divelab/Sys2Bench huggingface dataset:
Question: A certain bacteria colony doubles in size every day for 25 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
Options:
A)6.33
B)7.5
C)10
D)15
E)24
Rationale: If there is one bacteria colony, then it will reach the limit of its habitat in 25 days.
If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 24 times.
Answer: E.
Similar questions to practice:
Hope it helps.
Answer: E
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time, how many books of the special collection were loaned out during that month?
Options:
A)20
B)30
C)35
D)40
E)60
Rationale: I didn't understand How did we get 100?
Total = 75 books.
65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned.
Now, there are 57 books, thus 76-68=7 books are NOT returned.
{loaned out}*0.30=18 --> {loaned out}=60.
Answer:E.
Answer: E
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29,38, 48, ___?
Options:
A)35
B)36
C)37
D)59
E)89
Rationale: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 48 + 11 = 59.
correct answer D)59
Answer: D
Question: The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is
Options:
A)27
B)29
C)11
D)data inadequate
E)28
Rationale: Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given.
So, the data provided is inadequate
Answer: D
Answer: D
Question: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.
What is the expected amount of time it will take for the rat to finish the maze?
Options:
A)5min
B)6min
C)7min
D)8min
E)9min
Rationale: Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes.
Answer: E
Question: 3 years ago, Paula was 3 times as old as Karl. In 9 years, Paula will be twice as old as Karl. What is the sum of their ages now?
Options:
A)42
B)46
C)50
D)54
E)58
Rationale: P-3 = 3(K-3) and so P = 3K-6
P+9 = 2(K+9)
(3K-6)+9 = 2K+18
K = 15
P = 39
P+K = 54
The answer is D.
Answer: D
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is?
Options:
A)17
B)56
C)25
D)28
E)12
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Answer: C
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)290
B)350
C)287
D)272
E)112
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B
Answer: B
Question: A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 6km/hr. Total time of travel is 9 hours. What is the maximum distance he
can cover?
Options:
A)20km
B)40km
C)60km
D)80km
E)90km
Rationale: t=d/s, so
9=x/2*1/5+x/2*1/6(because half distance with 5 km/ph, and remaining half with 6km/hr)
9=x(18/120)
x=60km
ANSWER:C
Answer: C
Question: Students of three different classes appeared in common examination. Pass average of 10 students of first class was 45%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
Options:
A)74%
B)75%
C)67%
D)72%
E)None
Rationale: Solution:
Sum of pass students of first, second and third class,
= (45% of 10) + (60% of 15)+ (80% of 25)
= 4.5+9+20 = 33.5
Total students appeared,
= 10+15+25 = 50
Pass average,
= 33.5*100/50 = 67%.
Answer: Option C
Answer: C
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Options:
A)100
B)120
C)140
D)150
E)170
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: Option D
Answer: D
Question: A train 1020 m long running at 102 kmph crosses a platform in 50 sec. What is the length of the platform?
Options:
A)287
B)298
C)396
D)726
E)267
Rationale: D = 102 * 5/18 = 50
= 1416 â€“ 1020
= 396
Answer: C
Answer: C
Question: How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?
Options:
A)7
B)8
C)9
D)10
E)None of the above
Rationale: Sol.
112 pairs of shoes = 224 shoes.
= 224 ÷ 28
= 8
Answer : B
Answer: B
Question: Among 300 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
Options:
A)20
B)60
C)80
D)86
E)90
Rationale: 56%+44%-30%=70% who like either Strawberry, Apple, or both.
That means 100%-70% = 30% do not like either Apple of Strawberry jam.
30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
E
Answer: E
Question: A person crosses a 420 m long street in 5 minutes. What is his speed in km per hour?
Options:
A)5.2 km/hr.
B)8.2 km/hr.
C)7.2 km/hr.
D)3.2 km/hr.
E)5.04 km/hr.
Rationale: E
5.04 km/hr.
Speed=(420/5 * 60) m/sec
= 1.4 m/sec.
Converting m/sec to km/hr
=(2*18/5) km/hr
= 5.04 km/hr.
Answer is E
Answer: E
Question: Last year, Company X made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his Five other partners. In terms of q, how much did each of the other partners receive?
