mathewhe/aqua_rat huggingface dataset:
Question: What is the sum of the digits of integer k, if k = (10^40- 79)
(A) 345
(B) 340
(C) 343
(D) 349
(E) 338
Rationale: There are 41 digits in 10^40
When we subtract 79 from it, there will be 40 digits left.
10^40 can be written as 9999999....(40 times) + 1
So,
10^40 - 79 = 9999999....(40 times) + 1 - 79 = 9999999....(40 times) -78
Consider the last 2 digits,
99-78 = 21
The last 2 digits will be 21.
And our number would be 99999......99921 with 2 less 9s after subtraction.
Number of 9s left are 38 and the last two digits are 21
The sum of the digits will be
(38*9) + 2 + 1 =345
Answer:- A
Answer: (A) 345
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 8 min
(C) 9 min
(D) 6 min
(E) 1 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer:A
Answer: (A) 4 min
Question: Simplify: 256 x 256 - 144 x 144
(A) 761200
(B) 44800
(C) 761800
(D) 761500
(E) None of them
Rationale: (256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800
Answer is B
Answer: (B) 44800
Question: If the integer c is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when c is rounded to the nearest ten. which of the following is a possible value of c?
(A) 64
(B) 67
(C) 99
(D) 133
(E) 147
Rationale: We have to check options 1 by 1.
64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.
99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred c= 100=A
Answer: (A) 64
Question: 20-3*4^2+20 = ?
(A) 287
(B) -13
(C) -73
(D) 13
(E) None
Rationale: 20-3*4^2+20
= 20-3*16+20
=20-48+20=-8..
E
Answer: (E) None
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 50¢?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If the average price is 56, then Mary has 8 oranges and 2 apples (a ratio of 4:1).
For the average price to be 50, the ratio should be 1:1.
Mary must put back 6 oranges.
The answer is E.
Answer: (E) 6
Question: At a meeting of the 6 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
(A) 56
(B) 64
(C) 72
(D) 80
(E) 88
Rationale: 6 people can be arranged around a table in 5! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 5 units around a table is 4!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 5! - 2*4! = 3*4! = 72
The answer is C.
Answer: (C) 72
Question: If a - b = 3 and
a2+b2=29
, then find the value of ab
(A) 7
(B) 8.5
(C) 10
(D) 12
(E) 14
Rationale: Explanation:
2ab=(a2+b2)−(a−b)2
=> 2ab = 29 - 9 = 20
=> ab = 10
Option C
Answer: (C) 10
Question: A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?
(A) 11:10:15
(B) 20:17:23
(C) 19:19:18
(D) 5:4:9
(E) 1:3:6
Rationale: Explanation:
A:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3)
= 95 lakhs : 95 lakhs : 90 lakhs =19:19:18.
Answer IS C
Answer: (C) 19:19:18
Question: The average age of 12 men in a group is increased by 2 years when two men whose ages are 20 years and 22 years, are replaced by new members. What is the average age of the new men included?
(A) 22
(B) 767
(C) 77
(D) 33
(E) 99
Rationale: Explanation:
Total age of two men replaced = 20 + 22 = 42 years
Total increase in age on replacement = 2 × 12 = 24 years
Total age two new persons included = 42 + 24 = 66 years
Therefore, Average age of new persons = 66/2 = 33 years
Answer:D
Answer: (D) 33
Question: Three years ago the average age of a class of six members was 24 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
(A) A)1
(B) B)2
(C) C)3
(D) D)4
(E) E)6
Rationale: 6 * 27 = 162
7 * 24 = 168
`6
E
Answer: (E) E)6
Question: Last week David spent 20 percent of his wages on recreation. This week, his wages are 30 percent less than last weekʼs wages and he spent 20 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week
(A) 75%
(B) 72%
(C) 70%
(D) 73%
(E) 74%
Rationale: Say David's wages last week were $100, so he spent 0.20*100=$20 on recreation;
This week's wages is 0.70*100=$70, so he spends 0.2*70=$14 on recreation;
14/20=0.70, hence the amount he spends on recreation this week is 70% of the amount he spent on recreation last week: 20*0.7=14
Answer: C
Answer: (C) 70%
Question: A can do a work in 12 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work?
