
C.9
D.3
Answer: D.3
Explanation: total rebecca = x+15; total = x+20+18
x+15/x+33 = 50/100 therefore x =3
D
Question: In a ratio which is equal to 4:6, if the antecedent is 50, then the consequent is?
A.75
B.85
C.64
D.51
Answer: A.75
Explanation: We have 4/6 = 50/x
4x = 50*6
x = 75
consequent = 75
Answer is A
Question: In what ratio must tea at Rs.60 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.67.5 per Kg?
A.3 : 1
B.3 : 2
C.4 : 3
D.1 : 3
Answer: D.1 : 3
Explanation: Required ratio = 250 : 750 = 1 : 3
Answer D
Question: Which of the following represents 1<x<9?
A.|x|<3
B.|x+5|<4
C.|x-1|<9
D.|-5+x|<4
Answer: D.|-5+x|<4
Explanation: |x| is the distance of x from the origin on the number line.
|x - 5| is the distance of x from the point 5 on the number line.
|x + 3| is the distance of x from the point -3 on the number line. (That's because x + 3 = x - (-3))
So, we want to write 1<x<9 as a distance statement.
Step #1: find the middle of that region. The midpoint is at 5. So, this is about distance from 5 ---> |x - 5|
Step #2: how far can we get from 5? Well, up to almost 9, or down to almost 1 -- that is, almost 4. Thus:
distance from 5 < 4
|x - 5| < 4
ANSWER:D
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
A.288
B.270
C.999
D.278
Answer: B.270
Explanation: I = (500*9*6)/100 = 270
Answer:B
Question: An old priest fell on a bottom of the well of a church.
The well is 20 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
A.16-days
B.14-days
C.11-days
D.19-days
Answer: A.16-days
Explanation: A
16-days
In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)
Question: Find the odd one out:
125, 106, 84, 76, 65, 58, 53
A.33
B.84
C.26
D.18
Answer: B.84
Explanation: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 84 is the answer.
ANSWER: B
Question: If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Brad have?
A.$8
B.$9
C.$27
D.$32
Answer: B.$9
Explanation: Josh+Doug+Brad = 72 ; Joush = 3 brad, Josh =3/4 doug
Josh+1/3 Josh+ 4/3 Josh = 72 (substituted the given values)
Josh = 27. 27= 3/4 doug => doug =36
Josh+Doug+Brad = 72
27 + 36 + Brad = 72
Brad = 9
Answer is B.
Question: In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
A.33
B.Monday
C.299
D.299
Answer: B.Monday
Explanation: Ans: If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.
Answer:B
Question: If the square root of p^2 is an integer greater than 1, which of the following must be true?
I. p^2 has an odd number of positive factors
II. p^2 can be expressed as the product of an even number of positive prime factors
III. p has an even number of positive factors
A.I
B.II
C.III
D.I and II
Answer: D.I and II
Explanation: It is given that p2−−√p2>1 and is an integer..
Also p2−−√p2=p
so p^2 is a perfect square and p is an integer>1..
lets see three statements:-
I. p^2 has an odd number of positive factors-- TRUE
A perfect square has an Odd number of perfect square ..
WHY? Because all factors will have a different integer as a pair except p..
p*p=p^2.. so that will be just one factor
II. p^2 can be expressed as the product of an even number of positive prime factors
again TRUE
25 =5*5 ; 49= 7*7 ; 36 = 2*2*3*3
III. p has an even number of positive factors..
Since it uses 'HAS', if we find one which does not follow the statement is not true..
we already know that A perfect square has an Odd number of perfect square ..
so if p is a perfect square itself ans is No
ONLY I and II are true
ANSWER:D
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 25 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $260 before any discount?
A. $136.50
B. $145.60
C. $163.80
D. $182.00
Answer: A. $136.50
Explanation: 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 25% 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 $260 would be.....
($260)(.7)(.75) =
($260)(.525)=136.5
Final Answer:
A
Question: he ratio between the sale price and the cost price of an article is 4:7. What is the ratio between the profit and the cost price of that article?
A.2:6
B.3:7
C.3:8
D.2:1
Answer: B.3:7
Explanation: Let C.P. = Rs. 7x and S.P. = Rs. 4x.
Then, Gain = Rs. 3x
Required ratio = 3x : 7x = 3:7.
Answer:B
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
A.9x/80
B.13x/20
C.80/9x
D.10x
Answer: D.10x
Explanation: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 40% of the sales of imported tools = 0.40*{total}/4 = 2/5*{total}/4 = 2*{total}/20.
Since the sales of of Japanese tools was x, then 2*{total}/20 = x --> {total} = 10x.
Answer: D.
Question: The average of first ten prime numbers which are odd is?
A.15.7
B.15.0
C.15.2
D.15.8
Answer: D.15.8
Explanation: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 7 miles?
A.22/5
B.20/5
C.15/5
D.21/5
Answer: D.21/5
Explanation: 1 km is approxmately equal to 0.6 miles
So 7 km = 7*0.6 = 4.2 miles . Multiple & divide by 10
i.e 4.2*10/10 = 42/10 = 21/5
Answer : D
Question: A person’s age is 125% of what it was one decade ago, but 83(1/3)% of what it will be after one decade. What is his current age? [1 decade = 10 years]
A.50 years
B.60 years
C.30 years
D.70 years
Answer: A.50 years
Explanation: A
50 years
Let, current age is A years.
Then, 125% of (A – 10) = A
and, 83(1/3)% of (A + 10) = A
Therefore 125% of (A-10) = 83(1/3)% of (A+10)
or, (5/4) (A – 10) =(5/6)(A+10)
or, (5/4)A -(5/6)A = (50/6)+(50/4)
or, (5A/12)= (250/12) or,
A=50 years.
Question: If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
A. Two
B. Three
C. Four
D. Six
Answer: C. Four
Explanation: If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 14p have.
p = 3 --> 14p = 42--> 42 has 4 even divisors: 2, 6, 14, 42 .
Answer: C.
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 17th board counting from the bottom of the stack. How many boards are in the stack?
A.38
B.36
C.35
D.34
Answer: C.35
Explanation: Counting from the top, after the 20th board, there are 15 boards left to count.
The answer is C.
Question: A man is standing on a railway bridge which is 240 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
A.10 m/sec
B.15 m/sec
C.18 m/sec
D.20 m/sec
Answer: D.20 m/sec
Explanation: If length of train is l and speed of train is s, then
l/s = 8
(l+240)/s = 20
(l+240)/l = 20/8 =5/2
2l+480 =5*l
3*l= 480
l=160 mtrs
s= l/8 = 160/8 = 20 m/sec
ANSWER:D