divelab/Sys2Bench huggingface dataset:
Question: A straight line in the xy- plane has y-intercept of 12 and a slope of 4/7. Given the x-coordinate of the point is 49, find it's y-coordinate.
Options:
A)27
B)16
C)29.7
D)28
E)18
Rationale: Eq of line = Y = MX +C
M=4/7
C=12
X=49
Substitute the givens:
Y=(4/7 * 49) + 12,
Y=16 + 12 = 28
Correct option is D
Answer: D
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Options:
A)20
B)17
C)21
D)19
E)30
Rationale: Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years.
Required average = 57/3 = 19 years.
ANSWER D
Answer: D
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 15%?
Options:
A)32.8%
B)37.6%
C)38.5%
D)17.5%
E)37.2%
Rationale: Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 85
Gain % = 21/64 * 100 = 32.8%.
Answer: A
Answer: A
Question: A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train?
Options:
A)240
B)277
C)276
D)270
E)281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 280)/26 = 20
x = 240 m.
Answer: A
Answer: A
Question: Find the number of square tiles to cover the floor of a room measuring 4.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Options:
A)422
B)576
C)429
D)428
E)413
Rationale: Floor area to be covered by tiles = 4 * 9 = 36
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 36/0.0625 = 576
Answer : B
Answer: B
Question: The railway track length, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)300 m
B)245 m
C)350 m
D)250 m
E)260 m
Rationale: speed = (45*5/18) => 25/2 m/sec
time = 30 sec
length of bridge => x
=>130+x/30 = 25/2
2(130+x)=750
x=245 m
ANSWER B
Answer: B
Question: An athlete runs 200 metres race in 20 seconds. What is his speed?
Options:
A)23
B)38
C)37
D)36
E)28
Rationale: Speed=Distance/Time = 200/20 = 10 m/s = 10 * 18/5 = 36 km/hr
Answer :D
Answer: D
Question: A family pays $900 per year for an insurance plan that pays 80 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.
Options:
A)$1,000
B)$1,200
C)$1,300
D)$1,800
E)$2,200
Rationale: Upfront payment for insurance plan = 900$
Family needs to pay 20 % of first 1000 $ in expense = 200$
Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 900 + 200 = 1100 $
Total amount paid by insurance plan for first 1000 $ = 900 $
Total amount paid by family will equal amount paid by plan when medical expense = 1300 $
(Since insurance plan will pay 100% of amount that exceeds 1100$ )
Answer C
Answer: C
Question: A number is doubled and 15 is added. If the resultant is multiplied by 5, it becomes 125. What is that number?
Options:
A)5
B)10
C)8
D)None of these
E)Cannot be determined
Rationale: Solution
Let the number be x.
Then, 5(2x + 15) ‹=› 125
‹=› 2x+15 = 25
‹=› 2x= 10
x= 5.
Answer D
Answer: D
Question: It was calculated that 100 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 50 men to another project. How much longer will it take to complete the work?
Options:
A)45 days.
B)40 days.
C)38 days.
D)35 days.
E)30 days.
Rationale: One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 100)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 100)
The total no. of days required to complete the work = (100 * 20) / 50 = 40
Answer:B
Answer: B
Question: A can run 2 km distance in 2 min., while B can run this distance in 2 min 40 sec. By how much distance can A beat B?
Options:
A)150 m
B)100 m
C)500 m
D)180 m
E)190 m
Rationale: A takes time 2 minutes=120sec
B takes time 2.40 minutes=160sec
diffrence= 160-120=40sec
now we are to find distance covered in 40 sec by B
160sec=2000m
1sec=25/2 m
40sec=40 x 25/2=500m
ANSWER:C
Answer: C
Question: There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls?
Options:
A)12
B)32
C)5
D)28
E)35
Rationale: Explanation :
n(AuB)= n(A) + n(B) - n(AnB)....(1)
n(A) = number of kids playing with white color balls = 26
n(AUB) = total number of kids in the play school = 35
n(AnB) = number of kids playing with both white and yellow color balls = 19
we have to find,
n(B) = number of kids playing with yellow color balls
From (1), 35 = 26 + n(B) - 19
n(B) = 35 + 19 - 26 = 28
Hence, Answer is 28 kids play with yellow color
balls.
