RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The speed of a boat in upstream is 20 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.30 kmph
B.13 kmph
C.65 kmph
D.55 kmph
Answer: A.30 kmph
Explanation: Speed of the boat in still water
= (20+80)/2
= 50 kmph. Speed of the stream
= (80-20)/2
= 30 kmph.
Answer: A
Question: If 3^a - 3^(a-1) = 162 then a(a-1) =
A.12
B.16
C.20
D.30
Answer: C.20
Explanation: It seems like you were really close but you solved for a - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of a(a -1), e.g. (3)(4) = 12. Even then, had you figured a has to be a little bigger (plugging in 4 for a gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (a - 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.
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
A.1/3
B.1/5
C.1/7
D.1/9
Answer: A.1/3
Explanation: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A)
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 5, 12 and 13?
A.2.5
B.6.5
C.5
D.6.0
Answer: B.6.5
Explanation: Some of pyhtagron triplets we need to keep it in mind.
Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).
So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.
The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 13 / 2 = 6.5
Ans. B
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-5)(x+4)(2X+5) = 0?
A.a) 1/12
B.b) 1/6
C.c) 1/4
D.d) 1/3
Answer: A.a) 1/12
Explanation: x = -1
Prob = 1/12
Answer - A
Question: One drier dries certain quantity of material in 24 minutes. Another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?
A.1.00 minutes
B.1.20 minutes
C.1.50 minutes
D.1.85 minutes
Answer: D.1.85 minutes
Explanation: By guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes Therefore, answer 1.85 minutes will be correct. Answer-D
Question: How many integers from 101 to 700, inclusive, remains the value unchanged when the digits were reversed?
A. 50
B. 60
C. 70
D. 80
Answer: B. 60
Explanation: question is asking for palindrome
first digit possibilities - 1 through 6 = 6
7 is not possible here because it would result in a number greater than 7 (i.e 707 , 717..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 6*10 =60
Answer is B.
Question: A restaurant meal cost $55 and there was no tax. If the tip was more than 20 percent but less than 30 percent of the cost of the meal, then total amount paid must have been between:
A.$65 and $72
B.$66 and $71
C.$64 and $71
D.$63 and $70
Answer: A.$65 and $72
Explanation: let tip=t
meal cost=55
range of tip = from 20% of 55 to 30% of 55 = 11 to 16.5
hence range of amount paid= 55+T= 66 to 71.5 i.e. A
Question: A train 180 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.7
B.10
C.8
D.2
Answer: B.10
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 180 * 3/55
= 10 sec.
Answer B
Question: List I: 3, 6, 8, 10
List II: x, 3, 6, 8, 10
A.7
B.8
C.9
D.10
Answer: A.7
Explanation: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: A.
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
A.15343
B.16423
C.17576
D.17809
Answer: C.17576
Explanation: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Question: Look at this series: (1/9), (1/3), 1, ____ , 9, ... What number should fill the blank?
A.3
B.4
C.1
D.6
Answer: A.3
Explanation: A
3
This is a multiplication series; each number is 3 times the previous number.
Question: A pipe takes a hours to fill the tank. But because of a leakage it took 4 times of its original time. Find the time taken by the leakage to empty the tank
A.50 min
B.60 min
C.90 min
D.80 min
Answer: D.80 min
Explanation: pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/240
x=80 min
ANSWER:D
Question: The G.C.D. of 1.08, 0.36 and 0.5 is:
A.0.02
B.0.9
C.0.18
D.0.108
Answer: A.0.02
Explanation: Given numbers are 1.08, 0.36 and 0.50. H.C.F. of 108, 36 and 50 is 18,
H.C.F. of given numbers = 0.02.
Answer: Option A
Question: A man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:
A.70%
B.80%
C.90%
D.20%
Answer: D.20%
Explanation: Explanation:
Let the article be worth Rs. x.
C.P. 90% of Rs. x = Rs. 9x/10
S.P. = 110% of Rs. x = Rs. 11x/10
Gain = (11x/10 - 9x/10) = Rs. x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer:D
Question: A can do a piece of work in 16 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?
A.3 days
B.4 days
C.6 days
D.7 days
Answer: B.4 days
Explanation: B's 9 day's work = 9 x (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 16 x (1/4) = 4 days.
answer : B
Question: Find the sub-triplicate ratio of 27:125
A.3:5
B.3:9
C.3:6
D.3:1
Answer: A.3:5
Explanation: The sub-triplicate ration of 27 : 125 = 3:5
Answer:A
Question: the profit of certain article is 25 percent.had it been bought at 10 percent discount and sold for 20 percent more than the earliest cost,the profit would have been rs600.what is the cost price of the article.
