divelab/Sys2Bench huggingface dataset:
Question: If one is added to the numerator of the fraction it becomes one. If one is added to the denominator of the fraction it becomes 1/2. The fraction is?
Options:
A)1/2
B)3/5
C)2/3
D)2/5
E)3/5
Rationale: Explanation:
Let the fraction be x/y.
=> (x+1)/y = 1
=> x+1 = y—(1)
x/(y-1) = 1/2
=> 2x = (y+1)—(2)
=>Equating (1) and (2)
=> x+1 = 2x-1
=>x=2
Subsituting the value of x in (1)
=>y=3
=>2/3
ANSWER C
Answer: C
Question: Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 70 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?
Options:
A)10%
B)14%
C)18%
D)22%
E)26%
Rationale: Let I be the number of incandescent bulbs.
Let F be the number of fluorescent bulbs.
0.4I + 0.8F = 0.7(I+F)
0.1F = 0.3I
F = 3I
This means that for every 1 incandescent bulb, there are 3 fluorescent bulbs.
The percent of bulbs that are switched on which are incandescent is:
0.4I / (0.4I + 0.8F) = 0.4I / (0.4I + 0.8*3I) = 0.4I / 2.8I = 1/7 which is about 14%.
The answer is B.
Answer: B
Question: The probability that a computer company will get a computer hardware contract is 4/5 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 5/6, what is the probability that it will get both the contracts?
Options:
A)7/20
B)9/25
C)11/30
D)13/35
E)17/40
Rationale: Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 4/5, P(~B) =5/9
=> P(B) = 1- (3/5) = 2/5.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 5/6 = (4/5) + (2/5) - P(AB).
=> P(AB) = 11/30.
Hence, the required probability is 11/30.
The answer is C.
Answer: C
Question: There are 24 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?
Options:
A)10
B)20
C)40
D)50
E)70
Rationale: A
10
12 kids wear socks
8 kids wear shoes
6 wear both.
12 – 6 = 6 (wear only socks)
8 – 6 = 2 (wear only shoes)
6 (wear both)
hence, 24 -14 = 10
10 kids are with bare feet.
Answer: A
Question: Sophia finished 2323 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
Options:
A)140
B)320
C)745
D)270
E)350
Rationale: Let x be the total number of pages in the book, then she finished 23⋅x pages.
Then she has x−23⋅x=13⋅xpages left.
23⋅x−13⋅x=90
13⋅x=90
x=270
So the book is 270 pages long.
correct answer is D)270
Answer: D
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)11
B)1
C)2
D)7
E)9
Rationale: Explanation:
7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
Answer: D
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having only 1 woman in committee ?
Options:
A)11/18
B)5/18
C)6/19
D)17/18
E)16/18
Rationale: We may have (3 men and 2 women) = (7C3 x 6C2) = 525
or (4 men and 1 woman) = (7C4 x 6C1) = 210
or (5 men only) = (7C5) = 21
Required ways = 756
Probability of having only 1 woman in committee = 210 / 756 = 5/18
ans - B
Answer: B
Question: 1,5,6 ,25, 26,30,31, 125,126,130,131,150,151,155,156,……… What is the value of 33rd term in the
given series
Options:
A)3126
B)3226
C)3236
D)3246
E)3854
Rationale: 1st terms gives 2nd and 3rd terms
1st term is 1
2nd term 1*5=5 3rd term= 5+1=6
similarly,
4th term =5*5=25 5th term=25+1=26
1st term gives 2nd and 3rd values
2nd term gives 4th and 5th values
lke wise
16th term gives 32nd and 33rd values
16 th term is 125*5=625
32nd term is 625*5=3125 and 33rd value is 3126
ANSWER:A
Answer: A
Question: A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Options:
A)5
B)6
C)9
D)24
E)36
Rationale: list the people as 1,2,3,4,5,6 from shortest to tallest
First row leftmost -> Only 1 choice - the shortest -> Person 1
Last row rightmost -> only 1 choice - the tallest -> Person 6
First row second seat -> cannot be 4 or 5 because the constraint set on the second row would be violated. So First row second seat has to go to 2 or 3 (2 choices)
First row last seat -> If person 2 is seating on first row second seat, then the first row last seat can be person 3, person 4 or person 5 (3 choices)
First row last seat -> If person 3 is seating on the first row second seat, then the first row last seat can only be 4 or 5 (2 choices).
once we fix the first row, the last row can only be 1 certain choice in order to fit the constraint set by the question.
So we end up with
1,2,3/4/5 -> 3 ways
1,3,4/5 -> 2 ways
Total 5 ways.
