mathewhe/aqua_rat huggingface dataset:
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.5, 3.5, 5.5, 7.5, ... What number should come next?
(A) 4.7
(B) 3.6
(C) 9.5
(D) 5.0
(E) 4.4
Rationale: 9.5
In this simple addition series, each number increases by 2.0
Answer : C
Answer: (C) 9.5
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.8 km?
(A) 660 m
(B) 650 m
(C) 570 m
(D) 670 m
(E) 680 m
Rationale: Distance covered by Amar = (18/48)*1800 = 670 m
ANSWER:D
Answer: (D) 670 m
Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
(A) 21:22
(B) 7:8
(C) 2:1
(D) 21:24
(E) 14:16
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
= (120/100) 7x and (110/100) 8x
= 42x/5 and 44x/5
Therefore, The required ratio = (42x/5):(44x/5)
= 21 : 22. Answer is A.
Answer: (A) 21:22
Question: Akhil's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
Rationale: Akhil's club with a total membership of 30 has formed 3 committees Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.
Hence only M is 8. Now we need to consider only S, (S n R) and R.
(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.
30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.
22 = (12-x) + (5-x) + x + Neither.
Now the max value of x could be 5 and the min value of x could be 0.
When x is 5 (max), Neither is 10.
When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.
Answer 10 (D).
Answer: (D) 10
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 24 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Total Distance = 24 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 20 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 20 / 10 = 2 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 2 = 8+4 = 12 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 12 /4 = 3 hrs ... Answer A
Answer: (A) 3
Question: Find the compound interest on $15,624 for 9 months at 16% per annum compounded quarterly.
(A) $4152
(B) $1951
(C) $2258
(D) $8978
(E) $8875
Rationale: P=$15625, n=9 months=3 quarters, R=16% p.a=4% per quarter.
amount=$[15625*(1+(4/100)^3)] = $(15625*(26/25)*(26/25)*(26/25)) = $17576.
C.I = $(17576-15625)= $1951.
answer(B)
Answer: (B) $1951
Question: Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP?
(A) Rs.320
(B) Rs.450
(C) Rs.550
(D) Rs.640
(E) Rs.680
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: (C) Rs.550
Question: In what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 8 sec
(B) 7 sec
(C) 2 sec
(D) 6.5 sec
(E) 9 sec
Rationale: T = 65/36 * 18/5
= 6.5 sec
Answer:D
Answer: (D) 6.5 sec
Question: In a group of 22 boys, 13 play basketball and 15 play football. 3 of the boys play neither. how many play both ?
(A) 18
(B) 20
(C) 21
(D) 22
(E) 25
Rationale: 18 boys play something. If b play both, then
13+15-b = 18
Answer is A
Answer: (A) 18
Question: If n is an integer and 5^n > 40,000,000, what is the least possible value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: When you seperate the 40000000 into factors of 5 and 2 you get - > 10^7 x 2^2 = 5^7 x 2^9
2 to the ^ 9 = 512 so its 512 x 5^7
that means 5^7 x 5^x must be greater
5^x > 512
5^1=5
5^2=25
5^3= 125
5^4= 625 - > so x must be at least 4
5^(7+4)= 5^11
E
Answer: (E) 11
Question: Suppose we have six marbles: 3 yellow marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
(A) 180
(B) 160
(C) 149
(D) 150
(E) 175
Rationale: # ways to distribute yellow marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
A
Answer: (A) 180
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
(A) 2 : 5
(B) 5 : 2
(C) 3 : 5
(D) 1 : 1
(E) None of these
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
ANSWER:D
Answer: (D) 1 : 1
Question: There are 36 students in a certain geometry class. If two thirds of the students are boys and one half of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 27
Rationale: Total Students = 36
Two thirds of the students are boys = 2/3*36 = 24
One half of the boys are under six feet tall = 1/2*24 = 12 ...
Therefore Number of boys in the class under six feet tall = 12 ... Answer B....
Alternatively... Number of boys in the class under six feet tall = 1/2 of 2/3 of Total Students = 1/2*2/3*36 = 12...
Answer B
Answer: (B) 12
Question: If 2^z is a factor of 22!, which of the following could be the value of z?
I. 22
II. 23
III. 24
(A) I ​ only
(B) II only
(C) I​ and II
(D) I, II, and III
(E) None
Rationale: 22! contains all numbers from 1 to 22. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 11
Multiples of 4 = 5
Multiples of 8 = 2
Multiples of 16 = 1
Total count = 19
The answer is E.
Answer: (E) None
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?
(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) 24
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?
(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) 60
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29,38, 48, ___?
(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) 59
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
(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) data inadequate
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?
(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) 9min
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?
(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) 54
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is?
(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) 25
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?
(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) 350
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?
(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) 60km
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?
(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) 67%
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
(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) 150
Question: A train 1020 m long running at 102 kmph crosses a platform in 50 sec. What is the length of the platform?
(A) 287
(B) 298
(C) 396
(D) 726
(E) 267
Rationale: D = 102 * 5/18 = 50
= 1416 â€“ 1020
= 396
Answer: C
Answer: (C) 396
Question: How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?
(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) 8
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?
(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) 90
Question: A person crosses a 420 m long street in 5 minutes. What is his speed in km per hour?
(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) 5.04 km/hr.
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?
(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) q/10
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?
(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) 30
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?
(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) $22.50
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
(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) 158
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?
(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) 24.7
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?
(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) 9 cm
Question: The average of five numbers id 27. If one number is excluded, the average becomes 23. What is the excluded number?
(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) 43
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?
(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) 12hours
Question: The curved surface of a right circular cone of height 15cm and base diameter 16 cm is
(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) 136 ∏cm³
Question: A boy runs 200 metres in 36 seconds. What is his speed ?
(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) 20 km/hr
Question: 60% of a number is added to 120, the result is the same number. Find the number?
(A) 300
(B) 288
(C) 270
(D) 129
(E) 281
Rationale: (60/100) * X + 120 = X
2X = 600
X = 300
Answer:A
Answer: (A) 300
Question: If x= (10^50) - 57, what is the sum of all the digits of x?
(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) 439
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?
(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) 3/8
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
(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) None of the above
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?
(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) -1
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?
(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) 150
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(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) 108 kmph
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)
(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) a) I only
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?
(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) 16
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?
(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) 36%
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:
(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) Rs. 240
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?
(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) 5:24
Question: If z is the sum of x and y, then which one of the following must equal x – y ?
(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) z-2y