Answer : D
Answer: D
Question: If f(x)= 5x^3- 2x+4 and g(y)= 6y-4, then g(f(x)) =
Options:
A)11x^2+4x+4
B)30x^3-12x+20
C)8x^3-8x+32
D)30x^3+4x+4
E)30x^3-12x+44
Rationale: g(f(x)) = 6(f(x)) -4 = 6(5x^3- 2x+4) - 4 = 30x^3-12x+20 =>B
Answer: B
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table?
Options:
A)6925
B)6887
C)6728
D)6725
E)2871
Rationale: :
CP = SP * (100/(100 + profit%))
= 8587(100/124) = Rs. 6925.
Answer: A
Answer: A
Question: Veena ranks 65rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?
Options:
A)96
B)108
C)110
D)90
E)93
Rationale: total student=182
failed=22
paasd student=182-22=160
from bottom her rank is=160-65+1=96
ANSWER:A
Answer: A
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
A)109
B)108
C)109
D)106
E)101
Rationale: S = 180/6 * 18/5
= 108 kmph
AnswerB
Answer: B
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)794 m
B)704 m
C)454 m
D)186 m
E)176 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4
= 70400 cm
= 704 m
Answer: B
Answer: B
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.13 of money?
Options:
A)1300
B)1992
C)9921
D)2798
E)2789
Rationale: P = 13(100/10)2
=> P = 1300
Answer: A
Answer: A
Question: If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is:
Options:
A)22
B)77
C)50
D)77
E)23
Rationale: Let C.P. of each pen be Re. 1.
Then, C.P. of 8 pens = Rs. 8; S.P. of 8 pens = Rs. 12.
Gain % = 4/8 * 100 = 50%
Answer:C
Answer: C
Question: The third proportional to 2 and 6 is?
Options:
A)18
B)17
C)14
D)15
E)13
Rationale: (6*6)/2 = 18
Answer:A
Answer: A
Question: Ratio of the ages of Mahesh and Nilesh is 5:x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
Options:
A)14.9
B)14.5
C)14.3
D)14.2
E)14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be M, N and R respectively.
M/N = 5/x --- (1)
M = R - 18 --- (2)
R + 9 = 47 --- (3)
M - N = R --- (4)
(3) => R = 47 - 9 = 38 years
(2) => M = 38 - 18 = 20 years
(1) => 20/N = 5/x => N = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer: E
Answer: E
Question: What is the place value of 3 in the numeral 2734?
Options:
A)30
B)50
C)70
D)80
E)84
Rationale: Option 'A'
3 * 10 =30
Answer: A
Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
Options:
A)3/4
B)1/4
C)3/8
D)7/8
E)None of these
Rationale: Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) =	n(E)	/ n(S) =7/8.
ANSWER IS D
Answer: D
Question: A company produces 65000 bottles of water everyday. If a case can hold 13 bottles of water .How many cases are required by the company to hold its one day production
Options:
A)2000
B)4500
C)5000
D)8000
E)9000
Rationale: Number of bottles that can be held in a case = 13
Number of cases required to hold 65000 bottles = 65000/13=5000 cases.
So the answer is C =5000
Answer: C
Question: In jar X there are 3 silver coins and 5 gold coins, in jar Y there are 4 silver coins and 2 gold coins. A jar is randomly picked, what is the probability of picking up a gold coin out of jar Y?
Options:
A)2/5.
B)3/5.
C)1/5.
D)3/4.
E)1/6.
Rationale: Probability of picking up one jar out of two= 1/2
probability of picking 1 gold coin from jar Y= 2/6= 1/3
Hence the desired probability= 1/2*1/3= 1/6
E is the answer
Answer: E
Question: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 15 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
Options:
A)15%
B)20%
C)40%
D)13%
E)150%
Rationale: Let rate in R = 100x
then P = 75x
G = 100y
P = 85y
Thus
75 x=85y
or x = 1.13 y
Ans R = 113y
so increase = 13%
Answer: D
Answer: D
Question: If the perimeter of square region D and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of D
Options:
A)25:16
B)24:25
C)5:6
D)4:5
E)4:9
Rationale: We know Perimeter of a square (Pd) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)
Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)
Therefore,
Pd = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12
Area of the rectangle = 8*12 = 96 sq. units
Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B
Answer: B
Question: How many natural numbers are there between 43 and 200 which are exactly divisible by 6?