Answer: A.
Answer: A
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.985. Find the cost of each ice-cream cup?
Options:
A)25
B)76
C)29
D)12
E)20
Rationale: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 985
96 + 225 + 490 + 6x = 985
6x = 174 => x = 29.
Answer:C
Answer: C
Question: A right circular cylinder has a height of 25 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
Options:
A)500(π – 3)
B)500(π – 2.5)
C)500(π – 2)
D)500(π – 1)
E)625(π – 1.5)
Rationale: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
The square base has sides of sqrt(50) due to the 45-45-90 triangle
25*25*pi - 15*sqrt(50)^2
=625(π – 1.5)
E. 500(π – 1.5)
Answer: E
Question: On a game show, a contestant spins 2 different wheels; each wheel is numbered 1 to 5. What is the probability that the contestant will spin all tens?
Options:
A)2/41
B)3/6
C)7/9
D)1/25
E)23/45
Rationale: All 5s:
1st wheel = 5 = 1/5
2nd wheel = 5 = 1/5
(1/5)(1/5)= 1/25
Answer: D
Answer: D
Question: If the price has fallen by 14% what percent of its consumption be: increased so that the expenditure may be the same as before?
Options:
A)A)11%
B)B)10%
C)1/9 %
D)1/11 %
E)7/43%
Rationale: 100 – 14 = 86
86------14
100------? => 7/43%
ANSWER:E
Answer: E
Question: Two trains of length 100 m and 120 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)11 sec
B)70 sec
C)21 sec
D)20 sec
E)19 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 100 + 120 = 220 m.
The time required = d/s
= 220/20
= 11 sec.
Answer: A
Answer: A
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Coe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Coe?
Options:
A)15
B)60
C)75
D)90
E)105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Coe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins.D
Answer: D
Question: The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hourr. The distance travelled downstream in 24 mins is?
Options:
A)6 km
B)7 km
C)7.2 km
D)8 km
E)8.4 km
Rationale: speed of a boat in still water = 15 km/hr
Speed of the current = 3 km/hr
Speed downstream = (15+3) = 18 km/hr
Distance travelled downstream in 24 minutes =2460×18=2×185 = 7.2 km
C
Answer: C
Question: A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 3 girls and 1 boy?
Options:
A)4
B)3
C)2
D)1
E)1/2
Rationale: Sample space = 2^4 = 16.
Favourable events = {bbgg}, {bgbg}, {bggb}, {ggbb}, {gbgb}, {gbbg}.{bggg},{gbbb)
Probability = 8/16 = 1/2.
Ans (E).
Answer: E
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 190km apart?
Options:
A)1 1/4 hours
B)5 hours
C)4hours
D)3 3/4 hours
E)6hours
Rationale: To be (18+20) km apart, they take 1 hour
To be 190 km apart, they take 1/38 * 190 = 5 hrs
Answer is B
Answer: B
Question: A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options:
A)14 years
B)18 years
C)20 years
D)22 years
E)16 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :B
Answer: B
Question: If a > 1, which of the following is equal to (2a + 6)/(a^2 + 2a - 3)?
Options:
A)a
B)a + 3
C)2/(a - 1)
D)2a/(a - 3)
E)(a - 1)/2
Rationale: (2a + 6)/(a^2 + 2a - 3) = 2(a + 3) / (a + 3)(a - 1)
= 2/(a - 1)
Option C
Answer: C
Question: The average of four consecutive odd numbers is 24. Find the largest number.
Options:
A)25
B)27
C)29
D)31
E)32
Rationale: Explanation:
Let the numbers are x, x+2, x+4, x+6, then
=>x+(x+2)+(x+4)+(x+6)4=24
=>4x+12)4=24
=>x+3=24=>x=21
So largest number is 21 + 6 = 27
Answer: Option B
Answer: B
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)658 m
B)156 m
C)245 m
D)156 m
E)186 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Answer: C
Question: In his ranch, Doug Bo can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that he will be able to place a lasso around a cow’s neck at least once in 5 attempts?
Options:
A)1/5
B)15/32
C)1/2
D)31/32
E)1
Rationale: The probability of not placing a lasso around the cow's neck on 5 attempts is:
(1/2)(1/2)(1/2)(1/2)(1/2) = 1/32
The probability of placing a lasso around the cow's neck on 5 attempts is
1 - (1/32) = 31/32
correct answer option D
Answer: D
Question: In a certain match all the teams were to play with each other. If there are 5 teams, how many matches will have to be played?
