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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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MathRevolution wrote:
[GMAT math practice question]

(number properties) If $$x, y$$ are integers, is $$(x-y)(x+y)(x^2+y^2)$$ an odd number?

1) $$x$$ is an odd number
2) $$x-y$$ is an odd number

=>

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 $$(x-y)(x+y)(x^2+y^2) = x^4-y^4$$, the question asks if $$x$$ and $$y$$ have different parities.

By Condition 2), $$x$$ and $$y$$ must have different parities since $$x – y$$ is an odd number.
Condition 2) is sufficient.

Condition 1)
Since we don’t know whether $$y$$ is even or odd, condition 1) is not sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(inequality) If $$x, y, z$$ are positive integers, is $$xyz ≥ 64$$?

$$1) xy ≥ yz ≥ zx ≥ 16$$
$$2) x+y+z=64$$
_________________
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5693
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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fskilnik wrote:
Archit3110 wrote:
MathRevolution wrote:
[GMAT math practice question]

If $$a>b>c>d>0$$, is $$d<4$$?

$$1) \frac{1}{c} + \frac{1}{d} > \frac{1}{2}$$
$$2) (\frac{1}{a})+(\frac{1}{b})+(\frac{1}{c})+(\frac{1}{d})=1$$

#2
fraction of 1/a+1/b+1/c+1/d = 1
possible when all a=b=c=d are equal
so in sufficient to say that d<4
IMO A

Hi, Archit3110 !

Please check the parts in red.

Regards,
Fabio.

Fabio
understood thanks.. GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5693
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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MathRevolution wrote:
[GMAT math practice question]

(inequality) If $$x, y, z$$ are positive integers, is $$xyz ≥ 64$$?

$$1) xy ≥ yz ≥ zx ≥ 16$$
$$2) x+y+z=64$$

x,y,z are +ve integers

#1
$$1) xy ≥ yz ≥ zx ≥ 16$$

x=y=z; then only we can have $$1) xy ≥ yz ≥ zx ≥ 16$$
so x=y=z=4 atleast
so $$xyz ≥ 64$$; sufficient
#2

$$2) x+y+z=64$$
since x,y,z are + ve integers
so x= 62, y=z=1
so insufficient
IMO A

Originally posted by Archit3110 on 06 Feb 2019, 09:12.
Last edited by Archit3110 on 08 Feb 2019, 05:14, edited 1 time in total.
GMATH Teacher P
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Archit3110 wrote:
Fabio
understood thanks.. I am glad to know it, Archit3110!

I found your post by coincidence... if you want to "mention" me, so that I know I have a post of yours like this one, do not forget to use my "nickname" fskilnik , please!

("Fabio" is related to someone with no posts, who left this forum in 2009... I have checked that one minute ago.)

Regards and success in your studies!
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

If $$a>b>c>d>0$$, is $$d<4$$?

$$1) \frac{1}{c} + \frac{1}{d} > \frac{1}{2}$$
$$2) (\frac{1}{a})+(\frac{1}{b})+(\frac{1}{c})+(\frac{1}{d})=1$$

=>

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.
The original condition $$a>b>c>d>0$$ is equivalent to $$0 < \frac{1}{a} < \frac{1}{b} < \frac{1}{c} < \frac{1}{d}$$. The question asks if $$d < 4$$. This is equivalent to asking if $$\frac{1}{d} > \frac{1}{4}$$.

By condition $$1, \frac{1}{d} > \frac{1}{4}$$ since $$\frac{1}{c} < \frac{1}{d}$$. So, $$d < 4$$. Condition 1) is sufficient.

Condition 2)
Since $$0 < \frac{1}{a} < \frac{1}{b} < \frac{1}{c} < \frac{1}{d}$$ and $$(\frac{1}{a})+(\frac{1}{b})+(\frac{1}{c})+(\frac{1}{d})=1$$, we have $$\frac{1}{a}<\frac{1}{d}$$, $$\frac{1}{b}<\frac{1}{d}, \frac{1}{c}<\frac{1}{d}$$ and $$\frac{1}{a} +\frac{1}{b} + \frac{1}{c} + \frac{1}{d} < \frac{1}{d} +\frac{1}{d} +\frac{1}{d} + \frac{1}{d} = \frac{4}{d}.$$
Therefore, $$1 < \frac{4}{d}$$ and $$d < 4$$.
Condition 2) is sufficient.

Note: This question is a CMT4(B) question: condition 1) is easy to work with and condition 2) is hard. For CMT4(B) questions, D is most likely to be the answer.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(absolute value) $$3x+4y=?$$

$$1) 2|x|+3|y|=0$$
$$2) 3|x|+2|y|=0$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(inequality) If $$x, y, z$$ are positive integers, is $$xyz ≥ 64$$?

$$1) xy ≥ yz ≥ zx ≥ 16$$
$$2) x+y+z=64$$

=>

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 ($$x, y, z$$) and $$0$$ equations, E is most likely to be the answer. So, we should consider each condition on its own first. As condition 1) includes 3 equations, we should consider it first.

Condition 1)
Since $$xy ≥ 16, yz ≥ 16$$, and $$zx ≥ 16$$, we have $$(xyz)^2 ≥ 16^3$$ or $$xyz ≥ 64$$.
Condition 1) is sufficient.