(A) 3
(B) 5
(C) 8
(D) 2
(E) 6
Rationale: A rate = 1/12
B rate = 1/24
(A+B) rate = (1/12)+(1/24) = 1/8
A & B finish the work in 8 days
correct option is C
Answer: (C) 8
Question: If x and y are even integers, which of the following is an odd integer?
(A) xy
(B) y^2
(C) x+y+3
(D) x^2
(E) None of these
Rationale: even * even = even
even + odd = odd
Answer : C
Answer: (C) x+y+3
Question: A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 3/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 9/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 3/8 is spilled out.So again left with 0/8.
so 50% more than what he started was = 3/4+1/2*(3/4)=9/8
Amount of water needed to add = 9/8 - 0/8=9/8
ANSWER:E
Answer: (E) 9/8 cup
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2 : 7. What arethe measures of the 2 angles?
(A) 20°
(B) 70°
(C) 110°
(D) 120°
(E) 140°
Rationale: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Answer: (B) 70°
Question: If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be
(A) 2
(B) 4
(C) 6
(D) 7
(E) 14
Rationale: i just tried plugging in the numbers and found out that
4*11025 = 44, 100, which is a square of 210
B
Answer: (B) 4
Question: #p is defined as 2p+20 for any number p. What is p, if #(#(#p))=4?
(A) –108
(B) –44
(C) 10
(D) -17
(E) 18
Rationale: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = 4 ---> 8p= -136 ---> p = -17, D is the correct answer.
Answer: (D) -17
Question: If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend?
(A) $30.60
(B) $72.60
(C) $70.60
(D) $40.60
(E) $50.60
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 60.50 = (20/100)*60.50 = $12.1
Total spent
60.50 + 12.1 = $72.6
correct answer B
Answer: (B) $72.60
Question: Solve the equation:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3
(A) 1
(B) 1/2
(C) 2
(D) 2/1
(E) None
Rationale: Solution:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3 <=>
4x2 - 4x + 1 -10x2 – x = x – x3 - 8 + 12x - 6x2 + x3 <=>
18x = 9 <=> x = 1/2
Answer B
Answer: (B) 1/2
Question: If a , b, and c are integers and a∗b2/ca∗b2/cis a positive even integer, which of the following must
be true?
I. ab is even
II. ab > 0
III. c is even
(A) l
(B) ll only
(C) l and ll
(D) l and lll
(E) l,ll,and lll
Rationale: Given: a∗b2c=even>0a∗b2c=even>0 --> ab2=c∗even=evenab2=c∗even=even --> either aa is even or bb or both.
I. abab is even --> according to the above this must be true;
II. ab>0ab>0 --> not necessarily true, bb could be positive as well as negative (for example a=1a=1, c=1c=1 and b=−2b=−2);
III. cc is even --> not necessarily true, see above example.
Answer: A (I only).
Answer: (A) l
Question: Of the 40 electronics components that a factory must manufacture, 30 percent would be most e¢ ciently manufactured by Machine A and the remaining 70 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 40 components. If 70 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
(A)  30
(B)  32
(C)  60
(D)  35
(E)  36
Rationale: A can manufacture 30 % of 40 efficiently, which is 12.
B can manufacure 70 % of 40 efficiently, which is 28.
Now 80 % of 40 are produced by A. This means 32 parts. Since A can produce 12 efficiently, all 32 are produced efficiently. Rest (8) is produced by B, which can produce max. 28 parts efficiently.
Hence parts that were produced efficiently = 32+28 = 60. (C).
Answer: (C)  60
Question: What is the 36th digit to the right of the decimal point in the decimal expansion of 1/37?
(A)  0
(B)  2
(C)  4
(D)  7
(E)  9
Rationale: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (3rd, 6th, 9th, ...) to the right of the decimal point is 7, thus 36th digit to the right of the decimal point is also 7.
Answer: D.
