divelab/Sys2Bench huggingface dataset:
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 80 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 3 hours to travel 240 km, so C leaves 5 hours after A.
The answer is D.
Answer: D
Question: The speed of a car is 90 km in the first hour and 75 km in the second hour. What is the average speed of the car?
Options:
A)89 kmph
B)82.5 kmph
C)75 kmph
D)65 kmph
E)77 kmph
Rationale: S = (90 + 75)/2 = 82.5 kmph
B
Answer: B
Question: A train 330 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?
Options:
A)5
B)6
C)7
D)18
E)9
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 330 * 3/55 = 18 sec.
Answer: Option D
Answer: D
Question: Three shops that belonged to a chain were closed, and as a result the average (arithmetic mean) annual revenue per shop in the chain grew from $150,000 to $225,000. If the number of shops in the chain before the change was 8, approximately, what was the average annual revenue of the shops that were closed?
Options:
A)$25,000
B)$37,500
C)$58,333
D)$75,000
E)$91,666
Rationale: if the average annual revenue of the 5 shops which are still open is 225,000, it means that they make a total of 225,000∗5=1,125,000 $
let's call the average annual revenue of the 3 shops that have been closed x.
therefore, they make a total of 3∗x $
We know that the total revenue of the 8 shops that were open has to be 150,000
Thus (3x+1,125,000)/8=150,000
therefore x=25,000 answer A
Answer: A
Question: If Thursday was the day after the day before yesterday five days ago, What is the least number of days ago when Sunday was three days before the day after tomorrow?
Options:
A)Two
B)Three
C)Four
D)Five
E)Six
Rationale: Explanation :
Day after the day before yesterday is yesterday.
Now, five days ago, yesterday was Thursday.
So, five days ago, it was Friday.
Therefore today is Wednesday.
Now, three days before the day after tomorrow is yesterday.
Now, it is on Monday that we say Yesterday was Sunday.
Answer : A
Answer: A
Question: If n has 15 positive divisors, inclusive of 1 and n, then which of the following could be the number of divisors of 3n?
I. 20
II. 30
III. 40
Options:
A)II only
B)I and II only
C)I and III only
D)II and III only
E)I, II and III only
Rationale: n has 15 positive divisors --> n=p^14 (the # of factors (14+1)=15) or n=p^2q^4 (the # of factors (2+1)(4+1)=15).
If neither p nor q is 3, then:
3n=3p^14 will have (1+1)(14+1)=30 factors.
3n=3p^2q^4 will have (1+1)(2+1)(4+1)=30 factors.
If p = 3, then:
3n=3p^14 =3^15 will have (15+1)=16 factors.
3n=3p^2q^4 = 3^3 p^4 will have (3+1)(4+1)=20 factors.
If q = 3, then:
3n=3p^2 =q^4 will have(2+1) (5+1)=18 factors.
Answer: B.
Answer: B
Question: At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes?
Options:
A)100000
B)85236
C)89562
D)90083
E)95842
Rationale: winners votes = 100-45 = 55%
invalid votes = 83
polled votes = [(100*9000)/(2*55-100)]+83 = 90083
Answer is D
Answer: D
Question: John bought a 1-year, $30,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$3175
B)$3275
C)$3075
D)$3375
E)$3500
Rationale: 10 percent compounded semiannually --> 5% in 6 moths.
For the first 6 moths interest was 5% of $30,000, so $1500;
For the next 6 moths interest was 5% of $31,500, so $1575
Total interest for 1 year was $1500+$1575=$3075
Answer : C
Answer: C
Question: Two spheres of their radios in the ratio 4 : 3. Find its volumes ratio?
Options:
A)64:13
B)13:64
C)27:64
D)64:27
E)None of them
Rationale: Sphere volume (V) = 4/3 πR(power3) : 4/3 π r(power3) = 4(power3) : 3(power3)
= 64 : 27
Answer is 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. In how many ways can it be done?
Options:
A)407
B)756
C)347
D)248
E)112
Rationale: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756.
ANSWER B 756
Answer: B
Question: The sum of the present ages of A, B, C is 27 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?
Options:
A)10
B)6
C)8
D)9
E)7
Rationale: Three years ago:
a:b:c = 1:2:3
Let a = 1x, b = 2x, and c = 3x.
Today:
(x+3) + (2x+3) + (3x+3) = 27
x = 3
So the present age of A is x+3 = 6
The answer is B.
