divelab/Sys2Bench huggingface dataset:
Question: In how many ways can the letters of wordTREATMENTbe arranged such that all the Consonants always appear together?
Options:
A)9!
B)4!*6!
C)5!*5!
D)5!*4!*2!
E)6!*4!
Rationale: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (9 letters, 3 vowels e, a, e and 6 consonant t, r, t, m, n, t)
For all consonants together, consider them as 1 group {t, r, t, m, n, t} E A E --> this gives us 4! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 6! ways
Thus total arrangements with all consonants together = 4!*6! --> B is the correct answer.
Answer: B
Question: In right triangle ABC, AC is the hypotenuse. If AC is 40 and AB + BC = 60, what is the area of the triangle ABC?
Options:
A)225
B)450
C)25√2
D)500
E)200√2
Rationale: Square AB + BC = 60:
(AB)^2 + 2*AB*BC + (BC)^2 = 3600. Since (AC)^2 = (AB)^2 + (BC)^2 = 40^2 = 1600, then (AB)^2 + 2*AB*BC + (BC)^2 = 1600 + 2*AB*BC = 3600.
1600 + 2*AB*BC = 3600.
AB*BC = 1000.
The area = 1/2*AB*BC = 500.
Answer: D.
Answer: D
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)19%
B)11%
C)18%
D)218%
E)14%
Rationale: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer:C
Answer: C
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $50,000?
Options:
A)$38,796.
B)$48,720.
C)$38,976.
D)$39,679.
E)$36,796.
Rationale: 50,000 *1.16*.84=48,720
Answer B
Answer: B
Question: Two boys starts from the same place walking at the rate of
5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
Options:
A)17hr
B)14 hr
C)12 hr
D)20 hr
E)22 hr
Rationale: relative speed = 5.5 - 5 = 0.5 kmph
distance = 8.5 km
time = distance/speed = 8.5/0.5 = 17 hr
ANSWER A
Answer: A
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)72
B)67
C)28
D)26
E)27
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:A
Answer: A
Question: Rounded to three decimal places, 1.005^4 =
Options:
A)1.004
B)1.006
C)1.008
D)1.012
E)1.02
Rationale: As compared to 1, 0.005 is a very small quantity. Thus, we can write (1+0.005)^4 is nearly equal to (1+4*0.005) = 1.020.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.
E.
Answer: E
Question: A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally r% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?
Options:
A)100r/(1-r)
B)80r/(1-r)
C)75r/(1-r)
D)100r/(80-0.2r)
E)100r/(80+0.2r)
Rationale: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that r = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100r/(80+0.2r) >>> 100x10 / 82
Answer: E
Question: In the coordinate plane a slope of the line K is 3/2 times the y-intercept of the line K. What is the x-intercept of the line K?
Options:
A)-2
B)2/3
C)-2/3
D)1/4
E)3/2
Rationale: As Y=3/2mx+m, from 0=3/2mx+m we get x=2/3. Hence, the correct answer choice is B.
Answer: B
Question: Rahul went to a shop and bought things worth Rs. 30, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)25.7
B)24.7
C)23.7
D)22.7
E)26.7
Rationale: Total cost of the items he purchased = Rs.30
Given that out of this Rs.30, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (30−30/100−x)6/100 = 30/100
⇒ 6(30 −0.3 −x) = 30
⇒ (30− 0.3 − x) = 5
⇒ x = 30 − 0.3 − 5 = 24.7
B)
Answer: B
Question: Today is Wednesday. After 36 days, it will be :
Options:
A)Thursday
B)Saturday
C)Monday
D)Sunday
E)Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 35 days, it will be Wednesday.
After 36 days, it will be Thursday
Answer is A
Answer: A
Question: n May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Options:
A)64%
B)68%
C)72%
D)76%
E)80%
Rationale: Let total earning be 100$ then Mrs. Lee earns 60$.
If this increased by 20% in June then Mrs.Lee new income is 72$, and the family income is 112$.
% of mrs lee = 72*100/112 = ~64%
ANSWER:A
Answer: A
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/20 hours
B)39/28 hours
C)30/32 hours
D)30/13 hours
E)32/34 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 60/26 = 30/13 hours.