Options:
A)q/12
B)q/5
C)q/10
D)q/7
E)q/8
Rationale: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 5
Profit to each partner = (q/2)/5 = q/10
Answer: C
Answer: C
Question: How many ounces of a 60% salt solution must be added to 30 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
Options:
A)16.67
B)30
C)50
D)60.33
E)70
Rationale: let x=ounces of 60% salt solution to be added
.2*30+.6x=.4(30+x)
x=30
Answer B
Answer: B
Question: A pair of articles was bought for $50 at a discount of 10%. What must be the marked price of each of the article?
Options:
A)$25
B)$22.50
C)$29.65
D)$35.95
E)$45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
90% of x = 25
x = 25*.9 =$22.50
Answer is B
Answer: B
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
Options:
A)140
B)142
C)146
D)158
E)160
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: D
Question: Jerry went to a shop and bought things worth Rs. 30, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)21.3
D)21.5
E)24.7
Rationale: Total cost of the items he purchased = Rs.30
Given that out of this Rs.30, 30 % is given as tax
=> Total tax incurred = 30 % = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (30−30/100−x)6/100 = 30/100
⇒ 6(30 −0.3 −x) = 30
⇒ (30 − 0.3 − x) = 5
⇒ x = 30 − 0.3 − 5 = 24.7
E)
Answer: E
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Options:
A)7 cm
B)5 cm
C)2 cm
D)1 cm
E)9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h
= (4/3)π (12)3
=> h = 9 cm
Answer: E
Answer: E
Question: The average of five numbers id 27. If one number is excluded, the average becomes 23. What is the excluded number?
Options:
A)43
B)40
C)32.5
D)35
E)37
Rationale: Explanation:
Sum of 5 numbers = 5 × 27
Sum of 4 numbers after excluding one number = 4 × 23
Excluded number
= 5 × 27 - 4 × 23
= 135 - 92 = 43
Answer: Option A
Answer: A
Question: X can do a piece of work in 4 hours; Y and Z together can do it in 3 hours, while X and Z together can do it in 2 hours. How long will Y alone take to do it?
Options:
A)5hours
B)10hours
C)12hours
D)24hours
E)15hours
Rationale: X 1 hour's work =	1/4	;
Y+ Z's hour's work =1/3
X + Y + Z's 1 hour's work =1/4	+1/3	=7/12
Y's 1 hour's work =	(7/12-1/2	)=	1/12	.
Y alone will take 12 hours to do the work.
C
Answer: C
Question: The curved surface of a right circular cone of height 15cm and base diameter 16 cm is
Options:
A)40 ∏cm³
B)60 ∏cm³
C)136 ∏cm³
D)138 ∏cm³
E)None
Rationale: Sol.
h = 14 cm, r = 7 cm. So, l = √r² + h² = √8² + (15)² = 17 cm.
∴ Curved surface area = ∏rl = (∏ * 8 * 17) cm² = 136∏ cm²
Answer C
Answer: C
Question: A boy runs 200 metres in 36 seconds. What is his speed ?
Options:
A)20 km/hr
B)24 km/hr
C)30 km/hr
D)32 km/hr
E)34 km/hr
Rationale: 200/36 * 18/5 = 20 km/hr
ANSWER:A
Answer: A
Question: 60% of a number is added to 120, the result is the same number. Find the number?
Options:
A)300
B)288
C)270
D)129
E)281
Rationale: (60/100) * X + 120 = X
2X = 600
X = 300
Answer:A
Answer: A
Question: If x= (10^50) - 57, what is the sum of all the digits of x?
Options:
A)390
B)418
C)420
D)439
E)449
Rationale: 10^2 100-57=43 (result of two digits number)
10^3 1000-57=943 (result of three digits number)
10^4 10000-57=9943 (result of four digits number)
and so on... until 10^50
The result of the subtraction becomes a 50 digits number composed by 48 pairs of 9 followed by a 4 and 5. Therefore 48*9=432 and 432+(4+5)=439
The correct answer is D.
Answer: D
Question: Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast?
