divelab/Sys2Bench huggingface dataset:
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 20% ?
Options:
A) 0
B) 1.51
C) 2
D) 2.12
E) 4
Rationale: Let y be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = y/10
Probability that the second contestant selected is also a male = y-1/9
Total probability = y(y-1)/ 90 < 1/20 (this probability is less than 20%)
Solving for y we get, y(y-1)< 9/2. This implies that the maximum value of y can be 2.12.
Answer D!
Answer: D
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the
second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take
both the punctures together to make it flat ?
Options:
A)315min
B)325min
C)335min
D)345min
E)None of these
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st
puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(19+16)=(518)
So both punctures will make the type flat in
(185)mins=335mins
Answer: C
Answer: C
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Options:
A)40
B)80
C)90
D)100
E)120
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Answer: Option A
Answer: A
Question: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)25
B)27
C)29
D)32
E)55
Rationale: The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
E
Answer: E
Question: In a graduating class, 40 percent of the students are male. In this class, 60 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Options:
A)0.4
B)0.44
C)0.48
D)0.52
E)0.56
Rationale: Let x be the total number of students.
The number students who are younger than 25 is 0.4*0.4x+0.6*0.6x = 0.52x
The answer is D.
Answer: D
Question: Oak trees line both sides of a street for a length of 7/10 of a kilometer. If there is 14 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
Options:
A)a)	22
B)b)	23
C)c)	24
D)d)	44
E)e)	48
Rationale: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.
7/10 of 1 km = 700 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*14 = 700
Solve for x and we get x = 48, answer is E
Answer: E
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 6), the remainder is also D. If P/Q = 1020.75 and P/(Q + 6) = 816.6, then which of the following gives the correct set of {D, Q}?
Options:
A){6, 12}
B){6, 15}
C){9, 12}
D){9, 15}
E){18, 24}
Rationale: p/q= d=p/q+6
d= .75 q
d= .6(q+6)
we get d = 18 and q = 24. Answer = E.
Answer: E
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
Options:
A)1300000
B)12500
C)14000
D)12000
E)None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200.
(75/100 * 96/100 * 70/100 * x) = 655200.
=> x = (655200*100*100*100)/(75*96*70) = 1300000
Answer : A
Answer: A
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
Options:
A)three times as much
B)twice as much
C)the same
D)half as much
E)A third as much
Rationale: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
Speed = Distance/Time.
I.E Time = Distance/Speed.
times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.CORRECT ANSWER : B
Answer: B
Question: Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
Options:
A)18
B)20
C)24
D)36
E)42
Rationale: Use weighted average:
2% and 12% solutions mix to give 5% solution.
w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3
You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution.
If total 5% solution is actually 60 litres, you need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution.
Answer (E)
Answer: E
Question: If a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is
Options:
A)equilateral
B)isosceles
C)right-angled
D)obtuse-angled
E)None of these
Rationale: Explanation :
We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac = 3ab + 3bc + 3ac
Now assume values of a, b, c and substitute in this equation to check the options.
Shortcut:
(a – b)2 + (b – c)2 + (c – a)2 = 0.
Hence, a = b = c.
Answer : A
Answer: A
Question: jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all?
Options:
A)5
B)10
C)15
D)20
E)14
Rationale: 10+5=15. Answer is C
Answer: C
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 3 parts soda. Compare the strength of the wine.
Options:
A)35;36
B)15 : 18
C)7 : 4
D)14 : 5
E)None of these
Rationale: 5/8 : 9/12
LCM of 8,12 = 24
(5/8)*24 : (9/12)*24
15:18
Answer is B.
Answer: B
Question: Find the third proportional to 63 and 29.9?
Options:
A)14.09
B)14.29
C)14.19
D)14.16
E)None of these
Rationale: Explanation:
Formula = Third proportional = (b × b)/a
A = 63 and B = 29.9
(29.9 × 29.9)/ 63 = 894.01/63 = 14.19
Answer: Option C
Answer: C
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)120%
B)190%
C)100 percent
D)200%
E)101%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: C
Question: The ratio of the number of females to males at a party was 1:2 but when 3 females and 3 males left, the ratio became 1:3. How many people were at the party originally?
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: The total number of people are x females + 2x males.
3*(x-3) = 2x - 3
x = 6
There were 3x = 18 people at the party originally.
The answer is C.
Answer: C
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number?
Options:
A)40
B)45
C)55
D)45
E)50
Rationale: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -60 = 45
D
Answer: D
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 8% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
Options:
A)22%
B)23.9%
C)24%
D)25%
E)34%
Rationale: Since 8% of the customers who sample the candyare notcaught, then 88% of the customers who sample the candyarecaught:
{% of customers who sample candy}*0.92 = 0.22;
{% of customers who sample candy} = 0.239.