A.1800
B.2000
C.2200
D.2400
Answer: B.2000
Explanation: Let CP be x
Gain% = 25%
Then SP = x*125/100
SP = 5x/4
If it had been bought at 10% discount
Then CP = x*90/100
CP = 9x/10
sold at 20% more that the earliest cost... [earliest cost means x]
Then SP = x*120/100 = 600+9x/10
6x/5 = 6000+9x/10
12x = 6000+9x
3x = 6000
x = 2000
ANSWER:B
Question: A dishonest shopkeeper deceives by 15% at the time of purchase of article and also 15% at the time of sale.Find out the profit percentage
Profit%
A.32.25%.
B.32
C.42.25%
D.42
Answer: A.32.25%.
Explanation: Solution
=15+15+(15*15 / 100)=30 + 225/100 =30+2.25=32.25%.
Answer A
Question: A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %?
A.30%
B.40%
C.50%
D.56%
Answer: B.40%
Explanation: Gain=16 applesTotal 56 applesCP 56-16=40(16/40)*100=40%Ans B
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 16 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
A.13
B.13.5
C.14.4
D.14.5
Answer: C.14.4
Explanation: Ans is C
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x
for average miles per gallon = (d+x)/((d/12)+(x/16)) = 14.4 (formula avg speed = total distance/ total time)
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 45, find the other?
A.100
B.160
C.120
D.200
Answer: B.160
Explanation: Other number = 12*600/45= 160
Answer is B
Question: Which of the following numbers is divisible by 9?
A.23274
B.25181
C.31001
D.50123
Answer: A.23274
Explanation: 23274. This is the only option with last two digits divisible by 9
Answer:A
Question: If C.P. of 25 books is equal to S.P of 30 books , then your gain or loss is ?
A.23 1/3 gain %
B.30 10/23 loss %
C.16.7% loss %
D.30 1/3 loss %
Answer: C.16.7% loss %
Explanation: Say the cost price of 25 books is $25 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 25$, hence the loss = ($30 - $25)/$30 = ~16.7%.
Answer: C.
Question: At what rate of interest is an amount doubled in two years, when compounded annually?
A.41.4%
B.41.7%
C.41.4%
D.42.4%
Answer: B.41.7%
Explanation: Let the rate of interest be r. The amount gets doubled in two years
=> P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1
= 0.414 => r = 100(0.414)
= 41.4%
Answer:B
Question: John has on his shelf two books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
A.1/2
B.2/5
C.3/10
D.2/7
Answer: D.2/7
Explanation: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/8*2/7 + 2/8*4/7 = 2/7.
Answer: D
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor D of 2x and 3y?
A.1
B.D=Cannot be determined
C.2
D.5
Answer: B.D=Cannot be determined
Explanation: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Question: In what time will a train 55 m long cross an electric pole, it its speed be 36 km/hr?
A.5.5
B.4.5
C.3.5
D.2.5
Answer: A.5.5
Explanation: Speed = 36 * 5/18 = 10 m/sec
Time taken = 55/10 = 5.5 sec.
Answer: A
Question: A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
A.14
B.18
C.21
D.22
Answer: B.18
Explanation: Let the speed in highway be h mpg and in city be c mpg.
h = c+6
h miles are covered in 1 gallon
462 miles will be covered in 462/h.
Similarly c miles are covered in 1 gallon
336 miles will be covered in 336/c.
Both should be same (as car's fuel capacity does not change with speed)
=> 336/c = 448/h
=> 336/c = 448/(c+6)
=> 336c+336*6=448c
=>c=336*6/112=18
Answer B.
Question: A is 50% as efficient as B.C does half of the work done by A and B together .If C along does the work in 40 days then A,B,C
together can do the work in?
A.15 1/4 days
B.16 days
C.13 1/3 days
D.25 2/5 days
Answer: C.13 1/3 days
Explanation: A's 1 day's work:B's 1 day's work=150:100=3:2
let A's and B's 1 days work be 3x and 2x respectively
then C's 1st days work=(3x+2x)/2=5x/2
5 x/2=1/40
x=1/100
A's 1 day work=3/100
B's 1 day work=1/50
C's 1 day work=1/40
(A+B+C)'s 1 day work=(3/100+1/50+1/40)=15/200=3/40
so A,B,C together can do the work in 40/3=13 1/3 days
Answer(C)
Question: On a sum of money, the simple interest for 2 years is Rs. 325, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
A.15%
B.14.25%
C.9.23%
D.10.5%
Answer: C.9.23%
Explanation: Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 325 = 15
(R Ã— SI)/(2 Ã— 100) = 15
(R Ã— 325)/(2 Ã— 100) = 15
R = 9.23%
Answer: Option C
Question: Alex invested an amount of $500 for two years. Find the rate of compound interest that will fetch him an amount of $83.20 at the end of two years?
