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Math Revolution Approach (DS)

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Re: Math Revolution Approach (DS) [#permalink]

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New post 04 Apr 2018, 02:49
[GMAT math practice question]

Are there more girls than boys at a school?

1) 3/7 of the number of girls is more than 1/3 of the number of boys
2) 1/3 of the number of girls is more than 2/5 of the number of boys

=>

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 2 variables (b for boys and g for girls) and 0 equations, 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.

Conditions 1) & 2) together:
From condition 1:
(3/7)g > (1/3)b
=> 9g > 7b

From condition 2:
(1/3)g > (2/5)b
=> 5g > 6b
=> 6g > 5g > 6b
=> g > b

Both conditions together are sufficient.

Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1):

(3/7)g > (1/3)b
=> 9g > 7b

If g = 10 and b = 8, then the answer is ‘yes’.
If g = 8 and b = 8, then the answer is ‘no’.

Thus, condition 1) is not sufficient on its own.


Condition 2):

(1/3)g > (2/5)b
=> 5g > 6b
=> 6g > 5g > 6b
=> g > b

Thus, condition 2) is sufficient on its own.

Therefore, B is the answer.

Answer: B

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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Re: Math Revolution Approach (DS) [#permalink]

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New post 05 Apr 2018, 04:29
[GMAT math practice question]

Is √x+x>-√y?

1) √x+√y = 1
2) x>0

=>

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 2 variables (x and y) and 0 equations, E 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.

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

√x+x>-√y
=> √x+√y+ x>0
Since √x+√y≥0 is always true, we just need to check if x > 0.
Condition 2) is sufficient and since condition 1) is hard to check and condition 2) is easy to check, the answer is D by CMT (Common Mistake Type) 4B.

Condition 1)

We have x ≥ 0 from √x,
Then √x+√y + x ≥ 1 > 0.
Thus condition 1) is sufficient.


Condition 2)

Since √x+√y ≥ 0 and x > 1, we have √x+√y + x > 1 > 0.
Thus condition 2) is sufficient.

Therefore, D is the answer.


Answer: D

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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Re: Math Revolution Approach (DS) [#permalink]

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New post 06 Apr 2018, 00:49
[GMAT math practice question]

Is x – y > 0?

1) |x| + y > 0
2) x + |y| > 0

=>

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 2 variables (x and y) and 0 equations, 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.

Conditions 1) & 2) together:
If x = 2, and y = 1, then the answer is ‘yes’.
If x = 1, and y = 2, then the answer is ‘no’.

Since we don’t have a unique solution, both conditions are not sufficient, when taken together.

Therefore, the answer is E.

Answer: E

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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Re: Math Revolution Approach (DS) [#permalink]

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New post 08 Apr 2018, 18:10
[GMAT math practice question]

If the average (arithmetic mean) of 100 numbers is 50, what is the standard deviation of the numbers?

1) The smallest number is 50
2) The largest number is 50

=>

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 VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations. We often encounter this type of question in the GMAT quant exam these days. If the mean is equal to either the maximum or the minimum, or the range ( = Max – Min ) is zero, then the standard deviation is zero.

Condition 1)
All data items are greater than or equal to 50, and their average is 50.
It means that all data items are equal to 50.
Since all of the data items are equal, their standard deviation is 0.
This is sufficient.

Condition 2)
All data items are less than or equal to 50, and their average is 50.
It means that all data items are equal to 50.
Since all of the data items are equal, their standard deviation is 0.
This is sufficient too.

Therefore, the answer is D.

Answer: D

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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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Re: Math Revolution Approach (DS) [#permalink]

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New post 08 Apr 2018, 18:13
[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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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Re: Math Revolution Approach (DS) [#permalink]

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New post 12 Apr 2018, 01:56
[GMAT math practice question]

Is x>0?

1) (x+y)^2 > (x-y)^2
2) x+y > x-y

=>

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 2 variables (x and y) and 0 equations, 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.