Answer: (D)  7
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 78 respectively. The sum is:
(A) 1360
(B) 1450
(C) 1600
(D) 947
(E) None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 78 / (85 - 78) = Rs.947.
Answer D
Answer: (D) 947
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $60000. Find his total income?
(A) A)1200000
(B) B)562000
(C) C)800000
(D) D)500000
(E) E)652000
Rationale: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 60000
100% = 60000*100/5 = $1200000
Answer is A
Answer: (A) A)1200000
Question: In particular old age home, 60% are suffering from diabetic and at the same time 80% are suffering from blood pressure.If suppose 75% are suffering from diabetic,what percentage of old people suffering from blood pressure at the same old age home?
(A) 23
(B) 16
(C) 26
(D) 36
(E) 20
Rationale: given : % of people suffering from diabetics = 60%; % of people suffering from blood pressure = 80% (ie ) 0.8
total =75*100; Those who are suffering from diabetics= 75 - 60 = 15; Those who are suffering from blood pressure =
100 - 80=20; so those who are suffering from blood pressure =0.8*20=16; Total number of people suffering from blood pressure = 20+16 = 36. Answer: D
Answer: (D) 36
Question: If P/6 = Q/7 = R/8 then find P:R:Q
(A) 1:2:3
(B) 6:8:7
(C) 2:4:9
(D) 4:9:7
(E) 3:5:7
Rationale: Let P/6 = Q/7 = R/8 = K
P = 6K
Q = 7K
R = 8K
P:R:Q = 6:8:7
Answer is B
Answer: (B) 6:8:7
Question: ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region?
(A) 1:1
(B) 2:1
(C) 3:1
(D) 5:3
(E) 8:3
Rationale: Let's join the midpoints as shown in the figure then we'll get four small squares...
AODX be 1 and similarly all squares..and we can split the unit 1 into half and half as per the mid points...
Then shaded will be 1+1/2+1/2+1/2 = 5/2
and unshaded is 1/2+1/2+1/2 = 3/2..
shaded : unshaded is 5:3..
ANS option D.
Answer: (D) 5:3
Question: The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number?
(A) 3
(B) 7
(C) 8
(D) 11
(E) None of these
Rationale: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 51
5x + 20 = 255
x = 47
So, required difference = (47 + 8) – 47 = 8
ANSWER C
Answer: (C) 8
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 10th Rd and 5th Ave in the shortest possible time, how many different routes could he take?
(A) 45
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: Bills needs to walk 8 blocks north and 2 blocks east.
One possible solution is NNNNNNNNEE.
There are 10C8 = 45 possible solutions.
The answer is A.
Answer: (A) 45
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability W that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) W=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability W= 1/12 * 2 = 1/6
Ans E
Answer: (E) W=1/6
Question: How many numbers between 11 and 90 are divisible by 7?
(A) 7
(B) 9
(C) 11
(D) 8
(E) 10
Rationale: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, T^n = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Answer is C.
Answer: (C) 11
Question: HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is.
(A) 160
(B) 170
(C) 180
(D) 190
(E) 200
Rationale: 2472=8*3*103
1284=4*3*107
so n = 4*3*x
dividing by hcf
2472/12=2*103
1284/12=107
lcm/12=2*3*5*103*107
x=lcm/first*second
x=2*3*5*103*107/2*103*107=3*5=15
number is = 15*12=180
ANSWER:C
Answer: (C) 180
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 20km/hr, then find the area of square field.
(A) 125
(B) 225
(C) 325
(D) 425
(E) None of these
Rationale: Explanation :
D = 20*3/2 = 30 km. So side of square is 15km, so area – 225km^2
Answer – B
Answer: (B) 225
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
(A) 10000
(B) 10008
(C) 10005
(D) 10004
(E) 10001
Rationale: 100 * 100 = 10000
125 * 80 = 10000
No change
Answer:A
Answer: (A) 10000
Question: The H.C.F. and L.C.M. of two numbers are 15 and 5040 respectively If one of the numbers is 144, find the other number
(A) 400
(B) 256
(C) 120
(D) 420
(E) 525
Rationale: Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 15 * 5040
x = (15*5040)/144 = 525
Option E
Answer: (E) 525
Question: A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
(A) 3/40000
(B) 1/3600
(C) 9/2000
(D) 1/60
(E) 1/15
Rationale: There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.
