divelab/Sys2Bench huggingface dataset:
Question: Solve the equation :
A) (5x - 4)/2 = (0.5x + 1)/3,
B) 1 –[(x - 3)/5] = ( -3x + 3)/3,
C) (x + 1)/3 – (2x + 5)/2 = -3,
D) [3.(x - 1)]/2 + [2(x + 2)]/4 = (3x + 4.5)/5
Options:
A)1, - 3/4, 5/4, 1
B)1, - 3/4, 5/4, 2
C)3, - 3/4, 5/4, 1
D)1, - 3/4, 5/4, 4
E)None
Rationale: Solution:
A) (5x - 4)/2 – (0.5x + 1)/3 <=>
3(5x - 4) = 2(0.5x + 1) <=>
15x - 12 = x + 2 <=>
15x – x = 12 + 2<=>
14x = 14 <=> x = 1
B) 1 – [(x - 3)/5] = 3.(1 - x)/3<=>
1 –[(x - 3)/5] = 1 – x<=>
-x + 3 = - 5x <=>
5x – x = - 3 <=>
x = - 3/4
C) [3.(x - 1)]/2 + [2(x + 2)]/4 = (3x + 4.5)/5 <=>
[2(x + 1) - 3(2x + 5)]/6 = - 3 <=>
(2x + 2 - 6x -15) / 6 = - 3 <=>
-4x - 13 = -18 <=>
-4x = -18 + 13 <=>
-4x = -5 <=> x = 5/4
D) We reduce to common denominator, which for 2, 4 and 5 is 20
[3.(x - 1)] / 2 + [2(x + 2)] / 4 = (3x + 4.5) / 5 <=>
30(x - 1) + 10(x + 2) = 4(3x + 4.5) <=>
30x - 30 + 10x + 20 = 12x + 18 <=>
40x - 12x = 18 + 10 <=>
28x = 28 <=> x = 1
Answer A
Answer: A
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $19000 left with him. find salary..
Options:
A)$10900
B)$19000
C)$190000
D)$1900
E)None
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $19000, = [1-9/10] * Total salary = $19000, Total salary = $19000*10 = $190000, correct answer (C)
Answer: C
Question: A rectangle with width 8 and diagonal 30. find the area?
Options:
A)240square units
B)180square units
C)100square units
D)150square units
E)160square units
Rationale: Then the area is: 8" x 30" = 240 square inches, or 240 square units
hence A
Answer: A
Question: At an elementary school, 70% of the faculty members are women and 60% of the faculty members are married. If 2⁄3 of the men are single, what fraction of the women are married?
Options:
A)5⁄7
B)7⁄10
C)1⁄3
D)7⁄30
E)5⁄70
Rationale: Plugging in numbers for this. Assume 100 faculty members.
70 faculty members are women
30 faculty members are men
60 total faculty members are married
1/3 of men are married (10), which means 20 men are single
10 of the 60 married faculty members are men, which means that 50 women are married.
50/70 women are married, reduced to 5/7
Ans A
Answer: A
Question: A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six books. How many different arrangements of the ten books are possible?
Options:
A)(10!)/(4!)
B)(4!)(6!)
C)(4!)(7!)
D)(4!)(10!)
E)(4!)(6!)(10!)
Rationale: You can club the four Lincoln books as one, which leaves us with six other books plus this one to think about. So, these seven items can be arranged in 7! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 7!*4!, which is C.
Answer: C
Question: A can do a piece of work in 6 hours; B and C together can do it in 5 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
Options:
A)3 6/8 hours
B)4 6/8 hours
C)2 6/8 hours
D)5 5/8 hours
E)none of the above
Rationale: A's 1 hour's work = 1/6 ;
(B + C)'s 1 hour's work = 1/5 ;
(B + C)'s 1 hour's work = 1/3
(A + B + C)'s 1 hour's work = (1/6 + 1/5) = 11/30
B's 1 hour's work = (11/30 - 1/3) = 8/30
B alone will take 30/8 hours to do the work.
=3 6/8
Answer = A
Answer: A
Question: At a certain conference, 78% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
Options:
A) 18.0%
B) 62.0%
C) 79.2%
D) 86.67%
E) 82.0%
Rationale: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
78% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=78% where X is the number of people who registerd 2 weeks in advance and paid full fee. (ANSWER D)
Answer: D
Question: 1. 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?