Options:
A)1/5
B)2/7
C)3/8
D)7/20
E)1/2
Rationale: Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes.
Answer: C.
Answer: C
Question: If a, b, c are integers and ab>0, bc >0, ac<0, then which of the following must be true?
I.	a>0, b>0, c>0
II.	a=0, b=0, c=0
III.	a<0, b<0, c<0
Options:
A)I only
B)II only
C)III only
D)I, II and III
E)None of the above
Rationale: We could solve this easily using counter examples.
I is false. If a>0 and c>0, then ac>0. But since ac<0, it is false.
II is false. If a=0 or b=0 or c=0 then ab=bc=ac=0.
III is false. If a<0 and c<0, then ac>0. But since ac<0, it is false
So, the answer is E
Answer: E
Question: Four wolves, Wolverine, Man-hunter, Blue-wolf, and Jasmine, caught rabbits for their evening meal. If Man-hunter caught 3 more rabbits than Blue-wolf did, Jasmine caught 3 less than Wolverine did, and Wolverine caught 1 more than Man-hunter did, how many more fewer rabbits did Blue-wolf catch than Jasmine?
Options:
A)-3
B)-2
C)-5
D)-12
E)-1
Rationale: In this word problem, the first key is to turn the story into equations:
Man-hunter caught 3 more than Blue-wolf did: M = 3 + B
Jasmine caught 3 less than Wolverine did: J = W - 3
Wolverine caught 3 more than Man-hunter did: W = 1 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more rabbits did Blue-wolf catch than Jasmine did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.
Taking the first equation and solving for B, you have B = M - 3.
Taking the second equation and solving for J you have J = W - 3, and then with the third equation you can replace W with 1 + M so that both B and J are in terms of M: J = (1 + M) - 3.
So if B = M - 3 and J = M - 2, then:
B - J = (M - 3) - (M - 2)
B - J = M - 3 - M + 2 (remove the parentheses by distributing the multiplication)
B - J = -1, so the answer is E.
Answer: E
Question: Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C?
Options:
A)127
B)150
C)177
D)167
E)122
Rationale: A+B+C = 590
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 590 = Rs.150
Answer:B
Answer: B
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)128 kmph
B)108 kmph
C)181 kmph
D)188 kmph
E)111 kmph
Rationale: S = 180/6 * 18/5
= 108 kmph
Answer:B
Answer: B
Question: In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours, and the hot-water leak alone would fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?
I. 0 < t < h
II. c < t < h
III. (c/4) < t < (h/4)
Options:
A)a) I only
B)b) II only
C)c) III only
D)d) I and II
E)e) I and III
Rationale: I picked numbers for this problem
C = 2 hours
H = 3 hours
C<H
2 people working together formula is
1/C + 1/H = 1/t
1/2 + 1/3 = 1/t
t = 6/5 = 1.2
Substitute the values of C, H and t in the 3 choices given below
Only 1 are valid.Therefore A is the best answer
Answer: A
Question: If a sequence of 8 consecutive odd integers with increasing values has 7 as its 7th term, what is the sum of the terms of the sequence?
Options:
A)4
B)6
C)8
D)12
E)16
Rationale: Let x be the first term.
Then x + 12 = 7 and x = -5
The sum is: x + (x+2) +...+ (x+14) =
8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-5) +56 = 16
The answer is E.
Answer: E
Question: According to a survey conducted in two countries, China and India, 20% of the population are vegetarians. If the ratio of the population is 14:13, respectively, and the percentage of Chinese who are vegetarian is 5%, what percentage of Indians are vegetarians?
Options:
A)51%
B)54%
C)25%
D)36%
E)47%
Rationale: Let C and I be number Chinese and Indian, respectively, and v represent vegetarian.
C + I = total people.
C:I = 14:13
Cv/C = 5%
Iv/I = ?
[(14)(Cv/C) + (13)(Iv/I)]/(14 + 13) = 20%
[(14)(5%) + (13)(Iv/I)]/27 = 20%
Iv/I = 36%
Answer: D
Answer: D
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
Options:
A)Rs. 120
B)Rs. 160
C)Rs. 240
D)Rs. 300
E)None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 13660
=> 17x/12 = 13660
=> 13660 x 12/ 17 = Rs.960
Hence, B’s share = Rs. (960/4) = Rs. 240.