What is the probability of choosing ANY sibling from junior class? 60/1000 (as there are 60 of them).
What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be 1/800 (as there is only one sibling pair of chosen one).
So the probability of that the 2 students selected will be a sibling pair is: 60/1000∗1/800=3/40000
Answer: A.
Answer: (A) 3/40000
Question: If r ≠ 1 and if sr/(s - r) = 1, what is the value of s in terms of r?
(A) (r+1)/r
(B) (r - 1)/r
(C) r/(r + 1)
(D) r/(1-r)
(E) (1 - r)/r
Rationale: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
D
Answer: (D) r/(1-r)
Question: Worker W produces n units in 5 hours. Workers V and W work independently but at the same time, produce n units in 2 hours. How long would it take V alone to produce n units?
(A) 8/3 hours
(B) 10/3 hours
(C) 11/3 hours
(D) 12/3 hours
(E) 18/3 hours
Rationale: w's 1 hours production=n/5
(w+v)'s 1 hours production=n/2
v's 1 hours production
n/5+V=n/2
v's 1 hours production=n/2-n/5
=3n/10
n/(10/3)
ans=10/3 hours
ANSWER:B
Answer: (B) 10/3 hours
Question: A computer manufacturer produces a certain electronic component at a cost of $50 per component. Shipping costs for delivering the components are $8 per unit. Further, the manufacturer has costs of $16,000 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 200 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) 135
(B) 129
(C) 131
(D) 138
(E) 141
Rationale: $16000 is a fixed cost
Each component is $58 ($50 to produce, $8 to ship)
Manufacturer will be producing and selling 200 components
so therefore the equation to find price would be
200*p = 16000+(200*50)+(200*8)
p = (16000+10000+1600)/200
p = 138
Answer: D
Answer: (D) 138
Question: A fruit drink is made of orange, watermelon, and grape juice, where 35 percent of the drink is orange juice and 35 percent is watermelon juice. If the drink is made with 45 ounces of grape juice, how many ounces is the drink total?
(A) 120
(B) 140
(C) 150
(D) 180
(E) 200
Rationale: Let the total number of ounces in the drink be x.
% of orange = 35%
% of watermelon = 35%
% of grape = 100% - 70% = 30%
0.30x = 45
x = 150
Therefore there are a total of 150 ounces in the drink.
The answer is C.
Answer: (C) 150
Question: Find 44 % of 240
(A) 96
(B) 105.6
(C) 86
(D) 74
(E) 110
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 44 % of 240
44/100 × 240
=105.6
Answer:B
Answer: (B) 105.6
Question: Suresh and Ramesh started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of total profit of Rs. 15,000, what is Ramesh's share?
(A) Rs. 9375
(B) Rs. 9379
(C) Rs. 9376
(D) Rs. 9372
(E) Rs. 9371
Rationale: Explanation:
Ratio of Suresh and Ramesh's share = 24,000 : 40,000 = 3 : 5
Ramesh's share = Rs. (15000 x 5 / 8) = Rs. 9375
ANSWER: A
Answer: (A) Rs. 9375
Question: ?% of 360 = 108.0
(A) 277
(B) 36
(C) 64
(D) 72
(E) 30
Rationale: ?% of 360 = 108.0
or, ? = 108.0×100/360=30
Answer E
Answer: (E) 30
Question: what is the least number by which 46,800 must be divided to get a number perfect square
(A) 21
(B) 52
(C) 24
(D) 40
(E) 45
Rationale: 46,800/52=900
900=(30)^2
Ans-52
ANSWER:B
Answer: (B) 52
Question: What is 15 percent of 44?
(A) 6.6
(B) 7.8
(C) 8.9
(D) 9.4
(E) 10.2
Rationale: (15/100) * 44 = 6.6
The answer is A.