Options:
A)Rs.14400
B)Rs.26400
C)Rs.12000
D)Rs.12500
E)Rs.13000
Rationale: Explanation:
Ratio of the investment
=21000:17500=210:175=21000:17500=210:175 =42:35=6:5=42:35=6:5
Share of X in the profit
=26400Ã—611=2400Ã—6=14400
ANSWER IS A
Answer: A
Question: 1.12.91 is the first Sunday. Which is the fourth Tuesday of December 91?
Options:
A)20.12.91
B)22.12.91
C)24.12.91
D)25.12.91
E)26.12.91
Rationale: Explanation:
Given that 1.12.91 is the first Sunday
Hence we can assume that 3.12.91 is the first Tuesday
If we add 7 days to 3.12.91, we will get second Tuesday
If we add 14 days to 3.12.91, we will get third Tuesday
If we add 21 days to 3.12.91, we will get fourth Tuesday
=> fourth Tuesday = (3.12.91 + 21 days) = 24.12.91
Answer: Option C
Answer: C
Question: In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 3 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?
Options:
A)27/343
B)3/7
C)27/125
D)279/343
E)9/125
Rationale: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.
chances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel
chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33=12*23*2/35*17*3=552/1785
chances that at least 1 customer bought a coffee and a bagel= 1 - 552/1785 = 1233/1785 = 279/343
Answer D.
Answer: D
Question: Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
Options:
A)19/20
B)24/25
C)29/30
D)34/35
E)39/40
Rationale: P(no graduates) = 3C3 / 7C3 = 1/35
P(at least one graduate) = 1- 1/35 = 34/35
The answer is D.
Answer: D
Question: If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 4m + n?
Options:
A)11
B)18
C)55
D)25
E)33
Rationale: k^4=5400∗mn
k^4=3^3.2^3.5^2.mn
In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2
mn=3.2.5^2
mn = 150 = 10 * 15 (Least possible)
Answer = 4*10 + 15 = 55
ANSWER:C
Answer: C
Question: If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 15000 sheets of xerox paper?
Options:
A)$1250
B)$700
C)$1350
D)$900
E)$1000
Rationale: 30 sec approach - solve it using approximation
15000 sheet at full price, 5 cent = 750
15000 sheet at max discount price, 4 cent = 600
Your ans got to be between these two.
Ans B it is.
Answer: B
Question: A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half.
Options:
A)15 mins
B)20 mins
C)25 mins
D)30 mins
E)35 mins
Rationale: Explanation:
Let the total time be x mins.
Part filled in first half means in x/2 = 1/40
Part filled in second half means in x/2 =1/60 +1/40 =1/24
Total =X/2 X 1/40 + X/2 X 1/24 =1
x=30mins
ANSWER IS D
Answer: D
Question: How many five-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 3 ?
Options:
A)33
B)66
C)0
D)99
E)132
Rationale: A number ending with 3 can never be a perfect square.
Answer: C
Answer: C
Question: A total of 24 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
Options:
A) 32.2
B) 31.5
C) 32
D) 32.5
E) 33
Rationale: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 50 = 24 * 38 + 26 * Aw
=>1750 = 912 + 26 Aw
=> 26 Aw = 838
=>Aw = 32.2
Answer A
Answer: A
Question: How many different values of positive integer x, for which |x+7|<x, are there?
Options:
A)0
B)2
C)3
D)8
E)16
Rationale: Answer A
I opted to put the random value option.
i used 0 , 7 , -7 and the the extreme of 30 and -30..
i was able to solve it in 1:09
B
Answer: B
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years Q in which the population would be doubled assuming there is no emigration or immigration is
Options:
A)Q=20
B)Q=25
C)Q=30
D)Q=35
E)40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000=1000(1+(2/100))^n
n=35 Answer is D
Answer: D
Question: What is the greatest power that 2 can be raised to so that the resulting number is a factor of 20!?
Options:
A)4
B)8
C)10
D)20
E) 15
Rationale: the number of 2s in 20!= 20/2=10..
ans C
Answer: C
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Options:
A)10000
B)20000
C)22000
D)24000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: E
Question: Q-1: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 5?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 6
Two digit numbers divisible by 5 must end in either 0 or 5. Since there is no 0, all correct answers are a combination of the other digits and 5. There are six other numbers plus the 5 so there are 6 correct answers.
Correct answer is D.
Answer: D
Question: 8,13,23,43,83, (...)