Answer C
Answer: C
Question: The area of a square is 6400 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 cm less than the side of the square?
Options:
A)5:24
B)5:19
C)5:13
D)5:22
E)5:18
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 6400
a = (6400)^1/2 = 80
l = 3a and b = a - 30
b : l = a - 30 : 2a = 50 : 240 = 5:24
Answer: A
Answer: A
Question: If z is the sum of x and y, then which one of the following must equal x – y ?
Options:
A)z+y
B)x-2y
C)x+y
D)z-2y
E)2z-y
Rationale: Given z= x+y if you subtracts both side with -2y
z-2y = x-y
Answer : D
Answer: D
Question: Pipe A can fill a tank in 3 hours, pipe B in 15 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled ?
Options:
A)2.5 hours
B)2 hours
C)3.5 hours
D)3 hours
E)None of these
Rationale: Explanation:
Part filled by A in 1 hour = 1/3
Part filled by B in 1 hour = 1/15
Part filled by C in 1 hour = 1/24
Part filled by (A+B+C) in 1 hour =
1/3+1/15+1/24=93/120
So all pipes will fill the tank in 1.3 hours.
Option E
Answer: E
Question: Find the value of X, Y by solving the below equations
X + Y = 5
X - Y = -3
Options:
A)4, 1
B)3, 2
C)1, 4
D)4, 6
E)5, 4
Rationale: X + Y = 5 ---(I)
X - Y = -3 -----(II) by adding (I) and (II)
------------
2X = 2 ==> X = 2/2 = 1
By Replacing the value of X in (I) we get 1 + Y = 5 ==>
Y = 5 -1 = 4.
So, X = 1, Y = 4
Answer C) 1, 4
Answer: C
Question: A pupil's marks were wrongly entered as 85 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
Options:
A)30
B)80
C)20
D)25
E)26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (85 - 45)
=> X/2 = 40
=> X = 80.
ANSWER:B
Answer: B
Question: A batch of widgets costs p + 15 dollars for a company to produce and each batch sells for p(10 – p) dollars. For which of the following values of p does the company make a profit?
Options:
A)10
B)9
C)8
D)6
E)7
Rationale: to make profit, selling price should be greater than cost price
p(10-p) - p-15 >0
=> p^2-9*p+15<0
hence p=6
D
Answer: D
Question: Two quarts containing 2⁄5 water and 4⁄5 formula are mixed with three quarts containing 3⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?
Options:
A)34%
B)36%
C)38%
D)40%
E)45%
Rationale: 2/5 of 2 quarts = 4/5 quarts of water
3/10of 3 quarts = 9/10 quarts of water
4/5 = 0.8
9/10 = 0.9
Total water = 0.8 + 0.9= 1.7
Total quarts = 5
1.7/5 = 34%
Answer : A
Answer: A
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
Options:
A)38 min
B)36 min
C)31 min
D)40 min
E)49 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: D
Question: How many positive integers less than 100 have a remainder of 3 when divided by 13?
Options:
A)6
B)7
C)8
D)9
E)3
Rationale: We have to include 3 also.As 13*0 + 3 =3
If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3.
Answer is E
Answer: E
Question: If k and s are positive integers such that (2^k)(4^s) = 16, then 2k + s =
Options:
A) 2
B) 3
C) 4
D) 5
E) 6
Rationale: lets get the eq into simplest orm..
(2^k)(4^s) = 16..
(2^k)(2^2s) = 2^4..
or k+2s=4..
since k and s are positive integers, only k as 2 and s as 1 satisfy the Equation..
so 2k+s=2*2+1=5..
D
Answer: D
Question: A train 250 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)15 sec
B)9 sec
C)12 sec
D)15 sec
E)18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 250 m at 50/3 m / sec = 250 *3/ 50 sec = 15 sec
Answer : A.
Answer: A
Question: Two whole numbers whose sum is 36 cannot be in the ratio
Options:
A)2:4
B)3:4
C)3:6
D)1:3
E)3:36
Rationale: B) 3:4
Answer: B
Question: What is 3/4 of 4/5 of 2/3?