Answer: B
Question: If u = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
Options:
A)-2
B)-1
C)0
D)2
E)None of the above
Rationale: Let us transform the formula:
u = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Answer: D
Question: In the infinite sequence 12, 18, 24, 30, 36, . . . , where each term is 6 greater than the previous term, the 18th term is
Options:
A)635
B)758
C)96
D)126
E)114
Rationale: T(n) = a + (n-1) d
Here d =6, a=12, n=18
Solving we get T(n) = 114.
Answer: E
Answer: E
Question: When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 6. If 1 < m < 300, what is the greatest possible value of m?
Options:
A)157
B)177
C)197
D)227
E)257
Rationale: 13*9 = 117
Let's start with 6, and keep adding 13 until we find a number with the form 9k+2.
6, 19, 32, 45, 58, 71, 84, 97, 110 = 9*12+2
The next possible number is 110 + 117 = 227
The next possible number would be greater than 300.
The answer is D.
Answer: D
Question: Which of the following equations has a root in common with x^2−4x=0 ?
Options:
A)x^2-4x+4=0
B)x^2-2x+1=0
C)x^2-3x+2=0
D)x^2-7x+6=0
E)x^2-9x=0
Rationale: If we carefully look at the given equation we can arrange it in the following manner:
x(x-4) = 0
so the two roots are 0 and 4.
Now put 0 and 4 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 0: we get 4; Putting 4 we get 4. Reject this option.
(B) putting 0: we get 1; Putting 4 we get 9. Reject this option.
(C) putting 0: we get 2; Putting 4 we get 2. Reject this option.
(D) putting 0: we get 6; Putting 4 we get -6. Reject this option.
(E) putting 0: we get 0. This is the equation.
E is the answer.
Answer: E
Question: The two lines y=x and x=-5 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
Options:
A)7.5
B)10
C)12.5
D)15
E)17.5
Rationale: The point of intersection is (-5,-5).
The triangle has a base of length 5 and a height of 5.
area = (1/2)*base*height = (1/2)*5*5 = 12.5
The answer is C.
Answer: C
Question: A Techno company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs 42,000 and establishment charges are Rs 12,000. The annual output of the company is Rs 70,000. The annual output and manufacturing costs are directly proportional to the number of machines. The shareholders get 12.5 profit, which is directly proportional to the annual output of the company. If 7.14 machines remain closed throughout the year, then the percentage decrease in the amount of profit of the shareholders would be:
Options:
A)12%
B)12.5%
C)13.5%
D)13%
E)14%
Rationale: Explanation :
The original profit is:-
=>70,000−42,000−12,000=16,000.
If 7.14% of 14 i.e. one of the machines closed throughout the year, then the change in profit will be :-
=>(13/14)×[70,000−42,000].
=>14,000.
Thus, decrease in the profit % is:-
=>(2000/16000) × 100.
=>12.5%.
Answer : B
Answer: B
Question: Consider two statements
Statement 1 => If C is an integer and C=2p+1 where p is not an integer.
Statement 2 => If D is an integer and D=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of C and D respectively
Options:
A)1) Odd,Even
B)2) Odd,Odd
C)3) Even,Odd
D)4) Even,Even
E)5) Cannot be determined
Rationale: answer will be E
C = integer
C = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even C would odd
if n odd C would be even
ANSWER IS E
Answer: E
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is two times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The distance traveled by Ferry P is 18 km.
Then the distance traveled by Ferry Q is 36 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 36/9 = 4 hours, which is 1 hour more than Ferry P. The answer is A.
Answer: A
Question: Two persons , Ram & Lakshman , who are at a distance of 100 km from each other, move towards each other from two places P and Q at speeds of 20 kmph and 25 kmph respectively. Lakshman reaches P, returns immediately and meets Ram at R, who started on the return journey to P immediately after reaching Q. What is the distance between Q and R?
Options:
A)33 1/3 km
B)25 km
C)30km
D)27 1/3 km
E)None of these
Rationale: Ram takes 100/20 = 5 hours to cover the distance from P to Q. By that time Lakshman covers
covers 5 *25 = 125 km
Lakshman covers 25 km more than the distance PQ . Now the distance between them = 75 km
Time taken by them to meet = Distance/ Relative speed = 75/(20+25) = 75/45 = 5/3 hrs.
Distance between Q and R is nothing but the distance covered by Ram in 5/3 hours = 20 *5/3 = 100/3 km or 33 1/3 km
Answer: A
Answer: A
Question: Mark is playing poker at a casino. Mark starts playing with 130 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?