A.8%
B.10%
C.12%
D.7%
Answer: A.8%
Explanation: Let the rate of interest be R% p.a.
500[1 + R/100]^2 = 583.20
[1 + R/100]2 = (583.20)/500
= 11664/10000 = [108/100]2
[1 + R/100] = 108/100
R=8%
Answer is A
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C?
A.3377
B.2899
C.5000
D.2778
Answer: C.5000
Explanation: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 400
C's capital = 30000*1/6 = 5000
Answer: C
Question: Average of first seven multiples of 2 is
A.8
B.9
C.13
D.15
Answer: A.8
Explanation: Explanation:
Average=2(1+2+3+4+5+6+7) / 7=56 / 7=8
Option A
Question: In a division sum, the quotient is 120, the divisor 456 and the remainder 333, find the dividend?
A.55053
B.50553
C.5553
D.40532
Answer: A.55053
Explanation: 120 * 456 + 333 = 55053
ANSWER A
Question: select the no. which is different from series
1,4,9,16,23,25,36
A.25
B.36
C.23
D.9
Answer: C.23
Explanation: answer is 23 only rest every no. is square of any no.
answer C
Question: Today is Tuesday. The day after 59 days will be
A.Monday
B.Tuesday
C.Saturday
D.Friday
Answer: D.Friday
Explanation: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Tuesday, After 59 days, it will be = (Tuesday + 3 odd days)
= Friday. Answer : Option D
Question: A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was
A.665
B.287
C.297
D.255
Answer: A.665
Explanation: Explanation:
Let the total score be x.
(x + 92 - 85) / 8 = 84.
So, x + 7 = 672 => x = 665.
Answer: A
Question: A man's speed with the current is 18 km / hr and the speed of the current is 2 km / hr. The man's speed against the current is
A.8.5 km / hr
B.9 km / hr
C.14 km / hr
D.12.5 km / hr
Answer: C.14 km / hr
Explanation: Sol.
Man's rate in still in water = (18 - 2) km / hr = 16 km / hr.
Man's rate against the current = (16 - 2) km / hr = 14 km / hr.
Answer C
Question: A and B start from house at 10am. They travel fro their house on the MG road at 20kmph and 40 kmph. there is a Junction T on their path. A turns left at T junction at 12:00 noon, B reaches T earlier, and turns right. Both of them continue to travel till 2pm. What is the distance between A and B at 2 pm.
A.223
B.160
C.297
D.276
Answer: B.160
Explanation: Distnace between House and T junction = 20 x 2 = 40.
ie., B reached T at 11 am.
B continued to right after 11 am and travelled upto 2. So distance covered by him = 3 x 40 = 120
A reached T at 12 noon and travelled upto 2 So distanced travelled by him = 2 x 20 = 40
So total distance between them = 120 + 40 = 160 km
Answer:B
Question: In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only three of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?
A.1
B.3
C.4
D.5
Answer: A.1
Explanation: Total Private Schools = 9
Dist A: High Schools = 18 ==> Private Schools = ?
Dist B: High Schools = 17 ==> Private Schools = 3
Dist C: High Schools = 15 ==> Private Schools = 5
Therefore, 9 - 3 - 5 ==> 1
Answer A)
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 49 hrs and a machine of type S does the same job in 14 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
A.49/9
B.44/9
C.46/9
D.41/9
Answer: A.49/9
Explanation: Rate of machine R =1/49
Rate of machine S =1/14
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/49 +x/14 =1/2
9x=49
x=49/9
So no of machine R is 49/9
Answer A
Question: The simple interest on Rs.10000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest.
A.3087.82
B.3087.89
C.3087.85
D.3087.36
Answer: D.3087.36
Explanation: R = 100 I / PT
=> R = (100 * 7200)/ (10000 * 5) = 14.4%
CI = P{ [1 + R /100]n - 1}
= 10000 { [ 1 + 14.4 / 100]^2 - 1} = Rs.3087.36
Answer:D
Question: Two numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first?
A.10
B.15
C.20
D.30
Answer: A.10
Explanation: I II III
70 63 100
70 -------- 7
100 ------ ? => 10%
ANSWER A
Question: If 4-X < (2-5X)/3, which of the following is correct?
A.X < -5.
B.X > -5.
C.X > 5.
D.-5 < X < 0.
Answer: A.X < -5.
Explanation: 4-X < (2-5X)/3
12-3X < 2- 5X
10 < -2X
-10/2>X
-5>X
A is the answer
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40
B.74
C.38
D.76
Answer: A.40
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140
= 500 m
Required time = 500 * 2/25
= 40 sec
Answer: A
Question: 0---:-|---:--|-:--:-|--:---|-:----1
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance X between any two of the tick marks?