Conditions 1) & 2)
Condition 1) tells us that
(x+y)^2 > (x-y)^2
=> x^2 + 2xy + y^2 > x^2 - 2xy + y^2
=> 2xy > -2xy
=> 4xy > 0
=> xy > 0

Condition 2) tells us that
x + y > x – y
=> y > -y
=> 2y > 0
=> y > 0.

Since xy > 0 and y > 0, we have x > 0.

Thus, both conditions 1) & 2) together are sufficient.

In general, there are many questions involving integers and statistics to which we need to apply CMT(Common Mistake Type) 4.

Condition 1):
If x = -2 and y = -1, then the answer is “yes”.
If x = 1 and y = 2, then the answer is “no”.

Thus, condition 1) is not sufficient.

Condition 2):
If x = -3 and y = -1, then the answer is “yes”.
If x = -1 and y = -3, then the answer is “no”.
Thus condition 2) is not sufficient.

Therefore, C is the answer.

Answer: C

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Re: Math Revolution Approach (DS) [#permalink]

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New post 13 Apr 2018, 02:37
[GMAT math practice question]

Attachment:
4.11.png
4.11.png [ 2.14 KiB | Viewed 45 times ]


Events A, B, C and D are all possible outcomes of an experiment. In the table above, P(x) denotes the probability that event x occurs. What is P(A)?
1) P(A)+P(B)+P(C)=0.75
2) P(C)+P(D)=0.25

=>

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 P(A) = a = 1 – ( c + d ) – 0.25 = 0.75 – (c + d), then P(A) can be determined from the value of c + d. Thus, the answer is B.

Condition 1)
If P(A) = 0.5, P(B) = 0.25 and P(C) = 0, then we have P(A) = 0.5.
If P(A) = 0.4, P(B) = 0.25 and P(C) = 0.1, then we have P(A) = 0.4.
Thus, condition 1) is not sufficient.

Condition 2)
Since P(A) + P(B) + P(C) + P(D) = 1, P(B) = 0.25 and P(C) + P(D) = 0.25 from condition 2), we have P(A) = 0.5.
Thus, condition 2) is sufficient.

Therefore, the answer is B.
Answer: B
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Expert Post
Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]

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New post 15 Apr 2018, 18:41
[GMAT math practice question]

If the elements of set X are a, b, c and d, is the average (arithmetic mean) of a, b, c, and d contained in set X?

1) The average (arithmetic mean) of every pair of elements of set X is 10.
2) The average (arithmetic mean) of every three elements chosen from set X is 10.

=>
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 4 variables (a, b, c and d) and 0 equations, E 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.

Conditions 1) and 2):
Condition 1) gives rise to the following equations:
( a + b ) / 2 = 10 => a + b = 20
( a + c ) / 2 = 10 => a + c = 20

( c + d ) / 2 = 10 => c + d = 20

Condition 2) gives rise to the following equations:
( a + b + c ) / 3 = 10 => a + b + c = 30
( a + b + d ) / 3 = 10 => a + b + d = 30
( a + c + d ) / 3 = 10 => a + c + d = 30
( b + c + d ) / 3 = 10 => b + c + d = 30

Combining these equations yields a = b = c = d = 10.
Therefore, the average is 10, which is an element of set X, and conditions 1) and 2) are sufficient, when taken together.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Condition 1) gives rise to the following equations:
( a + b ) / 2 = 10 => a + b = 20
( a + c ) / 2 = 10 => a + c = 20

( c + d ) / 2 = 10 => c + d = 20

Combining these equations yields a = b = c = d = 10.

Condition 2)

Condition 2) gives rise to the following equations:
( a + b + c ) / 3 = 10 => a + b + c = 30
( a + b + d ) / 3 = 10 => a + b + d = 30
( a + c + d ) / 3 = 10 => a + c + d = 30
( b + c + d ) / 3 = 10 => b + c + d = 30

Combining these equations yields a = b = c = d = 10.