Options:
A)$1,960
B)$1,740
C)$1,820
D)$3,080
E)$2,640
Rationale: Total chips 130
20% of $100 chips = 26 chips * $100 = $2,600
80% of $20 chips = 104 chips * $20 = $2,080
If x is the number of chips bet and y is the amount of chips remaining:
x + y = 130
y = 130 - x ~ (1)
[First round bet] + [Second round bet] = $2,600 + $2,080
[0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $4,680
10x + 18x + 30y + 14y = 4680
28x + 44y = 4680 ~ (2)
Substitute (1) into (2) to solve for x:
28x + 44(130 - x) = 4680
28x + 5720 - 44x = 4680
16x = 1040
x = 65
Substituting x:
[First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(65)($100)+0.9(65)($20) = $650 + $1,170 = $1,820
Answer is C
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)29
B)27
C)36
D)88
E)21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
Answer: C
Question: Six water bottle gather at the place. Three teams of 3 bottle each will be packed. How many ways are there to create these 3 teams?
Options:
A)27
B)45
C)90
D)175
E)280
Rationale: Arrange the 6 water bottle in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (B)
You get 6!/(2! * 2! * 2!) * 2!
Answer : B
Answer: B
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability E that the number of men is equal to that of women?
Options:
A)E=18/35
B)16/35
C)14/35
D)13/35
E)12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: A
Question: A certain fraction of a 15% salt solution by weight was replaced by a 25% salt solution by weight. The resulting solution has 21 % salt by weight. What fraction of the original solution was replaced?
Options:
A)1/2
B)3/5
C)2/3
D)7/10
E)3/4
Rationale: 15% salt solution was mixed with 25% salt solution to give 21% salt solution. So we can find the ratio of the weights in which the two were mixed.
w1/w2 = (25 - 21)/(21 - 15) = 4/6 = 2/3
So for every 2 parts of 15% solution, we have 3 parts of 25% solution. So 3/5th of the original solution was replaced.
Answer (B)
Answer: B
Question: In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
Options:
A)3
B)7
C)8
D)6
E)0
Rationale: A : B = 100 : 90.
A : C = 100 : 87.
\inline \fn_jvn {\color{Black}\therefore \frac{B}{C}=\left ( \frac{B}{A} \times \frac{A}{C}\right )=\left ( \frac{90}{100}\times \frac{100}{87} \right )=\frac{30}{29}}
When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs \inline \fn_jvn {\color{Black}\left ( \frac{29}{30} \times 180\right )m}=174m
\inline \fn_jvn {\color{Blue}\therefore } B beats C by (180 - 174) m = 6 m.
Answer: D) 6m
Answer: D
Question: A 50 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)24.28
B)14.28
C)16.28
D)18.28
E)12.28
Rationale: 1: 2/5 = 5: 2
2/7 * 50 = 14.28
ANSWER:B
Answer: B
Question: An investor bought a 1-year $8,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$400
B)$440
C)$720
D)$800
E)$820
Rationale: 1.05*1.05*8000 = $8820
The answer is E.
Answer: E
Question: A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 10% longer than the smallest size, how long, in inches, is the shoe in size 15?
Options:
A)18.25
B)20.75
C)22.25
D)24.25
E)26.75
Rationale: Let x be the length of the size 8 shoe.
Then 0.1x = 9/4
x = 90/4 inches
The size 15 shoe has a length of 90/4 + 7/4 = 97/4 = 24.25 inches
The answer is D.
Answer: D
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%
D)200%
E)101%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: C
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 15
III. P is a multiple of 23
Options:
A)I only
B)II only
C)III only
D)None of the above
E)All of the above
Rationale: Answer = B) II only
Answer: B
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 50.
Options:
A)3
B)4
C)12
D)32
E)35
Rationale: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by50, remainder will be -4 i.e. n will be 4 less than a multiple of 50. So you must add 12 to n to make it a multiple of 50
C
Answer: C
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 7 students?
Options:
A)14 years
B)17 years
C)19 years
D)38 years
E)None
Rationale: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 7
= 38 years.
Answer D
Answer: D
Question: How many quarters are equal to 6 dollars?
Options:
A)1
B)8
C)12
D)9
E)24
Rationale: 6 * 4 = 24 quarters
Answer : E
Answer: E
Question: The ratio of investments of A, B and C is 10:12:14. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.