Options:
A)26
B)25
C)24
D)22
E)23
Rationale: 43/6 = 7, remainder = 1. Hence 5 more should be added to 43 to get the minimum
number divisible by 6 between 43 and 200.
=> Minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48
200/6 = 33, remainder = 2. Hence 2 should be decreased from 200 to get the maximum
number divisible by 6 between 43 and 200.
=> Maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198
Hence, natural numbers numbers divisible by 6 between 43 and 200 are 48, 54, 60,...198
This is Arithmetic Progression with a = 48, d = 6, l=198
Number of terms =(l−a)/d+1=(198−48)/6+1=150/6+1=25+1=26
Answer is A
Answer: A
Question: If x and y are positive integers and 25x=10y what is the least possible value of xy?
Options:
A) 14
B) 25
C) 63
D) 84
E) 252
Rationale: 25x=10y
=> x/y = 2/5
=> 5x=2y
5(3)=2(3) => x*y=9 But it is not given
5(5)=2(5) => x*y=25
B
Answer: B
Question: A person's present age is two-fifth of the age of his mother. After 10 years, he will be one - half of the age of his mother. How old is the mother at present ?
Options:
A)A)25
B)B)40
C)C)32
D)D)50
E)E)28
Rationale: Let the mother's present age be x years
Then the person's present age = 2x/5
(2x/5)+10 = 1/2(x+10)
2(2x+50) = 5 (x+10)
x = 50
Answer is D
Answer: D
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
Options:
A)Tuesday
B)Friday
C)Monday
D)Sunday
E)MondSD
Rationale: On 31st December, 2005 it was Saturday.
Number of odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday
Answer: B
Answer: B
Question: In covering a distance of 30 km, A takes 2 hours more than B. If Abhay doubles his speed, then he would take 1 hour less than B. A's speed is:
Options:
A)5 kmph
B)6 kmph
C)6.25 kmph
D)7.5 kmph
E)8.5 kmph
Rationale: Let A's speed be x km/hr.
Then, 30/x -30/2x = 3
--> 6x = 30
--> x = 5 km/hr.
Answer : A.
Answer: A
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 49 as quotient. What is the correct quotient ?
Options:
A)0
B)12
C)13
D)20
E)28
Rationale: 12*49=588
588%21=28
ANSWER:E
Answer: E
Question: Three solid metallic balls of radii, 3 cm, 4cm and 5 cm are
melted and moulded into a single solid ball. The radius of the
new ball is
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Total volume of three metallic balls(spheres)= (4/3)*Pi*(3^3+4^3+5^3)
=(4/3)*Pi*216= Volume of new ball with radius 'r'
so (4/3)*Pi*r^3=(4/3)*Pi*216
r^3=216 , r=6
ANSWER:B
Answer: B
Question: The average of first six prime numbers which are between 30 and 70 is
Options:
A)35.4
B)42
C)45.7
D)57
E)67
Rationale: Explanation :
first six prime numbers which are between 30 and 70 = 31, 37, 41, 43, 47, 53
average = (31 + 37 +41 + 43 + 47 + 53)/6
= 42
Answer : B
Answer: B
Question: JAK, KBL, LCM, MDN, _____
Options:
A)NEO
B)SAS
C)DFG
D)JKL
E)JHN
Rationale: This is an alternating series in alphabetical order. The middle letters follow the order ABCDE. The first and third letters are alphabetical beginning with J. The third letter is repeated as a first letter in each subsequent three-letter segment.
ANSWER:A
Answer: A
Question: If G is to be chosen at random from the set {5,8,7,1} and K is to be chosen at random from the set {14,8,3}, what is the probability that GK will be even?