Options:
A)40
B)45
C)60
D)10
E)None of the above
Rationale: 5c2
=10
ANSWER:D
Answer: D
Question: If a cost college Rs0.70 a companyto produce a program for yhe home coming football game.if Rs 15000 was received for addvertisement in the pgm ,how many copies rs 0.50 a copy must be sold to make a profit of Rs 8000
Options:
A)15000
B)25000
C)45000
D)32000
E)35000
Rationale: let no. of pages be x
while selling with 0.70paise/page total cost=0.70*x
while selling with 0.50paise/page toatal cost=0.50*x
now according to question-
(0.70x - 0.50x) + 8000 = 15000
therefore, x=35000 copies must be sold
ANSWER:E
Answer: E
Question: If three numbers in the raƟo 3 : 2: 5 be such that the sum of their squares is 1862, the middle
number will be
Options:
A)10
B)14
C)18
D)22
E)None of these
Rationale: Explanation:
Let the numbers be 3x, 2x and 5x.
Then,
9x + 4x + 25x =1862
⇒
38x = 1862
⇒
x = 49
⇒
x = 7.
middle number = 2x = 14
Answer: B
Answer: B
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)Rs.200
B)Rs.250
C)Rs.300
D)Rs.350
E)Rs.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
B)
Answer: B
Question: What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?
Options:
A)Rs. 400. 00
B)Rs. 120. 00
C)Rs. 510. 00
D)Rs. 520. 00
E)Rs. 220. 00
Rationale: Explanation:
SI for 2 years = 568 – 520 = Rs. 48
SI for 5 years = Rs. 120
Principal = 520-120 = Rs. 400
Answer: A
Answer: A
Question: How much time will take for an amount of Rs. 330 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)5 5/11years
B)6 5/11years
C)7 5/11years
D)12 5/11years
E)15 2/11years
Rationale: Time = (100 * 81) / (350 * 4.5) = 5 5/11years
ANSWER:A
Answer: A
Question: The price for a loaf of bread in April was $1.17, in May the price was $1.30, and in June the price was $1.05. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
Options:
A)$1.13
B)$1.14
C)$1.15
D)$1.16
E)$1.17
Rationale: Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(117) + 130x + (4x/3)(105) / (2x/3 + x + 4x/3) =
(78 + 130 + 140) / (3) = 348/3 = $1.16
The answer is D.
Answer: D
Question: A taxi charges q dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.
Options:
A)qn – c/8(100)
B)cq + 4n-8/200
C)q + (4cn-8c)/100
D)q + 100cn/4
E)4cq(n-2) – 100
Rationale: This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost q is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost q, or subtract the additional cost from q. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
Answer: C
Question: The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder T of Y divided by 5?
Options:
A)T=1.
B)T=2.
C)3.
D)4.
E)5.
Rationale: X divided by 10 gives reminder of 2. X can be 2/12/22....
X+Y divided by 5 is 4. X + Y can be 4/ 9/ 19....
If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2
Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2
Hence the answer must be 2 (B)
Also....
x+y=5m+4 and x=10K+2
hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B
Answer: B
Question: A person travels from P to Q a speed of 80 km/hr and returns by increasing his speed by 10%. What is his average speed for both the trips?
Options:
A)33
B)77
C)48
D)84
E)21
Rationale: Speed on return trip = 110% of 80 = 88 km/hr.
Average speed of trip = 80 + 88 /2 = 168/2 = 84 km/hr
Answer : D
Answer: D
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
Options:
A)2 days
B)3 days
C)4 days
D)5 days
E)6 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
B
Answer: B
Question: Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 11 years older than Larry, how old is Annie?
Options:
A)4
B)8
C)19
D)26
E)34
Rationale: J = L+11
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+16
Let's subtract equation (1) from equation (2)
A+9 = 13
A = 4
The answer is A.
Answer: A
Question: A man in a train travelling at 30km/hr notices that a train going in the opposite direction passes him in 9 sec.If the length of this train is 200m find its speed .
Options:
A)30 km/hr
B)40 km/hr
C)50 km/hr
D)60 km/hr
E)70 km/hr
Rationale: relative speed of trains = 200/9 mtrs/sec = 200*18/(9*5)= 80 km/hr
speed of 2nd train = 80-30=50 km/hr
ANSWER:C
Answer: C
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Options:
A)4/5 km
B)4/8 km
C)6/5 km
D)4/0 km
E)4/4 km
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer:A
Answer: A
Question: Buffalo gives 4 liter milk, cow gives (1/2) liter milk and goat gives 1/4 liter milk. you have to get 20 liter milk by 20 animals.what is the number of goats?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Assume number of respective animals are x,y,z.
x+y+z=20---(1) as the total number of animal has to be 20
Amt of milk will be 4x+(1/2)y+(1/4)z=20---(2)
Solving equation 1 and 2 we get
15x+y=60 ----(3)
Since buffalo gives 4litre and total milk is 20, x < 5
But from eq 3, x cannot be more than 4;
Further if x=1 or 2; y>20... Not possible, since total animal is 20
Thus, x=3, y=15, z=2
2goats
ANSWER:B
Answer: B
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 300 milliliters of solution X to create a solution that is 15 percent alcohol by volume?