Options:
A)123
B)223
C)143
D)163
E)113
Rationale: 8
8Ã— 2 - 3 = 13
13 Ã— 2 - 3= 23
23 Ã— 2 - 3 = 43
43 Ã— 2 - 3 = 83
83 Ã— 2 - 3 = 163
Answer is D
Answer: D
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)12
C)14
D)16
E)17
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: A
Question: The original price of a suit is $160. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?
Options:
A)$140
B)$145
C)$150
D)$155
E)$160
Rationale: 0.75*(1.25*160) = $150
The answer is C.
Answer: C
Question: There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
Options:
A)320
B)345
C)375
D)380
E)400
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
C
Answer: C
Question: A fortune teller has a unique way of predicting his customer’s prognosis. He has three parrots kept in three different cages. Each cage has three cards with a one digit non-zero number inscribed on every card. No two cards have the same number and no cage contains two cards with the number totaling ten. Further the total of numbers on the three cards in the first cage is greater by two than that in the second and by four than that in the third. When a customer asks for his prognosis, the fortune teller lets out the three parrots, which randomly pick one card out of their respective cages. Before the prognosis is made, the fortune teller totals the numbers on the three cards picked out by the parrots and charges the customer the same number of rupees as the total of the numbers on the cards. One day a customer paid seven rupees for his prognosis.
Which of the following combinations of cards may be picked for prognosis?
Options:
A)5, 7, 8
B)7, 9, 4
C)2, 6, 3
D)1, 3, 8
E)None of these
Rationale: considering the cages named as A B and C
according to the given conditon A=2B and A=4C
the customer paid the amount as the sum of three cards ,i,e card A,card B and card C=7
A+B+C=7 so, A+(A/2)+(A/4)=7
Solving, we get A=4
therefore a,b,c=4,2,1
ANSWER:E
Answer: E
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 30 percent alcohol?
Options:
A) 100/7
B) 5
C) 20/3
D) 8
E) 39/4
Rationale: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 30% of (100+x)
OR
20+x=(100+x)3/10
200+10x=300+3x
7x=100
x=100/7
Ans:A
Answer: A
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)4 years
B)8 years
C)2 years
D)4 years
E)6 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.
ANSWER E
Answer: E
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ?
Options:
A)1000
B)800
C)1400
D)1200
E)None of them
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000.
Answer is A
Answer: A
Question: When two dice are rolled, what is the probability that the difference between the two numbers is 3?
Options:
A) 1/9
B) 2/9
C) 1/3
D) 2/3
E) None of the above
Rationale: We have 6 outcomes that satisfy the question:
1-4
2-5
3-6
4-1
5-2
6-3
the probability is (1/6*1/6)*6= 1/6.
I think the answer is E
Answer: E
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 3360, then what is the smallest possible value of n?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 3360=2^5*3*5*7
2^5 means that n must be at least 8. That is, We need 2, 4, 6, and 8.
The answer is C.
Answer: C
Question: Amy's sells kale at x dollar per pound for the first 30 pounds and .8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?
Options:
A)24
B)25
C)26
D)27
E)46
Rationale: For Amy's deal to be better, the cost has to be less or equal to Lucia's
Assuming 'n' is the number of pounds of kale, the equation is
30x + (n-30) (0.8x) <= 14x + (n-14)(0.9x)
Resolve it:
==> 30x + 0.8nx - 24x <= 14x + 0.9nx - 12.6x
==> 4.6x <=0.1nx
==> 46x < =nx
==> x (n-46) > = 0
as x cannot be 0,
==> n - 46 >=0
==> n > = 46
so the minimum value is 46
'E' would be the correct answer
Answer: E
Question: When m is divided by 9, the remainder is 3. When m is divided by 13, the remainder is 9. If 1 < m < 200, what is the greatest possible value of m?
Options:
A)47
B)65
C)103
D)117
E)165
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
165 = 162 + 3 (162 divisible by 9)
165 = 156 + 9 (156 divisible by 13)
it fits the result
Answer = E
Answer: E
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 8% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)1
B)2
C)8
D)4
E)5
Rationale: 1250 = D(100/4)8
D = 8
Answer: C
Answer: C
Question: Bill bought 100 packets of candy. He was able to sell 1/2 of them at a 20% profit, another 1/4 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Bill after selling those 100 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!!
Options:
A)0
B)Profit of $87.5
C)Loss of $25
D)Profit of $80
E)Profit of $85
Rationale: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
50 packets was sold at a 20% profit --> gives profit of 10*0.2*50 = $100.
25 packets was sold at a 5% loss --> gives loss of 10*0.05*25 = $12.5.