Options:
A)1
B)5
C)8
D)4
E)3
Rationale: Method-1
GK will be even when
1) G is even and K is odd, Probability of G even is (1/4) and Probability of K odd is (1/3), so Probability of Case(1) = (1/4)*(1/3) = (1/12)
2) G is Odd and K is Even, Probability of G Odd is (3/4) and Probability of K Even is (2/3), so Probability of Case(2) = (3/4)*(2/3) = (6/12)
3) G is even and K is Even, Probability of G even is (1/4) and Probability of K Even is (2/3), so Probability of Case(1) = (1/4)*(2/3) = (2/12)
Total Favorable Probability = (1/12)+(6/12)+(2/12) = (12/12) = 1
Answer: option A
Answer: A
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in?
Options:
A)7
B)12
C)5
D)14
E)13/3
Rationale: P --> Pump, L ---> Leak
Pipe----------P---------L------------(P-L)--
Time---------2---------x-------------7/3
*
Rate-------7/3---------x-------------2
Work------14/3-------14/3---------14/3
Time required to empty the tank if leakage present = (14/3)/((7/3) - 2)
= (14/3)/(1/3)
= 14
Ans -D
Answer: D
Question: Find the simple interest on Rs. 68,000 at 16 2/3% per year for 9 months.
Options:
A)7500
B)6500
C)8500
D)9500
E)None of them
Rationale: P = Rs.68000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(68,000*(50/3)*(3/4)*(1/100))= Rs.8500
Answer is C.
Answer: C
Question: The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)12.5N
E)20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 + 1.5x$500 = $500 + $750 =$1250
This is 12.5 times the 1992 number, so the correct answer is 12.5N.
D
Answer: D
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 9 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball (in centimeters)?
Options:
A)50/4
B)70/6
C)80/7
D)90/8
E)100/9
Rationale: A straight line will join the two centers and the point of contact, thus making similar triangles.
1/9 = (r-10)/r
r = 9r - 90
r = 90/8
The answer is D.
Answer: D
Question: Peeta asks Katniss, 'It is 6 pm as per my watch right now.Do you know what will be the time 23, 999, 999 hours later?'
Katniss knows the answer. Do you ?
Options:
A)3pm
B)6pm
C)4am
D)7am
E)8pm
Rationale: A
3pm
The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: A
Question: If a tap could fill entire tank in 18 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage
Options:
A)12hrs
B)24hrs
C)36hrs
D)48hrs
E)52hrs
Rationale: time take to fill[withleakage] =18hrs so workdone in 1hr=1/18
time tkae to fill[without leakage]=12hrs so workdone in 1hr=1/12
if u subtract both u'll get time taken by leakage to empty...
1/18-1/12=1/36 so 36hrs
ANSWER:C
Answer: C
Question: In a simultaneous throw of two coins, the probability of getting atleast one headis:
Options:
A)1/4
B)2/5
C)7/9
D)4/5
E)3/4
Rationale: n(S)=4
E = even getting at least one head
N(E)=3
P(E)=3/4
Ans: E
Answer: E
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 20 per cent larger than the original. By what percentage has the area of the logo increased?
Options:
A)50
B)80
C)100
D)44
E)250
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 4.8 , so radius is 2.4
New area = 5.76π
Increase in area is 1.76π
% increase in area = 1.76/4*100
So, % increase is 44%
Answer will be (D)
Answer: D
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team H, but each box of Team A’s has 60% fewer booklets than each box of Team H’s. Which of the following could be the total number of booklets distributed by the two groups?
Options:
A)2,000
B)3,200
C)4,100
D)4,800
E)4,900
Rationale: Let x be the no of booklets in each box that team H distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team H. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team H=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Answer: C
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $250, what were her original savings?
Options:
A)$500
B)$600
C)$700
D)$800
E)$1000
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $250. So 1 / 4 of her savings is $250. So her original savings are 4 times $250 = $1000
correct answer E
Answer: E
Question: To produce an annual income of Rs. 1200 from a 15 % stock at 90,the amount of stock needed is :
Options:
A)s. 10,000
B)s. 10,800
C)s. 14,400
D)s. 16,000
E)s. 46,000
Rationale: Solution
For an income of Rs. 15, stock needed = Rs. 100.