Answer: B.
Answer: B
Question: The least number which must be subtracted from 6709 to make it exactly divisible by 9 is:
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: On dividing 6709 by 9, we get remainder= 4
Therefore, required number to be subtracted= 4
ANSWER:C
Answer: C
Question: If 3^k - 3^(k-1) = 162 then k(k-1) =
Options:
A)12
B)16
C)20
D)30
E)81
Rationale: It seems like you were really close but you solved for k - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of k(k -1), e.g. (3)(4) = 12. Even then, had you figured k has to be a little bigger (plugging in 4 for k gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (k - 1) exponent place.
Again, a quick plugging in should get you (C) 20 as, the only other answer with consecutive integers as factors is far too big.
Answer: C
Question: 10 is added to a certain number, the sum is multiplied by 2, the product is divided by 2 and 2 is subtracted from the quotient. The remainder left is half of 88. What is the number?
Options:
A)21
B)20
C)25
D)36
E)45
Rationale: Let number is X.
When 10 added to it,
= (X+10)
2 multiplied to sum,
= 2 *(X +10)
Now,
= [{2 *(X +10)} /2]
And,
= [{2 *(X +10)} /2] - 2
According to question,
[{2 *(X +10)} /2] - 2 = half of 88
[(2X + 20) /2) = 44 +2
X + 10 = 46
X + 10 = 46
X = 46 - 10
X = 36
So, required number is: 36.
ANSWER : D
Answer: D
Question: If f(a)=4a+6b+8, what is the value of (f(3a)-f(2b)) ?
Options:
A)6a+8b+6
B)8a-6b
C)5a+3b-8
D)6a+7b+3
E)8a-2b+9
Rationale: f(a)=4a+6b+8
f(3a) = 12a+6b+8
f(2b) = 4a+12b+8
(f(3a)-f(2b)) = 12a+6b+8-4a-12b-8 = 8a-6b
Answer is B
Answer: B
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40
ANSWER:D
Answer: D
Question: A square and a rectangle have equal areas. If their perimeters are p1 and p2 respectively, then
Options:
A)p1 < p2
B)p1 = p2
C)p1 > p2
D)none of these
E)Cannot be determined
Rationale: Solution
A square and a rectangle with equal areas will satisfy the relation p1 < p2.
Answer A
Answer: A
Question: Mr. stenley employed a certain number of typist for his project. 8 days later 20% of the typist left the job and it was found that it took as much time to complete the rest work from then as the entire work needed with all the employed typists. The average speed of a typist is 20 pages/hour. Minimum how many typist could be employed?
Options:
A)10
B)5
C)15
D)4
E)3
Rationale: Explanation:
Since 20% (i.e 1/5) typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.
Answer: B
Answer: B
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Options:
A)Rs. 4980
B)Rs. 4991
C)Rs. 4996
D)Rs. 4997
E)Rs. 5000
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
B)
Answer: B
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 5 o’clock in the afternoon?
Options:
A)60°
B)90°
C)270°
D)320°
E)None of these
Rationale: Sol.
Angle traced by the hour hand in 9 hours = [360/12 * 9]° = 270°
Answer C
Answer: C
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
Options:
A)22
B)32
C)25
D)88
E)11
Rationale: Explanation:
cost price = (225 + 15) = 240 sell price = 300
gain = (60/240)*100 = 25%
Answer: C) 25%
Answer: C
Question: A train 125 m long passes a person, running at 5 km/hr in the same direction in which that the train is going, in 10 seconds. The speed of the train is:
Options:
A)40 km/hr
B)60 km/hr
C)55 km/hr
D)50 km/hr
E)65 km/hr
Rationale: speed of train related to a person = 125/10 m/s
=>25/2
(25/2*18/5) km/hr
=45 km/hr
so speed consider as x and relative speed consider (x-5)
x-5 = 45 => x = 50 km/hr
ANSWER D
Answer: D
Question: How many three-digit numbers that do not contain the digits 2 or 5 are there?
Options:
A)488
B)996
C)228
D)456
E)1986
Rationale: We can have 7 digits ( 1,3,4,6,7,8,9) for the first place ( hundred's place).
and similarly 8 digits for tenth's and unit digit. ( 0,1,3,4,6,7,8,9)
So in total 7*8*8= 488
Hence B
Answer: B
Question: Each of the following equations T has at least one solution EXCEPT
Options:
A)T=–2^n = (–2)^-n
B)T=2^-n = (–2)^n
C)T=2^n = (–2)^-n
D)(–2)^n = –2^n
E)(–2)^-n = –2^-n
Rationale: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.
Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.
In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.
If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: A
Question: A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days?
Options:
A)3.75 days
B)3.78 days
C)3.25 days
D)3.15 days
E)2.7 days
Rationale: 1/4 + 1/8 = 3/8
8/3 = 2.7 days
Answer: E
Answer: E
Question: The average age of students in section A of 50 students is 14 years and the average age of students in section B of 30 students is 6 years. Find the average age of students in both sections taken together?
Options:
A)20years
B)15years
C)18years
D)9years
E)11years
Rationale: The required average = (50*14+30*6)/50+30 = 11 years
Answer is E
Answer: E
Question: The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)266
B)288
C)245
D)776
E)225
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X
= 225 m.
Answer:E
Answer: E
Question: Find the middle one when The sum of three consecutive even numbers is 36?
Options:
A)10
B)12
C)14
D)15
E)16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: B
Question: What is the value of âˆš81% ?
Options:
A)25%
B)36%
C)42%
D)60%
E)90%
Rationale: Explanation: br>âˆš81%
=âˆš81/âˆš100
=9/10
=90/100=90%
correct answer is E)90%
Answer: E
Question: 26 men can complete a piece of work in 8 days. In how many days will 25 men complete the same work?
Options:
A)7 1/3 days
B)9 1/3 days
C)8 2/3 days
D)8 1/3 days
E)9 1/3 days
Rationale: Let the required number of days be p
More men, less days (indirect proportion)
Hence we can write as
26 : 25 :: p : 8
26*8=25*p
p=26*8/25
p=8 1/3 days
ANSWER:D
Answer: D
Question: A train 110 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
Options:
A)54 kmph
B)60 kmph
C)66 kmph
D)72 kmph
E)82 kmph
Rationale: speed of train relative to man: 110/6 * 18/5 km/hr
= 66 km/hr
let speed of train= x
therefore x+6 = 66
x= 66-6
x=60 km/hr
ANSWER:B
Answer: B
Question: How many 6 letter words ( with or without meaning) can be formed using all the following 5 lettersV, P,Q,R,S,and T so that letter P is to the left of letter R?
Options:
A)320
B)300
C)400
D)480
E)360
Rationale: Two positions can be selected out of 6 positions in 6C2 ways = 15ways.
And the remaining 4 letters can be placed in 4 posions in 4! Ways = 24 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 4 letters can be arranged
Final Answer = 24 x 15 =360 ways
E
Answer: E
Question: If sq. root of(x)/|y| = -1 which of the following must be true?
Options:
A)x = -y
B)x = y
C)x = y^2
D)x^2 = y^2
E)x^3 = y^3
Rationale: sq. root of(x)/|y| = -1
sq. root of(x)= -1 |y|
Squaring both sides
+ or - (x) = (-1 |y|) ^2= y^2
C is the answer
Answer: C
Question: 35 - [23 - {15 - x}] = 12 × 2 ÷ 1/2
Options:
A)34
B)32
C)17
D)27
E)28
Rationale: Explanation:
35 - [23 - {19 - (15 - x)}] = 12 × 2 × 2 = 48
=> 35 - 23 + (19 - 15 + x) = 48
=> 12 + 4 + x = 48
=> x = 48 - (4 + 12) = 32
Answer: Option B
Answer: B
Question: A boat goes 100 km downstream in 8 hours, and 75 Km upstream in 15 hours. The speed of the stream is?
Options:
A)3
B)6.5
C)5.5
D)4
E)3.75
Rationale: 100 --- 10 DS = 12.5
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (12.5 - 5)/2
= 3.75 kmph.Answer:E
Answer: E
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
Options:
A)33
B)77
C)12
D)88
E)91
Rationale: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205. S.I. for 5 years = Rs. (2205/3) x 5 = Rs. 3675 Principal = Rs. (9800 - 3675) = Rs. 6125. Hence, rate = (100 x 3675)/( 6125 x 5) % = 12%
Answer: C:
Answer: C
Question: Set M contains numbers that satisfy the condition that, if integer x is in the set then x-3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.
I.-7
II. -1
III. 2
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II and III
Rationale: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.
Now, if -4 is in the set, then -4-3=-7mustbe in the set. Could -1 or 2 be in the set? Certainly, but we don't know that for sure.
Answer: A.