A.1/70
B.1/35
C.2/35
D.1/12
Answer: B.1/35
Explanation: divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1
1/5 2/5 3/5 4/5 5/5
expressing the same in terms of the lcm of 5,7 ,i.e 35
0 7/35 14/35 21/35 28/35 35/35
5/35 10/35 15/35 20/35 25/35 30/35
by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.
X=1/35
Answer is B.
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 846 in 4 years. The sum is?
A.s. 738
B.s. 638
C.s. 650
D.s. 762
Answer: D.s. 762
Explanation: S.I. for 1 year = (846 - 825) = Rs. 29
S.I. for 3 years = 21 * 3 = Rs. 63
Principal = (825 - 63) = Rs. 762.
ANSWER:D
Question: A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors?
A.5%
B.10%
C.15%
D.20%
Answer: D.20%
Explanation: Solution: let the total number of flags be 100(even number)
let the total number of 'blue' flags alone be 'a'
let the total number of 'red' flags alone be 'b'
let the total number of 'both' flags be 'c'
We have given,
total number of blue flags = 60% = 60 = a+c
total number of red flags=55%=55=b+c
total number of flags = a+b+c=100 (since all the flags have been utilized)
So, substituting for c in the third equation, we have,
60-c+c+60-c=100
c=20
Option D.
Question: You are riding a horse. In front of you, there is a fire engine. A helicopter is following you. To your left a sports car is driving. To your right there is a depth.How can you arrange that you will all stop simultaneously, without crashing and without mutual communication?
A.helicopter man stop it
B.you stop it
C.man go to stop it.
D.no idea
Answer: C.man go to stop it.
Explanation: You ask the man of the merry-go-round to stop it.
Answer C
Question: How much 90% of 40 is greater than 80% of 30?
A.12
B.14
C.16
D.17
Answer: A.12
Explanation: (90/100) * 40 – (80/100) * 30
36 - 24 = 12
Answer: A
Question: A batsman scored 18 runs in his 18th innings and that makes his average 18. Find his average upto the 17th innings?
A.17
B.18
C.19
D.20
Answer: B.18
Explanation: total innings=18
avg=18
so total run at 18th innings is 18*18=324
total at 17th inning=324-18=306
now 306/17=18
ANSWER:B
Question: There are ten different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A.72
B.48
C.64
D.24
Answer: C.64
Explanation: Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 3*2*1 = 8 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2 = 8). So we have 8*8 = 64.
Please correct me if im wrong.
Answer C.
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
A.33/99
B.33/91
C.36/91
D.33/97
Answer: B.33/91
Explanation: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= 33/91
Answer: B
Question: Five women can do a work in ten days. 7 men can complete the same work in 5 days. What is the ratio between the capacity of a man and a woman?
A.10:7
B.11:10
C.2:3
D.3:2
Answer: A.10:7
Explanation: Explanation:
(50 Ã— 10) women can complete the work in 1 day.
âˆ´ 1 woman's 1 day's work = 1/50
(7 Ã— 5) men can complete the work in 1 day.
âˆ´ 1 man's 1 day's work = 1/35
so, required ratio =1/50 : 1/35= 10:7
Answer: A
Question: Last year the price per share of Stock N increased by a percent and the earnings per share of Stock N increased by b percent, where a is greater than b. By what percent did the ratio of price per share to earnings per share increase, in terms of a and b?
A.100*(a-b) %
B.100*(a-b)/(100+b) %
C.(100+b) %
D.(a-b)/(100+b) %
Answer: B.100*(a-b)/(100+b) %
Explanation: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+a/100) and the new earning is: E*(1 +b/100)
The new P/E is: (1+a/100)P/(1+b/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+a/100)/(1+b/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(a-b)/(100+b) %
Answer : B
Question: In a 100 m race,A covers the distance in 36 seconds and B in 45 second.In this race A beats B by :
A.20 m
B.25 m
C.22.5 m
D.9 m
Answer: A.20 m
Explanation: Solution
Distance covered by B in 9 sec. = (100/45x9)m =20m.
∴ A beats B by 20 metres.
Answer A
Question: What is the least common multiple of 15, 16, and 24?
A.60
B.120
C.240
D.360
Answer: C.240
Explanation: Let us first write the numbers in the form of prime factors:
15 = 3*5
16 = 2^4
24 = 2 * 17^1
The LCM would be the largest powers of the prime numbers from all these three numbers.
Hence LCM = 240
Option C
Question: Angela, Bernie, and Colleen can complete a job, all working together, in 2 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?
A.8 hours
B.10/3 hours
C.12 hours
D.16 hours
Answer: B.10/3 hours
Explanation: A+B+C complete the job in 2 hours.
A+B complete the job in 5 hours.
A+B and C complete the job in 2 hours -->1/(A+B) + 1/C = 1/2-->1/5+1/C=1/2 ----> C=10/3 hours. ANS B