Answer:D
Answer: D
Question: A man rows down stream 32km and 14 km upstream. if he takes 6 hrs to covereach distance, then the velocity of the current is
Options:
A)1/2kmph
B)1.5kmph
C)1 3/2kmph
D)2kmph
E)4kmph
Rationale: Rate down stream=(32/6)kmph;
Rate up stream=(14/6)kmph;
velocity of the current =1/2(32/6-14/6)kmph
=1.5kmph
Answer(B)
Answer: B
Question: A large box contains 20 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
Options:
A)250
B)500
C)450
D)550
E)650
Rationale: The number of chocolate bars is equal to
20 * 25 = 500
correct answer B
Answer: B
Question: The average of 9 numbers is 8 and the average of 7 other numbers is 6. What is the average of all 16 numbers?
Options:
A)9
B)8
C)7 1⁄8
D)7 1⁄2
E)7 1⁄4
Rationale: The average of 9 numbers is 8....
The sum of those numbers is (9)(8) = 72.
The average of 7 other numbers is 6....
The sum of those numbers is (7)(6) = 42
The sum of ALL 16 numbers is 72+42 = 114. The average of those numbers is 114/16 = 57/8 = 7 1/8.
Final Answer:
[Reveal]Spoiler:
C
Answer: C
Question: A trader sold an article on a certain price with 40% profit. If he sold double of previous selling price then find its profit %
Options:
A)140%
B)180%
C)120%
D)100%
E)150%
Rationale: let cost price = 100%
selling price = 140%
new s.p. = 280%
p% = 280-100 = 180%
Answer is B
Answer: B
Question: length =9 feet
breadth =37−9/2=14 feet
Area =9×14=126 square feet
Options:
A)126 sq. ft
B)156 sq. ft.
C)216 sq. ft.
D)145 sq. ft.
E)122 sq. ft.
Rationale: A
126 sq. ft.
length =9 feet
breadth =37−9/2=14 feet
Area =9×14=126 square feet
Answer: A
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount Q of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
Options:
A)2
B)2 1/2
C)3
D)3 1/2
E)4
Rationale: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture Q, so not acceptable.
So correct ans is 2.5 gallons. B
Answer: B
Question: If log 27 = 1.497, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.998
Rationale: log 27 = 1.497
log (3cube ) = 1.497
3 log 3 = 1.497
log 3 = 0.499
log 9 = log(3square ) = 2 log 3 = (2 x 0.499) = 0.998.
Answer: Option E
Answer: E
Question: A man rides at the rate of 50km/hr. But stops 30minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 250 kilometers?
Options:
A)5hr
B)6hr 30min
C)8hr 10min
D)7hr 20min
E)8hr
Rationale: speed of man = 50km/hr
number of rests = (250/25)-1 = 9
time taken for the man = (250/50)+9*(20/60) = 8 hr
Answer is E
Answer: E
Question: The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?
Options:
A)80
B)90
C)100
D)120
E)130
Rationale: Let the number of candidate who passed = y
Then, 39y + 15(120 - y) =120 x 35
⇒ 24y= 4200 -1800
∴ y= 2400 / 24 = 100
C
Answer: C
Question: Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $870 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
Options:
A)670
B)650
C)698
D)744
E)700
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 870 - 815 = 55
Interest earned for 3 years = 55*3 = 165
Amount invested = 815 - 165=650
Answer: B
Answer: B
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:
Options:
A)4120 m cube
B)4140 m cube
C)5140 m cube
D)5120 m cube
E)None of these
Rationale: Explanation:
l = (48 - 16)m = 32 m, [because 8+8 = 16]
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m cube
= 5120 m cube.
Option D
Answer: D
Question: The average of first five multiples of 5 is
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: Solution
Average	= 5(1+2+3+4+5) / 5
= 75 / 5.
= 15
Answer E
Answer: E
Question: At what rate of CI per year will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Options:
A)3%
B)6%
C)7%
D)8%
E)9%
Rationale: Let the rate be R% p.a.
Then, 1200 x 1 +	R 2	= 1348.32
100
1 +	R 2	=	134832	=	11236
100	120000	10000
1 +	R 2	= 106 2
100	100
1 +	R	=	106
100	100
R = 6%
B
Answer: B
Question: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 10 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
Options:
A)1/4
B)9/14
C)2/3
D)7/8
E)1/6
Rationale: Say total male = 40
Total female =60
Required ratio =( .1/40)/ (.9/60) = 1/6 E is the answer
Answer: E
Question: John had a stock of 900 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
Options:
A)50.4%
B)23.8%
C)66.5%
D)34.9%
E)55.3%
Rationale: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 900 - N = 900 - 402 = 498
Percentage
Books not sold / total number of books = 498/900 = 0.553 = 55.3%
correct answer E
Answer: E
Question: If (x - 1)(x - 2) = x^2 + x, what is a possible value of x?