Therefore, the answer is D.

Answer: D

Since conditions 1) and 2) are equivalent, D is the answer by Tip 1) of the VA method.

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Expert Post
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Joined: 16 Aug 2015
Posts: 5255
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Re: Math Revolution Approach (DS) [#permalink]

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New post 15 Apr 2018, 18:43
[GMAT math practice question]

When a positive integer n is divided by 5, the remainder is 2. What is the remainder when n is divided by 3?

1) n is divisible by 2
2) When n is divided by 15, the remainder is 2.

=>

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.

We have 1 variable (n) and 1 equation. So, D is most likely to be the answer, and we should consider each of the conditions on its own first.

Plugging-in numbers is the suggested approach to remainder questions.

Condition 1)
The possible values of n are
n = 2, 4, 6, 8, …
When these are divided by 3, the remainders are 0, 1 and 2.
Since the answer is not unique, condition 1) is not sufficient.

Condition 2)
The possible values of n are
n = 17, 32, 47, 62, …
When these are divided by 3, the remainder is always 2.
Since the answer is unique, condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

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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Re: Math Revolution Approach (DS) [#permalink]

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New post 18 Apr 2018, 04:53
[GMAT math practice question]

Is the total of the sales prices of 3 products greater than $23?

1) The price of the cheapest of the 3 products is at least $8
2) The price of the second cheapest of the 3 products is at least $12.

=>

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.

If a question includes the expression “greater than”, we should determine the smallest possible value, since all other possibilities are greater than the minimum. Each of the conditions includes the expression “at least”, so this gives us some minimum values.

Condition 1)
Since the cheapest of the three products costs at least $8, the minimum total cost of the three products is
$8 + $8 + $8 = $24 > $23.
Thus, condition 1) is sufficient.

Condition 2)
Since the second cheapest of the three products costs at least $12, the minimum total cost of the three products is
$0 + $12 + $12 = $24 > $23.
Thus, condition 2) is sufficient.

Answer: D
_________________

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Re: Math Revolution Approach (DS) [#permalink]

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New post 19 Apr 2018, 02:47
[GMAT math practice question]

Is x>0?

1) x^3+x^2+x = 1
2) x^2 – 4x - 5 > 0

=>
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 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1):
x^3+x^2+x = 1
=> x(x^2+x+1) = 1
=> x = 1 / (x^2+x+1)
=> x = 1 / (x^2+x+1) > 0 since x2+x+1 > 0.

Thus, condition 1) is sufficient.


Condition 2):
x^2 – 4x -5 > 0
=> (x+1)(x-5) > 0
=> x < 1 or x > 5

Since the solution set of the inequality, x > 0, from the question does not include the solution set of the inequality from condition 2), x < 1 or x > 5, condition 2) is not sufficient.


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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Re: Math Revolution Approach (DS) [#permalink]

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New post 20 Apr 2018, 01:07
[GMAT math practice question]

Each of three consecutive positive integers is less than 100. Their sum of is a multiple of 10. What is the smallest of the three integers?

1) Their median is a multiple of 9
2) Two of the integers are prime numbers.

=>

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.

Let the integers be x – 1, x and x + 1 where x is a positive integer. Since their sum, x – 1 + x + x + 1 = 3x is a multiple of 10, x must be a multiple of 10.

Since we have 1 variable (x) 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)
The median, x, of the three integers is a multiple of 9 and a multiple of 10.
Since x < 100, we must have x = 90.
Therefore, the smallest of the integers is x – 1 = 89.
Thus, condition 1) is sufficient.

Condition 2)
If x = 30, the integers are 29, 30, 31 and the smallest integer is 29.
If x = 90, the integers are 89, 90, 91 and the smallest integer is 89.
Since we do not obtain a unique answer, condition 2) is not sufficient.


Therefore, the answer is A.

Answer: A
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Re: Math Revolution Approach (DS)   [#permalink] 20 Apr 2018, 01:07

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