The overall Profit is $100 - $12.5 = $87.5.
Answer: B.
Answer: B
Question: When E is divided by 9, the remainder is 4. All of the following are possible values of E, except for which of the following?
Options:
A)13
B)31
C)49
D)57
E)67
Rationale: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed E in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
Answer: D
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
Options:
A)10
B)28
C)26
D)11
E)12
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10
= 10 sec.
Answer:A
Answer: A
Question: A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
Options:
A)100 m
B)120 m
C)130 m
D)150 m
E)None of these
Rationale: Explanation :
Solution: Relative speed = (9 - 8) = 1 km/hr.
Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.
.'. Distance between the criminal and policeman = (265 - 50) m = 215 m.
Answer : E
Answer: E
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Options:
A)29
B)84
C)42
D)28
E)64
Rationale: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
ANSWER: D
Answer: D
Question: P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
Options:
A)10
B)11
C)13
D)12
E)15
Rationale: Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days
Answer is D.
Answer: D
Question: A man sells 4000 common shares of a Company x (each of par value Rs. 10), which pays a dividend of 40% at Rs. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Rs. 25) that pays a dividend of 15%. If the market value of Company Y is Rs. 15, find the number of shares of Company Y purchased by the man
Options:
A)4000
B)8000
C)3000
D)6000
E)5000
Rationale: Just too much information is given in the question to confuse. This is a straight and simple question
Market Value of Company X (his selling price) = Rs.30
Total shares sold = 4000
Amount he gets = Rs.(4000 × 30)
He invests this amount in ordinary shares of Company Y
Market Value of Company Y(His purchasing price) = 15
Number of shares of company Y which he purchases = 4000×30/15=8000
Answer is B.
Answer: B
Question: The sum of two positive integers multiplied by the larger number is 204. The difference multiplied by the smaller number is 35. The larger number is
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: let a and b be the 2 no.s , and a being the smaller
(a+b)*b=204
(b-a)*a=35
on solving
we get
b^2+a^2 = 169=13^2
remembering the pythagorean triplets of 5,12,13.
We get the values of a=5 and b=12
ANSWER:E
Answer: E
Question: Of all the homes on Gotham Street, 2/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Options:
A)a) 7/15
B)b) 3/15
C)c) 4/15
D)d) 2/5
E)e)1/5
Rationale: let total homes be 15
termite ridden= 2/3(15)= 10
termite ridden and collapsing = 3/5(10)=6
thus homes that are termite ridden, but not collapsing = 10-6=4
thus required ratio = 4/15
Answer C
Answer: C
Question: How many positive factors do 120 and 96 have in common?
Options:
A)8
B)12
C)16
D)18
E)24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 120 and 96 is 24
Number of factors of 24 = 8
Answer :A
Answer: A
Question: Kiran received Rs. 6000 as his share out of the total profit of Rs.9000 which he and Arun earned at the end of one year. If Kiran invested Rs. 30,000 for 6 months, whereas Arun invested his amount for the whole year, what was the amount invested by Arun?
Options:
A)Rs.5000
B)Rs.6000
C)Rs.7000
D)Rs.7500
E)Rs.6500
Rationale: Suppose Arun invested Rs.x. Then, Kiran : Arun = (30000 * 6) : (x * 12)
Therefore, 180000/ 12x = 6000/3000
or x = 18000/24
= 7500.
ANSWER:D
Answer: D
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 19 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
Options:
A)33 years
B)44 years
C)35 years
D)36 years
E)37 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*19 + 3*28 + 3*30 + x + x + 11 = 11*28.
=> 57+84+90+2x+11=308
so 2x = 66
so x = 33.
Age of the captain = (x+11)
= 44 years.
Answer : B
Answer: B
Question: A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 2 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
Options:
A)880mx/P
B)440P/mx
C)352mx/P
D)1760mx/P
E)5P/352mx
Rationale: 1 square foot needs 2/5P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For two stripes, the total area is 880mx square feet.
The number of gallons needed is (880mx)*(2/5P) = 352mx/P gallons.
The answer is C.
Answer: C
Question: If 2^98=256L+N , where Land N are integers and 0≤N≤4 , what is the value of N ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: If 2^98= 256L + N and 0<=N<=4, what is the value of N?
To solve this, note that 2^8 = 256, so 2^98 = 2^[(8*12)+2]=4*[256*256*......12 times]
As this is a multiple of 256, N can only be 0.
ANSWER:A
Answer: A