For an income of Rs. 1500, stock needed = Rs. 10/12x15000=10,000
Answer A
Answer: A
Question: The boys in the class have an average height of 140 cm and the girls in the class have an average height of 150 cm. If the overall class average height is 144 cm, what is the ratio of boys to girls in the class?
Options:
A)1/2
B)3/2
C)3/4
D)4/3
E)4/5
Rationale: (150G + 140B) / (G+B) = 144
150G + 140B = 144(G+B)
6G=4B
B/G = 3/2
The answer is B.
Answer: B
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Options:
A)3:5
B)4:5
C)5:5
D)4:3
E)2:1
Rationale: third no is x
first no - 120% of x = 6x/5
second no = 150x/100= 3x/2
ration of first nos = 6x/5:3x/2 = 12x:15x
= 4:5
ANSWER B
Answer: B
Question: One-fourth of the students at a nursery school are 5 years old or older. If 15 students have not yet reached their fourth birthday, and a total of 25 students are not between 4 years old and 5 years old, how many children are in the nursery school?
Options:
A)20
B)25
C)30
D)35
E)40
Rationale: x/4 students are > 5 yrs
15 students are < 4 yrs
x/4+15 = 25
x/4 = 10
x = 40
Answer: E
Answer: E
Question: Find the HCF of
2/3,4/6,8/27
Options:
A)2/27
B)8/3
C)2/3
D)2/27
E)1/7
Rationale: Explanation:
Whenever we have to solve this sort of question, remember the formula.
HCF =
HCF of Numerators/LCM of Denominators
So answers will be option 1
Option A
Answer: A
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
A)2 days
B)5 days
C)8 days
D)7 days
E)9 days
Rationale: C
8 days
A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: C
Question: what are the total number of divisors of 600?
Options:
A)24
B)40
C)16
D)20
E)30
Rationale: The prime factorization of 600
600 = (2^3)(3^1)(5^2)
The number of divisors (including 1 and the number itself) is the product of one plus the exponents.
(3+1)(1+1)(2+1) = 24
ANSWER:A
Answer: A
Question: In Solution P, the proportion of water to alcohol is 3:1. In Solution Q, the proportion of water to alcohol is 2:1. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?
Options:
A)25%
B)29%
C)33%
D)37%
E)41%
Rationale: Let V be the total volume of the new solution.
The amount of alcohol added from Solution P is (1/4)*V/2=(1/8)*V
The amount of alcohol added from Solution Q is (1/3)*V/2=(1/6)*V
The total amount of alcohol in the new solution is (1/8+1/6)*V=(7/24)*V
The alcohol concentration is 7/24=29% (approximately)
The answer is B.
Answer: B
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 360 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)8/3
B)3/8
C)8/5
D)5/8
E)20/9
Rationale: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 600/3 = 200 km/hour
Distance traveled by Freddy = 360 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 360/4 = 90 km/hour
Ratio of average speed of Eddy to Freddy = 200/90 = 20/9
Answer E
Answer: E
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was:
Options:
A)12 years.
B)14 years.
C)17 years.
D)20 years.
E)19 years.
Rationale: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24
Son's age 4 years back (24- 4) = 20 years.
ANSWER :D
Answer: D
Question: The average age of 36 students in a group is 18 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Options:
A)35 years
B)55 years
C)51 years
D)54 years
E)None of these
Rationale: Explanation:
Age of the teacher = (37 * 19 - 36 * 18) years = 55 years. Answer: B
Answer: B
Question: For which of the following values of n is (100+n)/n NOT an integer?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: This problem is easiest solved by plugging in each answer choice.
A) (100 + 1)/1 = 101/1 = 101
Answer choice A yields an integer.
B) (100 + 2)/2 = 102/2 = 51
Answer choice B yields an integer.
C) (100 + 3)/3 = 103/3 = 34, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choice C is correct, we should still test the other answer choices.
D) (100 + 4)/4 = 104/4 = 26
Answer choice D yields an integer.
E) (100 + 5)/5 = 105/5 = 21
Answer choice E yields an integer.
Thus, the correct answer is answer choice C.
Answer: C