Options:
A) 1/2
B) 2
C) -1
D) 1
E) -2
Rationale: Rearranging the given expression:
(x - 1)(x - 2) = x^2 + x
i.e. x^2 - 3x + 2 = x^2 + x
i.e. -4x = -2
i.e. x = -4/-2 = 2
Answer: Option B
Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Answer: B
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/6 hours to fill the tank. The leak can drain all the water of the tank in?
Options:
A)17 hr
B)19 hr
C)10 hr
D)24 hr
E)26 hr
Rationale: Work done by the tank in 1 hour
= (1/2 - 2 1/6)
= 1/26 Leak will empty the tank in 26 hrs.
Answer:E
Answer: E
Question: 6, 11, 21, 36, 56, 81, 111, 146, 186, ?
Options:
A)511
B)711
C)811
D)231
E)911
Rationale: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....
Answer : D.
Answer: D
Question: How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
Options:
A)48
B)12
C)72
D)100
E)720
Rationale: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 2*4!=48.
Answer A.
Answer: A
Question: A completes a work in 12 days and B complete the same work in 18 days. If both of them work together, then the number of days required to complete the work will be
Options:
A)8 days
B)9 days
C)10 days
D)12 days
E)7.2 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 18/ 30 = 7.2 days.
E
Answer: E
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.4, what is the probability that Malachi will return home at the end of the day on the following Monday?
Options:
A)0.008
B)0.144
C)0.488
D)0.512
E)0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probablity of rain = 0.4
Therefore, probability of no rain = 0.6
0.6*0.6*0.4 = 0.144
Hence B
Answer: B
Question: If "YELLOW" is given a color code of 92, what is the difference between "BROWN" and "RED"?
Options:
A)40
B)52
C)119
D)45
E)32
Rationale: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
BROWN- 72
RED- 27
Answer: D
Answer: D
Question: What is the sum of the integers from -170 to 171, inclusive?
Options:
A)181
B)171
C)191
D)201
E)202
Rationale: in an arithmetic progression,
the nth term is given by tn=a+(n-1)d
here tn=171, a=-170, d=1
hence, 171=-170+(n-1)
or n=342
Sum of n terms can be calculated by sn=n/2(a+l)
a=first term, l=last term, n=no. of terms
sn=342*(-170+171)/2
sn=342*1/2
sn=171
Answer : B
Answer: B
Question: The interior surfaces of a children's room (including ceiling, floor and 4 faces) are to be painted by 6 different colors. In how many ways can be this be done?
Options:
A)A.720
B)B.256
C)C.1
D)D.12
E)E.36
Rationale: If I have to paint 6 faces with 6 different colour...
First face can have 6c1 options,
2nd would have 5c1, and subsequent ones would have 4c1, 3c1, 2c1 and 1 options respectively.
Total options = 6c1 X 5c1 x 4c1 x 3c1 x 2c1 x 1 = 720 distinct ways
Correct answer - A
Answer: A
Question: If the probability that the Detroit Lions win the Super Bowl is 1/20 and the probability that the Detroit Tigers win the World Series is 1/6, what is the probability that either the Bears win the Super Bowl or the Cub win the World Series (but not both)?
Options:
A)1/2
B)2/7
C)1/3
D)1/4
E)1/5
Rationale: 19/20*1/6 + 1/20*5/6 = 24/120 = 1/5
The answer is E.
Answer: E
Question: What is the difference between the biggest and the smallest fraction among 2/3 , 3/4 , 4/5 and 5/6?
Options:
A)1/6
B)1/12
C)1/20
D)1/30
E)None of these
Rationale: Explanation:
Converting each of the given fractions into decimal form, we get
Since 0.833>0.8>0.75>0.66
So,
Required Difference = 5/6-2/3=1/6
ANSWER IS A
Answer: A
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)1:98
C)1:26
D)1:97
E)1:56
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer:A
Answer: A
Question: The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate W, in cubic meters per minutes, at which the water is flowing into the swimming pool?
Options:
A)0.125
B)0.25
C)0.5
D)0.75
E)Not enough information to determine the rate
Rationale: The correct answer is E.