Options:
A)50
B)100
C)150
D)200
E)250
Rationale: 15% is 5%-points higher than 10% but 15%-points lower than 30%.
Thus there should be 3 parts of solution X for 1 part of solution Y.
We should add 100 ml of solution Y.
The answer is B.
Answer: B
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 50%?
Options:
A)125%
B)150%
C)100%
D)90%
E)85%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 50% increase A surface = 6* ((1.5a)^2) = 6*2.25*a^2
The increase in the surface area = (6*2.25*a^2 - 6*a^2)/6*a^2 = (6*a^2(2.25-1))/(6*a^2) = 2.25-1=1.25 = 125%
Answer :A
Answer: A
Question: Bob's pizza recipe calls for 2 ounces of baking soda for every 2 cups of flour used. He needs to use 12 cups of flour to make 6 pizzas for a party. If 12 cups of flour is used, then how many ounces of baking soda are needed?
Options:
A)24
B)12
C)2
D)6
E)18
Rationale: Number of ounces per 2 cups of flour is 2
Number of cups of flour used in total is 6
Ounces needed is 12
Answer 12
The correct answer is B.
Answer: B
Question: If $0.2 is commission for sales of $1,000, what percent of sales amount is the commission?
Options:
A)2%
B)0.2%
C)0.02%
D)0.002%
E)0.0002%
Rationale: % of sales amount of commission = (Commission/Total Value) *100 = (0.2/1000) * 100 = 0.02%. Answer C.
Answer: C
Question: A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 3 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
Options:
A)4.2
B)5.2
C)6
D)8
E)10
Rationale: Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+3)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=4.2 m/s
A
Answer: A
Question: Josh spends a total of $4.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?
Options:
A)99
B)100
C)81
D)109
E)140
Rationale: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=4.5 ---> x+10y=90 ...(1)
Also, x+y=N ...(2)
Solving 1 and 2 , we get, N = 90-9y ---> only value satisfied is when y = 1---> N = 90-9=81.
C is the correct answer. Other options are not equal to multiples of 9 removed from 90.
Answer: C
Question: A computer manufacturer produces a certain electronic component at a cost of $75 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)$28
B)$187
C)$110
D)$138
E)$192
Rationale: This question can be solved easily using a equation model.
150*p = 16500(fixed cost) + 150*75+150*2.
= 16500 + 11250 + 300
P= $187
B
Answer: B
Question: A, B and C started a partnership business by investing Rs.5000, Rs.8000, Rs.9000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
Options:
A)70000
B)60000
C)88000
D)90000
E)50000
Rationale: A:B:C =5000:8000:9000
=5:8:9
Let total profit =p
Then pÃ—9/22=36000
p=(36000Ã—22)/9=88000
Answer is C.
Answer: C
Question: A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is:
Options:
A)10
B)20
C)40
D)73
E)None of the above
Rationale: Let there be x pupils in the class.
Total increase in marks = (x × 1⁄2) = x⁄2.
∴ x⁄2 = (83 - 63) ⇒ x⁄2 = 20 ⇒ x = 40.
Answer C
Answer: C
Question: The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 20 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes.
Options:
A)$0.94
B)$0.96
C)$0.98
D)$1.00
E)$1.09
Rationale: Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 20% are damaged --> Available tomatoes to sell = 80
80 * x - 80 = 0.08 * 80
80x - 80 = 6.4
80x = 86.64
x = 86.64/80 = 87/80 (approx) = 1.0875
x is slightly under 1.0875 = 1.09
Answer: E
Answer: E
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (6,6) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
Options:
A)(-2,6)
B)(0,4)
C)(2,-6)
D)(2,6)
E)(4,8)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,6) or (6,0), then the area is 1/2*6*6=18. Thus A must be at (4,8).
Answer: E.
Answer: E
Question: The average age of 3 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is?
Options:
A)10years
B)15years
C)20years
D)25years
E)18years
Rationale: Total age of 3 boys = 25*3 = 75
ratio of their ages = 3:5:7
Age of the youngest = 75*3/15 = 15 years
Answer is B
Answer: B