Options:
A)1/4
B)2/5
C)9/16
D)5/8
E)16/9
Rationale: 3/4 * 4/5 * 2/3= 2/5
Answer: B
Answer: B
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is?
Options:
A)500
B)277
C)266
D)188
E)123
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer: A
Answer: A
Question: By selling a watch for Rs.720/-, a man loses 20% what is that watch cost price
Options:
A)s. 700/-
B)s. 800/-
C)s. 880/-
D)s. 900/-
E)s. 990/-
Rationale: 80 % ------> 720 (80 * 9 = 720)
100 % ------>900 (100 * 9 = 900)
Cost price = Rs. 900/-
D
Answer: D
Question: A girl was asked to state his age in years. Her reply was , "Take my age 5 years hence, multiply it by 5 and subtract 5 times my age 5 years ago and you will know how old I am." What was the age of the person ?
Options:
A)50
B)92
C)27
D)26
E)19
Rationale: Explanation:
Let the present age of girl be x years.
Then, 5(x + 5) - 5(x - 5 ) = x <=> (5x + 25) - (5x - 25) = x <=> x = 50..
Answer: A
Answer: A
Question: A man purchases 2 watches for $ 580. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
Options:
A)$ 260 and $ 300
B)$210 and $ 350
C)$224 and $336
D)$560 and $560
E)$232 and $ 348
Rationale: x + y = 580 --- (1)
1.15x + 0.9y = 580 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*116)/(3*116) = 232/348
Answer: E
Answer: E
Question: A team of 30 men is supposed to do a work in 38 days. After 25 days, 5 more men were employed and the work finished one day earlier. How many days would it have been delayed if 5 more men were not employed?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 35 men do the rest of the job in 12days (38-25-1 = 12days)
30 men can do the rest of the job in 12*35/30 = 14 days
Thus the work would have been finished in 25+14 = 39daya that is 39-38 = 1 day after the scheduled time
Answer is A
Answer: A
Question: If y exceeds x by 10%, then x is less than y by?
Options:
A)1/3%
B)1/5%
C)1/7%
D)1/9%
E)1/11%
Rationale: X=100	y=110
110------10
100-------? => 9 1/11%
Answer:E
Answer: E
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration E of the acid in the mixture?
Options:
A)1/2
B)1/3
C)1/4
D)1/6
E)1/5
Rationale: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration E would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Answer: D
Question: David walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 4 hours 20 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways.
Options:
A)5 h 20 min
B)4 h 15 min
C)6 h
D)7 h
E)6 h 20 min
Rationale: 1.Walking to to a viewpoint+Driving back=4 hours 20 minutes
2.Driving to a viewpoint+Driving back=4 hours 20 minutes - 2 hours=2 hours 20 minutes, thereforeone way driving=2 hours 20 minutes/2 =1 hours 10 minutes.
3. From 1.one way driving=4 hours 20 minutes-1 hours 10 minutes=3 hours 10 minutes.
4.Walking to to a viewpoint+Walking back=3 hours 10 minutes+3 hours 10 minutes=6 hours 20 minutes.
Answer: E
Answer: E
Question: Two trains each 150 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
Options:
A)7.8 sec
B)7.2 sec
C)8.2 sec
D)6.2 sec
E)9.2 sec
Rationale: D = 150 m + 150 m = 300 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 300 * 3/125 = 7.2 sec
ANSWER:B
Answer: B
Question: A bag contains 4 white balls, 4 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
Options:
A)1/2
B)1/5
C)3/8
D)5/11
E)2/7
Rationale: The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 2/10 = 1/5.
The answer is B.
Answer: B
Question: If x/y =3/2, then (x-y)/x?
Options:
A)-1/2
B)-1/3
C)1/3
D)1/2
E)5/2
Rationale: we have this law of fraction:
a/b=c/d= (a-c)/(b-d)
x/y=3/2 ---> x/3=y/2= (x-y)/(3-2)=(x-y)/(1) ---> (x-y)/x= 1/3
Answer: C
Answer: C