hi...
what is given?
let the apples be A..
1) 4.5 percent failed to pass inspection so \(\frac{95.5}{100} * A\) passed inspection.
2) Of the apples that failed inspection, 2/3 of them were rotten and the rest was unmatured- \(\frac{2}{3} * \frac{4.5}{100} *\)A rotten and \(\frac{1}{3}*\frac{4.5}{100} *A\) unmatured
3)how many of apples inspected last week at the plant were unmatured? = \(\frac{1}{3}*\frac{4.5}{100} *A\)

what we require is A.

lets see the statements..
(1) 450 of apples inspected last week at the orchard failed to pass inspection.
so \(\frac{4.5A}{100} = 450...... A= 10000\)..
suff

(2) 9,550 of apples inspected last week at the orchard passed inspection
so 95.5% of A = 9550..... A = 10000
suff

D
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[GMAT math practice question]

X is proportional to Y. If Y is increased by 30%, by approximately what percent is X^2 increased?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

=>

X = kY for some k.
Since (1.3kY)^2 = 1.69k^2Y^2 = 1.69(kY)^2 = 1.69X^2, we have (1.69X^2 – X^2) / X^2 = 0.69, which is approximately 70%.

Therefore, the answer is E.

Answer: E
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[GMAT math practice question]

Alice studies for a hours on each of Monday, Tuesday, and Thursday. She also studies for b hours on Wednesday, and for c hours on Friday. What is her median study time for the school week?

1) a=10
2) b+c=30

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Depending on their values, it is possible to rearrange a, a, a, b, c into ascending order in the following ways:
a, a, a, b, c
a, a, a, c, b
b, a, a, a, c
c, a, a, a, b
b, c, a, a, a
c, b, a, a, a
In every order, the median (middle value) is a. So, the question asks for the value of a.

Thus, only condition 1) is sufficient.


Therefore, A is the answer.

Answer: A
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[GMAT math practice question]

If 50-√7<x<50+√7, then x=?

1) x is an odd integer
2) √x is an integer.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since 2< √7< 3, we have 47< x < 53 from the original condition ‘50-√7<x<50+√7’.

Condition 1)
As x is an odd integer, it could be 49 or 51.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
If √x is an integer, then x is the square of an integer.
49 is the only perfect square of an integer between 47 and 53.
Thus, x=49 and condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
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[GMAT math practice question]

If the average (arithmetic mean) price of apples, bananas and oranges is $3.00 per pound, what is their median price?

1) The price of apples is $3.00 per pound.
2) The price of bananas is $2.97 per pound.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (a for apples, b for bananas and o for oranges) and 1 equation ( ( a + b + o ) / 3 = 3), C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

This question is a new type of GMAT question. The average is provided in the original condition and the question asks for the value of the median. The same average applies for each of the conditions.

Conditions 1) & 2)
If a = 3.00 and b = 2.97, then ( a + b + o ) / 3 = 3.
So,
3.00 + 2.97 + o = 9
and
o = 3.03. Therefore, the median is 3.00.
Thus, both conditions together are sufficient.

Condition 1)
We consider three cases.
Case 1: a = b = c = 3.00
Since all prices are the same, the median is 3.00.

Case 2: b < 3.00
If b < 3.00, then we must have c > 3.00.
Therefore, the median is 3 since b < a < c.

Case 3: b > 3.00
If b > 3.00, then we must have c < 3.00.
Therefore, the median is 3 since c < a < b.

Thus, condition 1) is sufficient on its own.

Condition 2)
If a = 3.00, b = 2.97 and c = 3.03, then the median is 3.00.
If a = 2.00, b = 2.97 and c = 3.00, then the median is 2.97.
Since we don’t have a unique solution, condition 2) is not sufficient on its own.

Therefore, A is the answer.

Answer: A

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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[GMAT math practice question]

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

A. 1/3
B. 3/4
C. 1/2
D. 5/8
E. 3/8

=>

The total number of ways the two balls may be selected is 4C2 = ( 4 * 3 ) / ( 1 * 2 ) = 6.
There are three ways in which the numbers on the two balls selected can have a difference of 1: ( 1, 2 ), ( 2, 3 ), and ( 3, 4 ).

Thus, the probability is 3/6 or 1/2

Therefore, C is the answer.
Answer: C
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[GMAT math practice question]

Which of the following relationships must be inversely proportional to each other?

I. Work done and working time
II. Speed and Traveling Time
III. Profit and Cost

A. I only
B. II only
C. III only
D. II and III
E. I and II

=>

Statement I
Let R be the work rate, W be the work done and T be the working time. Then R = W/T and T = W*R. Therefore, T and W are directly proportional.

Statement II
Let V be the speed, D be the distance and T be the traveling time. Then
V = D/T, and V and T are inversely proportional.

Statement III
Let P be the profit, R be the revenue and C be the cost. Then
P = R – C, and P and C are neither directly nor inversely proportional.

Therefore, B is the answer.

Answer B
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[GMAT math practice question]

If the sum of the squares of two positive integers is 106, what is the sum of the two integers?

A. 13
B. 14
C. 15
D. 16
E. 17

=>
x^2 + y^2 = 106.
We can plug-in the numbers from 1 to 10 to find the values of x and y that work.
We find that 9^2 + 5^2 = 81 + 25 = 106. So, the two numbers are 5 and 9, and their sum is 9 + 5 = 14.

Therefore, the answer is B.
Answer: B
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[GMAT math practice question]

Alice works from Monday to Friday only. How many days does she work in April?

1) April 1 is Saturday or Sunday
2) April 28 is Saturday or Sunday

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
When the day on which a specific date, for example, the first of April 2018 is fixed, we can determine the days on which other dates in April fall.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If April 1st is Saturday, Alice works on the 3rd - 7th, 10th - 14th, 17th - 21st, 24th - 28th. This means she works on 20 days.
If April 1st is Sunday, Alice works on the 2nd - 6th, 9th - 13th, 16th - 20th, 23rd - 27th and 30th. This means she works on 21 days.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
If April 28th is Saturday, Alice works on the 2nd - 6th, 9th - 13th, 16th - 20th, 23rd - 27th and 30th. This means she works on 21 days.
If April 28th is Sunday, Alice works on the 1st - 5th, 8th - 12th, 15th - 19th, 22nd - 26th, 29th and 30th. This means she works on 22 days.

Since we don't have a unique solution, condition 2) is not sufficient.
Conditions 1) & 2) together:
If the 1st of April is a Saturday or Sunday and the 28th of April is a Saturday or Sunday, the 1st of April must be a Saturday.
So, Alice works on the 2nd - 6th, 9th - 13th, 16th - 20th, 23rd - 27th and 30th. Therefore, she works on 21 days.
Since we have a unique solution, both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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[GMAT math practice question] 4/30 trend 5.10

If the profit on a product is 20 percent of its sales price, what percent is the profit of the cost price?

A. 20%
B. 25%
C. 30%
D. 33+(1/3)%
E. 35%

=>

Let P, R and C be the profit, the sales price (revenue) and the cost price of the product, respectively.
Then P = R – C.
Since P is 20 percent of the sales price, the IVY method tells us that P = 20*(1/100)*R.
So, P = (1/5)R or R = 5P.
Plugging this into P = R – C yields P = 5P – C or C = 4P.
It follows that P = (1/4)C, and P is 25 percent of C.

Therefore, B is the answer.
Answer B
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