Condition 2)
If $$x = 20, y = 20$$ and $$z = 24$$, then $$xyz = 9600 ≥ 64$$ and the answer is ‘yes’.
If $$x = 1, y = 1$$ and $$z = 62$$, then $$xyz = 62 < 64$$ and the answer is ‘no’.
Since condition 2) does not yield a unique answer, condition 2) is not sufficient.

This is a CMT(Common Mistake Type) 4(A) question. If a question is from one of the key question areas and C should be the answer, CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(function) Does $$f(x)=ax^4+bx^3+cx^2+dx+e$$ have ($$x-2$$) as a factor?

$$1) f(2)=0$$
$$2) f(-2)=0$$
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Manager  G
Joined: 15 Nov 2015
Posts: 158
Location: India
GMAT 1: 700 Q47 V39
GPA: 3.7

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MathRevolution wrote:
[GMAT math practice question]

(absolute value) $$3x+4y=?$$

$$1) 2|x|+3|y|=0$$
$$2) 3|x|+2|y|=0$$

IMO D

Modulus of any variable is a positive number.

if sum of 2 modulus variables is zero then it means the variable has a value zero

therefore 3x+4y = 0

Hence D
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5693
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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MathRevolution wrote:
[GMAT math practice question]

(absolute value) $$3x+4y=?$$

$$1) 2|x|+3|y|=0$$
$$2) 3|x|+2|y|=0$$

#1 :
$$1) 2|x|+3|y|=0$$
whenx=y=0 sufficient
#2
again at x=y=0. sufficient
IMO D
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(absolute value) $$3x+4y=?$$

$$1) 2|x|+3|y|=0$$
$$2) 3|x|+2|y|=0$$

=>
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.

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

Condition 1)
Since $$|x| ≥ 0, |y| ≥ 0$$ and $$2|x| + 3|y| = 0,$$ we have $$x = y = 0.$$
Therefore, $$3x + 4y = 0.$$
Condition 1) is sufficient.

Condition 2)
Since $$|x| ≥ 0, |y| ≥ 0$$ and $$3|x| + 2|y| = 0$$, we have $$x = y = 0.$$
Therefore, $$3x + 4y = 0$$. Condition 2) is sufficient.

FYI: Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(function) Does $$f(x)=ax^4+bx^3+cx^2+dx+e$$ have ($$x-2$$) as a factor?

$$1) f(2)=0$$
$$2) f(-2)=0$$

=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The statement that $$f(x)=ax^4+bx^3+cx^2+dx+e$$ has $$(x-2)$$ as a factor is equivalent to saying $$f(x) = (x-2)g(x)$$ for some function $$g(x)$$. This is equivalent to the requirement that $$f(2) = 0$$.

Thus condition 1) is sufficient.

Condition 2)
If $$f(x) = (x-2)(x+2)(x-1)(x+1)$$, then $$f(x)$$ has $$x-2$$ as a factor, The answer is ‘yes’.
If $$f(x) = x(x+2)(x+1)(x-1)$$, then $$f(x)$$ doesn’t have $$x-2$$ as a factor. The answer is ‘no’.
Since condition 2) does not yield a unique answer, condition 2) is not sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(geometry) What is the area of a right triangle?

1) The length of one side is $$3$$
2) The length of one side is $$4$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(inequality) Is $$3(a-b)>0$$?

$$1) a^3>b^3$$
$$2) a>b$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(geometry) What is the area of a right triangle?

1) The length of one side is $$3$$
2) The length of one side is $$4$$

=>

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 questions about triangles involve three variables, E is most likely to be the answer.

Conditions 1) & 2)
If the sides given are legs, then the area of the right triangle is $$(\frac{1}{2})*3*4 = 6.$$
If one leg has length $$3$$ and the hypotenuse has length $$4$$, then, by Pythagoras’ theorem, the length of the other leg is $$\sqrt{(4^2 – 3^2)} = √7$$, and the area of the triangle is $$(\frac{1}{2})*3*√7 =\frac{(3√7)}{2}.$$
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(algebra) $$x^3-y^3=?$$

$$1) x-y=0$$
$$2) |x|=|y|$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(inequality) Is $$3(a-b)>0$$?

$$1) a^3>b^3$$
$$2) a>b$$

=>

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.

Asking if $$3(a-b)>0$$ is equivalent to asking if $$a – b > 0$$, or, equivalently, if $$a > b.$$
Thus, condition 2) is sufficient.

Condition 1)
$$a^3>b^3$$
$$=> a^3-b^3 > 0$$
$$=> (a-b)(a^2+ab+b^2) > 0$$
$$=> a - b > 0$$ since $$a^2+ab+b^2 > 0$$
$$=> a > b$$
Thus, condition 1) is sufficient too.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(absolute value) Is $$|a|<1$$?

$$1) a^2<1$$
$$2) \frac{1}{(1-a^2)}>0$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8425
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(algebra) $$x^3-y^3=?$$

$$1) x-y=0$$
$$2) |x|=|y|$$

=>

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.

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

$$x^3-y^3 = (x-y)(x^2+xy+y^2)$$

Condition 1)
If $$x – y = 0$$, then $$x^3-y^3 = (x-y)(x^2+xy+y^2) = 0.$$
Thus, condition 1) is sufficient.

Condition 2)
If $$x = 1$$ and $$y = 1$$, then $$x^3-y^3 = 1 – 1 = 0.$$
If $$x = 1$$ and $$y = -1$$, then $$x^3-y^3 = 1 –(-1) = 2.$$
Condition 2) is not sufficient since it does not yield a unique solution.

_________________ Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 15 Feb 2019, 01:18

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