Options:
A)2:3:6
B)4:6:8
C)3:2:4
D)2:4:3
E)2:5:3
Rationale: The ratio of investments of A, B and C is 10:12:14 or 5:6:7. [divided by 2]
The ratio of shares of A, B and C is 5:9:14.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (14/7) = 1:3/2:2 = 2:3:4 or 4:6:8
ANSWER:B
Answer: B
Question: The average of runs of a cricket player of 10 innings was 36. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options:
A)76
B)80
C)85
D)87
E)89
Rationale: Explanation:
Average = total runs / no.of innings = 36
So, total = Average x no.of innings = 36 x 10 = 360.
Now increase in avg = 4runs. So, new avg = 36+4 = 40runs
Total runs = new avg x new no. of innings = 40 x 11 = 440
Runs made in the 11th inning = 440 - 360 =80 Answer: B
Answer: B
Question: If |x - 25| = 50 what is the sum of all the values of x.
Options:
A)0
B)-100
C)-50
D)50
E)100
Rationale: There will be two cases
x-25 = 50 and x-25 = -50
Solve for x => x=50+25=> x=75 or x= -50+25=> x=-25
The sum of both values will be 75 + -25 =50
Answer is D
Answer: D
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
Options:
A)7 : 8
B)7 : 2
C)7 : 1
D)7 : 6
E)7 : 3
Rationale: Explanation:
Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100 = y(7)(n)/100
=> x/y = 7/6
x : y = 7 : 6
Answer: D
Answer: D
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 3 feet, 7 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
Options:
A)$880
B)$1050
C)$1280
D)$1460
E)$1640
Rationale: The total surface area is 2(2*3 + 3*7 + 2*7) = 82 square feet
The total cost is 82*$20 = $1640
The answer is E.
Answer: E
Question: Mike needs 30% to pass. If he scored 212 marks and falls short by 28 marks, what was the maximum marks he could have got?
Options:
A)343
B)677
C)800
D)867
E)932
Rationale: If Mike had scored 28 marks more, he could have scored 30%
Therefore, Mike required 212 + 28 = 240 marks
Let the maximum marks be m.
Then 30 % of m = 240
(30/100) × m = 240
m = (240 × 100)/30
m = 24000/30
m = 800
Answer:C
Answer: C
Question: A Museum decorated with bunch of lights and those lights glow for every 13 seconds. How many times did it glow between 1:57:58 and 3:20:47??
Options:
A)380
B)381
C)382
D)383
E)384
Rationale: find out difference between both times that is 1:22:49 total no of seconds that is 4969 then divided by 13 so the ans is
382
ANSWER:C
Answer: C
Question: The total surface area of a cuboid length 12 m, breadth 10 m and height 8 m.
Options:
A)576
B)566
C)596
D)556
E)586
Rationale: Total surface area of cuboid
= 2 (lb+bh+lh)
= 2 (120 + 80+ 96)
= 2 (296) => 596 m(power2)
Answer is C.
Answer: C
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 51 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
Options:
A)31
B)33
C)35
D)37
E)39
Rationale: Total weight of the 4 dogs = (25+31+51+41) = 148
Avg = 148/4 = 37
Total weight of 5 dogs = 148+y or 4(37)+y
Average of 5 dogs as per Question = 37
Equation:
4(37) + y = 5 (37), or y = 37.
Choose D
Answer: D
Question: If 20% of a class averages 80% on a test, 50% of the class averages 60% on the test, and the remainder of the class averages 40% on the test, what is the overall class average?
Options:
A)80%
B)74%
C)58%
D)56%
E)50%
Rationale: 2 students scored 80%
5 students scored 60%
3 students scored 40%
(2)(80) + 5(60) + 3(40) =
160 + 300 + 120 =
580
580/10 students = 58 --> 58% average
ANSWER:C
Answer: C
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
Options:
A)228
B)640
C)267
D)187
E)171
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer: B
Answer: B
Question: ohn invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
Options:
A)3/5
B)2/3
C)7/10
D)3/4
E)4/5
Rationale: X(1+10/100) + Y(1-15/100) = X+Y
this gives 2X = 3Y
or X/Y = 3/2
So, fraction invested in X = 3/5
ANSWER:A
Answer: A
Question: If after 600 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
Options:
A)180 grams
B)220 grams
C)250 grams
D)350 grams
E)1200 grams
Rationale: I too think 1200 grams should be the answer.
My reasoning is
The h20 content in 200 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be set up
600*1 + 0.76X = 0.84 (X+600)
0.08X = 96
8X = 9600
X = 1200 (ANS E)
Answer: E