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# Math Revolution DS Expert - Ask Me Anything about GMAT DS

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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20 Jan 2019, 17:39
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(absolute value) Is $$ab<0$$?

$$1) |a+b| = - ( a + b )$$
$$2) |a+b| + 1 = |a| + |b|$$

=>

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.

You should remember that the inequality $$|x+y| < |x| + |y|$$ is equivalent to the inequality $$xy < 0.$$

Condition 2) tells us that $$|a+b| + 1 = |a| + |b|.$$ Thus, $$|a + b| < |a| + |b|$$ and $$ab < 0$$.
Thus, condition 2) is sufficient.

Condition 1)
If $$a = -2$$ and $$b = 1$$, then the answer is ‘yes’.
If $$a = -1$$ and $$b = -1$$, then the answer is ‘no’.
Since it does not yield a unique solution, condition 1) is not sufficient.

_________________

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.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 21 Jan 2019, 00:14 [Math Revolution GMAT math practice question] (number properties) $$n$$ is a $$3$$ digit integer of the form $$ab6$$. Is $$n$$ divisible by $$4$$? 1) $$a+b$$ is an even integer 2) $$ab$$ is an odd integer. _________________ 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. "Only$149 for 3 month Online Course"
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21 Jan 2019, 04:24
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number properties) $$n$$ is a $$3$$ digit integer of the form $$ab6$$. Is $$n$$ divisible by $$4$$?

1) $$a+b$$ is an even integer
2) $$ab$$ is an odd integer.

$$n = \left\langle {ab6} \right\rangle \,\,\,\, \Rightarrow \left\{ \matrix{ \,n > 0\,\,\,\left( {{\rm{implicitly}}} \right) \hfill \cr \,a \in \left\{ {1,2,3, \ldots ,9} \right\} \hfill \cr \,b \in \left\{ {0,1,2,3, \ldots ,9} \right\} \hfill \cr} \right.$$

$${{\left\langle {ab6} \right\rangle } \over 4}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}$$

$$\left( 1 \right)\,\,\,a + b = {\rm{even}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,ab = {\rm{odd}}\,\,\, \Rightarrow \,\,\,b = {\rm{odd}}\,\,\, \Rightarrow \,\,\,\left\langle {b6} \right\rangle \in \left\{ {16,36,56,76,96} \right\}\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,$$

The correct answer is therefore (B).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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21 Jan 2019, 06:44
MathRevolution wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(absolute value) Is $$ab<0$$?

$$1) |a+b| = - ( a + b )$$
$$2) |a+b| + 1 = |a| + |b|$$

=>

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.

You should remember that the inequality $$|x+y| < |x| + |y|$$ is equivalent to the inequality $$xy < 0.$$

Condition 2) tells us that $$|a+b| + 1 = |a| + |b|.$$ Thus, $$|a + b| < |a| + |b|$$ and $$ab < 0$$.
Thus, condition 2) is sufficient.

Condition 1)
If $$a = -2$$ and $$b = 1$$, then the answer is ‘yes’.
If $$a = -1$$ and $$b = -1$$, then the answer is ‘no’.
Since it does not yield a unique solution, condition 1) is not sufficient.

MathRevolution

You should remember that the inequality $$|x+y| < |x| + |y|$$ is equivalent to the inequality $$xy < 0.$$

BUT HERE #2
$$2) |a+b| + 1 = |a| + |b|$$

ITS NOT > BUT = .. SO HOW IS THAT RELATION VALID?

IMO

#2:
|a+b| + 1 = |a| + |b|[/m]

this can be written as:
-a-b+1 = a+b
1= 2 ( a+b)
a+b= 1/2
this would be possible when either of values of a & b are either + & -ve or if one of the values of a & b is 0 and other is 1/2 ; so insufficient

combining 1 & 2 :
- ( a + b )+1 = |a| + |b|
or say 1/2 = a+b
again this would be possible when either of values of a & b are either + & -ve or if one of the values of a & b is 0 and other is 1/2 ; so insufficient

IMO E
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21 Jan 2019, 23:29
[Math Revolution GMAT math practice question]

(absolute values) If $$y=|x-1|+|x+1|,$$ then $$y=$$?