There are not enough info to answer the question.
A 840 cubic meters rectangle is built from: height*length*width.
From the question we know the volume of the pool and the filling rate.
A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = E
Answer: E
Question: An alloy of copper and zinc contains copper and zinc in the ratio 6 : 4. Another alloy of copper and zinc contains copper and zinc in the ratio 3 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?
Options:
A)12 : 1
B)1 : 2
C)4 : 1
D)2 : 5
E)2 : 6
Rationale: Let Alloy_1 be x units, and let Alloy_2 be y units.
So, fraction of copper in Alloy_1 = 6x/10, and fraction of zinc in Alloy_1 = 4x/10
Similarly, fraction of copper in Alloy_2 = 3y/10, and fraction of zinc in Alloy_2 = 7y/10.
Mixing them, we get
copper = 6x/10 +3y/10; zinc = 4x/10 + 7y/10
So, 6x+3y = 4x+7y
-> 2x = 4y
-> x/y =2/4 = 1/2
So, they must be mixed in the ratio 1 : 2
Answer : B
Answer: B
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)125/128
B)125/178
C)125/126
D)125/129
E)125/122
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer: C
Answer: C
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
Options:
A)7889890 m
B)2334356 m
C)1536001 m
D)1232431 m
E)2435467 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: C
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 5 feet and a height of 10 feet, how far did the oil level drop in the stationary tank?
Options:
A)2.5 ft
B)1 ft
C)0.5 ft
D)0.25 ft
E)0.025 ft
Rationale: In order to fill up the tank, same volume is shifted from one tank to the other.
pi r1^2h1= pi r2^2 h2
5*5*10= 100 *100 *h2
h2= .025 ft
E is the answer
Answer: E
Question: The average of seven numbers is 18. The average of first three numbers is 12 and the average of last three numbers is 19. What is the middle number?
Options:
A)25
B)27
C)29
D)33
E)34
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 12+3 X 19 = 99
So, the middle number is (126 - 93 ) = 33
D
Answer: D
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 240 per month. What is his monthly salary?
Options:
A)5000
B)2999
C)6000
D)2990
E)2771
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 â€“ 96 =Rs. 4
100 ------ 4
? --------- 240 => 6000
Answer: C
Answer: C
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 2688 Nis, how much more money does Nick contribute than Archi?
Options:
A)128 Nis
B)212 Nis
C)234 Nis
D)245 Nis
E)288 Nis
Rationale: E:N:A 5:3:2.5
so total = 5x + 3x + 2.5 x = 10.5 x = 2688
so x = 256
Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 256 = 128
So A. 128 Nis is the correct answer
Answer: A
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
Options:
A)1/5
B)1/7
C)1/9
D)2/5
E)3/7
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
D)
Answer: D
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
Options:
A)8 1/5
B)8 1/9
C)8 1/4
D)8 1/2
E)8 1/1
Rationale: 3/12 + (3 + x)/15 = 1
x = 8 1/4
Answer:C
Answer: C
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Options:
A)21 years
B)22 years
C)23 years
D)24 years
E)26 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+26.
=> 2(x+2) = (x+26+2)
=> 2x+4 = x+28
=> x = 24 years
Option D
Answer: D
Question: What is the sum of the greatest common factor and the lowest common multiple of 12 and 16?
Options:
A)19
B)22
C)52
D)36
E)38
Rationale: Prime factorization of the given numbers
12= 2^2 * 3
48= 2^4 *3
Greatest common factor = 4
Lowest common multiple =48
Sum = 4+ 48 = 52
Answer C
Answer: C
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Options:
A)19 years
B)54 years
C)16 years
D)15 years
E)14 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/3
= 19 years.
Answer:A
Answer: A
Question: If fy > 0 and yz < 0, which of the following must be negative:
Options:
A)fyz
B)fy(z^2)
C)f(y^2)z
D)x(y^2)(z^2)
E)(x^2)(y^2)(z^2)
Rationale: fy > 0 means that fy is positive.
yz < 0 means that yz is negative.
f(y^2)z = (fy)(yz) = positive*negative = negative. Thus option C is always negative.
Answer: C
Question: The difference between the place values of two eights in the numerical 38140482 is
Options:
A)7999920
B)799920
C)7920
D)79920
E)None of them
Rationale: Required difference = (8000000-80)
=7999920.
Answer is A
Answer: A