Answer: (A) 6.6
Question: Rohit and Rohan can complete a work in 12 days and 6 days respectively. How much time will they take when working together?
(A) 4
(B) 3
(C) 5
(D) 2
(E) 1
Rationale: Time taken by Rohit and Rohan = xy/ x+y
=12*6/(12+6)
= 4 days
ANSWER:A
Answer: (A) 4
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
(A) 7396
(B) 6847
(C) 4262
(D) 8798
(E) 9563
Rationale: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is A.
Answer: (A) 7396
Question: Two cars are traveling towards each other. If car A is traveling at a speed of 70 mph and car B is traveling 10% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?
(A) Five hours and 30 minutes.
(B) Seven hours and 30 minutes.
(C) Eight hours and 20 minutes.
(D) Nine hours and 15 minutes.
(E) Ten hours and 20 minutes.
Rationale: Speed of second train= 70*90/100= 63
Time= toral distance /total speed
705/ (70+63)= 705/133= 5.___
A is the answer
Answer: (A) Five hours and 30 minutes.
Question: The sum of money will be double itself in 10 years and simple interest find rate of interest?
(A) A)5%
(B) B)10%
(C) C)15%
(D) D)20%
(E) E)25%
Rationale: T = 10 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/10x =10%
Answer is B
Answer: (B) B)10%
Question: A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase?
(A) 80%
(B) 90%
(C) 70%
(D) 60%
(E) 50%
Rationale: Ans. Let previous income = Rs. 100
Previous savings = 10% of Rs. 100 = Rs. 10
Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120
Increased savings = 15% of Rs. 120 = Rs. 18
Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8
Therefore, Percent increase in savings = 8/10 x 100 = 80%
Answer A
Answer: (A) 80%
Question: If 9 is a factor of 2a, then which of the following may not be an integer?
(A) 6a/54 + 2a/3
(B) (4a-18)/9
(C) (2a+27)/9
(D) (81-4a^2)/81
(E) (2a-3)/3
Rationale: I got the right answer A after plugging in 18 for a.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6a/54 + 2a/3 = 3/6 * 2a/9 + 2a/3.
Since 9 is a factor of 2a, 3 is also factor of 2a. So 2a/3 is an integer, as is 2a/9. But 3/6 = 1/2, so if 2a/9 is not even, the expression 3/6 * 2a/9 will not be even."
But, isn't 2a/9 always even? 9 is a factor of 2a, which means that we could have 2(9), 2(2)(9), 2(3)(9), and so forth. The 9 in the denominator cancels out the 9 in the numerator. So we are left with 2 * something. So 2a/9 is even.A
Answer: (A) 6a/54 + 2a/3
Question: If a and b are both even numbers, which of the following is an even number?
(A) a + b+3
(B) a + b + 1
(C) ab
(D) ab + 1
(E) NONE
Rationale: Sol.
Product of two odd numbers is always odd and adding 1 gives even.
Answer C
Answer: (C) ab
Question: The present ages of three persons in proportions 4 : 7 : 8. Eight years ago, the sum of their ages was 71. Find their present ages (in years).
(A) 15, 20, 28
(B) 24, 28, 36
(C) 20, 35, 40
(D) 33,42,43
(E) of these
Rationale: Let their present ages be 4x, 7x and 8x years respectively.
Then, (4x - 8) + (7x - 8) + (8x - 8) = 71
19x = 95
x = 5.
Their present ages are 4x = 20 years, 7x = 35 years and 8x = 40 years respectively.
ANSWER:C
Answer: (C) 20, 35, 40
Question: If x+y=290, x-y=200, for integers of x and y, y=?
(A) 200
(B) 245
(C) 50
(D) 115
(E) 150
Rationale: x+y = 290
x-y = 200
2x = 90
x = 45
y = 245
Answer is B
Answer: (B) 245
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job. How long should it take both A and B, working together but independently, to do the same job?
(A) 70 hours
(B) 40/9 hours
(C) 9 hours
(D) 16 hours
(E) 20 hours
Rationale: A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.
ANSWER B 40/9 hours
Answer: (B) 40/9 hours