Answer: A
Question: Carol spends 1/4 of her savings on a stereo and 1/6 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
Options:
A)1/4
B)2/7
C)5/12
D)1/2
E)11/24
Rationale: Total Savings = S
Amount spent on stereo = (1/4)S
Amount spent on television = (1-1/6)(1/4)S = (5/6)*(1/4)*S = (5/24)S
(Stereo + TV)/Total Savings = S(1/4 + 5/24)/S = 11/24
Answer: E
Answer: E
Question: A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1
B)7.5
C)2.25
D)1.5
E)4
Rationale: M = 3
S = x
DS = 3 + x
US = 3 - x
3 + x = (3 - x)2
3 + x = 3 -2x
3x = 3
x = 1
ANSWER:A
Answer: A
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 4 p.c?
Options:
A)28000
B)29000
C)37000
D)38400
E)40000
Rationale: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(96/100) = 38400
Option D
Answer: D
Question: You have 5 sticks of lengths 10, 20, 30, 40, 50 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
Options:
A)3
B)6
C)7
D)10
E)12
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Based on this there can be only 3 triangles formed: (20, 30, 40), (20, 40, 50), (30, 40, 50)
Answer; A.
Answer: A
Question: A clockwise rotation around point Z (that is, a rotation
in the direction of the arrow) transforms the shaded
quadrilateral to the unshaded quadrilateral. The angle
of rotation is approximately
Options:
A)180o
B)270o
C)360o
D)45o
E)135o
Rationale: The measure of \PZQ formed by the bottom edge of the shaded
quadrilateral, ZQ, and this same edge after the rotation, ZP, is
approximately 90.
The transformation of the shaded quadrilateral to the unshaded
quadrilateral is a clockwise rotation around point Z through an an-
gle equal to the measure of re
ex angle PZQ.
The measure of \PZQ added to the measure of re
ex \PZQ is
equal to the measure of one complete rotation, or 360.
Therefore, the measure of re
ex angle PZQ is approximately
360o - 90o or 270o.
Thus the clockwise rotation around point Z is through an angle of
approximately 270o
correct answer B
Answer: B
Question: An error 19% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
Options:
A)6.64%
B)41.61%
C)45.64%
D)46.64%
E)10.64%
Rationale: Percentage error in calculated area
=(19+19+(19Ã—19)/100)%=41.61%
ANSWER:B
Answer: B
Question: Find 95 ×× 98
Options:
A)93/198
B)93/12
C)93/13
D)93/10
E)93/11
Rationale: Here both numbers are less than 100. So they are deficient of - 5 and - 2 compared with 100. So
Answer:	D
Answer: D
Question: The total of company C's assets in 1994 was 250% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)12.5N
E)17.5N
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 250% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 + 2.5x$500 = $500 + $1250 =$1750
This is 17.5 times the 1992 number, so the correct answer is 17.5N.
E
Answer: E
Question: Set S is the prime integers between 0 and 45. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
Options:
A)15/56
B)3/8
C)15/28
D)5/8
E)11/14
Rationale: Total number of combinations=14C3=364...............(1)
Total number of combinations including 2 and two other numbers=13C2=78......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(364-78)=286
So, probability=286/364=11/14
E
Answer: E
Question: A drink vendor has 50 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
Options:
A)135
B)237
C)281
D)300
E)380
Rationale: The number of liters in each can = HCF of 50, 144 and 368 = 2 liters.
Number of cans of Maaza = 50/2 = 25
Number of cans of Pepsi = 144/2 = 72
Number of cans of Sprite = 368/2 = 184
The total number of cans required = 25 + 72 + 184 = 281 cans.
ANSWER:C
Answer: C
Question: The sum of all two digit numbers divisible by 9 is
Options:
A)910
B)585
C)785
D)685
E)885
Rationale: Required numbers are 18,27 . . . . . 99
This is an A.P. in which a=18,d=9 and l=99.
Let the number of terms in it be n.Then t=99
So a+(n-1)d=99.
18+(n-1)*9=99,
18+9n-9=99
9+9n=99
9n=99-9
n = 90/9
then n=10.
Required sum
=n/2(a+l)
=10/2(18+99)
=585
Answer is B.
Answer: B
Question: x + y = 19 , and x + 3y = 1. Find the value of x + 2y
Options:
A)20
B)18
C)11
D)10
E)5
Rationale: Add these two equations
2x + 4y = 20
Divide by 2 ( to Get x + 2y)
Answer will be D. 10
Answer: D
Question: The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 2.50 + 0.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
Options:
A) $ 2.50
B) $ 3.00
C) $ 3.50
D) $ 4.00
E) $ 5.00
Rationale: Number of wheels in truck = 18
Number of wheels on its front axle =2
number of wheels remaining = 16
number of axles remaining axles = 16/4 = 4
Total number of axles = 5
T = 2.50 + 0.50( x − 2)
= 2.50 + .5*3
= 2.5 +1.5 = 4 $
Answer D
Answer: D