$$1) x>-1$$
$$2) x<1$$
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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.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" SVP Joined: 18 Aug 2017 Posts: 1775 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 22 Jan 2019, 02:42 MathRevolution wrote: [Math Revolution GMAT math practice question] (number properties) $$n$$ is a $$3$$ digit integer of the form $$ab6$$. Is $$n$$ divisible by $$4$$? 1) $$a+b$$ is an even integer 2) $$ab$$ is an odd integer. given n= ab6 is it divisible by 4 any no which is two times divisible by 2 would be divisible by 4 #1 a+b is an even integer here a,b can both be odd or even so in sufficient #2 ab is an odd integer means both ab are odd integers so ab6 is not divisible by 4 sufficient IM O B _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. SVP Joined: 18 Aug 2017 Posts: 1775 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 22 Jan 2019, 02:47 MathRevolution wrote: [Math Revolution GMAT math practice question] (absolute values) If $$y=|x-1|+|x+1|,$$ then $$y=$$? $$1) x>-1$$ $$2) x<1$$ IMO e would be sufficeint #1: x>-1 ; x can be any no from -1 to infinity #2 x<1 : x can be any value <1 to infinity from 1 & 2 range of 1>x>-1 ; x can be 0 ,0.5 , -0.5 .. combining both we get answer different values of y IMO E _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 730 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 22 Jan 2019, 06:14 MathRevolution wrote: [Math Revolution GMAT math practice question] (absolute values) If $$y=|x-1|+|x+1|,$$ then $$y=$$? $$1) x>-1$$ $$2) x<1$$ $$y = \left| {x - 1} \right| + \left| {x + 1} \right|$$ $$? = y$$ $$\left( 1 \right)\,\,x > - 1\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,? = 2\, \hfill \cr \,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,? = 4\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,x < 1\,\,\,\left\{ \matrix{ \,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,? = 2\, \hfill \cr \,{\rm{Take}}\,\,x = - 2\,\,\,\, \Rightarrow \,\,\,? = 4\, \hfill \cr} \right.$$ $$\left( {1 + 2} \right) - 1 < x < 1\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,\left| {x - 1} \right| = 1 - x \hfill \cr \,\left| {x + 1} \right| = x + 1 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 2$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 730 Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 22 Jan 2019, 06:19 Archit3110 wrote: from 1 & 2 range of 1>x>-1 ; x can be 0 ,0.5 , -0.5 .. combining both we get answer different values of y Hi, Archit3110 ! Please read my solution above, and take into account that -1<x<1 implies: (a) -1<x hence x+1 > 0 , hence |x+1| = x+1 (b) x<1 hence x-1 < 0 , hence |x-1| = -(x-1) = 1-x Then y = (x+1) + (1-x) = 2 , therefore x will have infinite possible values (between -1 and 1), but y will be always 2 (when -1<x<1). I hope I could help you! 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 Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 23 Jan 2019, 00:06 MathRevolution wrote: [Math Revolution GMAT math practice question] (number properties) $$n$$ is a $$3$$ digit integer of the form $$ab6$$. Is $$n$$ divisible by $$4$$? 1) $$a+b$$ is an even integer 2) $$ab$$ is an odd 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. We can determine whether $$a$$ number is divisible by $$4$$ from its final two digits. Numbers with the final digits $$16, 36, 56, 76$$ and $$96$$ are divisible by $$4$$ and those with final digits $$06, 26, 46, 66$$ and $$88$$ are not divisible by $$4$$. Thus, asking whether $$n$$ is divisible by $$4$$ is equivalent to asking whether $$b$$ is odd. Since it implies that both $$a$$ and $$b$$ are odd integers, condition 2) is sufficient. Condition 1) There are two cases to consider. If $$a$$ is an even integer and $$b$$ is an odd integer, the answer is ‘yes’. If $$a$$ is an odd integer and $$b$$ is an even integer, the answer is ‘no’. Since it does not yield a unique solution, condition 1) is not sufficient. Therefore, B is the answer. Answer: B _________________ 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. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
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GPA: 3.82

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23 Jan 2019, 00:08
[Math Revolution GMAT math practice question]

(algebra) $$x=$$?

$$1) x^3-x=0$$
$$2) x=-x$$
_________________

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.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 24 Jan 2019, 05:24 MathRevolution wrote: [Math Revolution GMAT math practice question] (absolute values) If $$y=|x-1|+|x+1|,$$ then $$y=$$? $$1) x>-1$$ $$2) x<1$$ => 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. There are three ranges of values of x to consider. If $$x > 1$$, then $$y = | x – 1 | + | x + 1 | = x – 1 + x + 1 = 2x$$ and we don’t have a unique value of $$y$$. If $$-1 ≤ x ≤ 1$$, then $$y = | x – 1 | + | x + 1 | = - ( x – 1 ) + x + 1 = 2$$ and we have a unique value of $$y$$. If $$x < 1$$, then $$y = | x – 1 | + | x + 1 | = -( x – 1 ) – ( x + 1 ) = -2x$$ and we don’t have a unique value of $$y$$. Asking for the value of $$y$$ is equivalent asking if $$-1 ≤ x ≤ 1$$. Both conditions yield the inequality $$-1 < x < 1$$, when applied together. Therefore, both conditions are sufficient, when taken together. In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient. Therefore, C is the answer. Answer: C _________________ 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. "Only$149 for 3 month Online Course"
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24 Jan 2019, 05:27
[Math Revolution GMAT math practice question]

If $$x$$ and $$y$$ are non-zero numbers and $$x≠±y$$, then $$\frac{( x^2 + y^2 )}{( x^2 - y^2 )}=?$$

$$1) |\frac{x}{y}|=\frac{1}{3}$$
$$2) y=-3x$$
_________________

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 25 Jan 2019, 01:28 MathRevolution wrote: [Math Revolution GMAT math practice question] (algebra) $$x=$$? $$1) x^3-x=0$$ $$2) x=-x$$ => 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) $$x^3-x = 0$$ $$=> x(x^2-1) = 0$$ $$=> x(x+1)(x-1) = 0$$ $$=> x = 0, x = -1$$ or $$x = 1.$$ Since it does not yield a unique solution, condition 1) is not sufficient. Condition 2) $$x = -x$$ $$=> 2x = 0$$ $$=> x = 0.$$ Since it gives a unique solution, condition 2) is sufficient. Therefore, B is the answer. Answer: B _________________ 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. "Only$149 for 3 month Online Course"
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25 Jan 2019, 01:29
[Math Revolution GMAT math practice question]

(exponents) $$m+n=?$$

$$1) (4^m)(2^n)=16$$
$$2) (2^{2m})(4^n)=64$$
_________________

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.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 27 Jan 2019, 17:23 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x$$ and $$y$$ are non-zero numbers and $$x≠±y$$, then $$\frac{( x^2 + y^2 )}{( x^2 - y^2 )}=?$$ $$1) |\frac{x}{y}|=\frac{1}{3}$$ $$2) y=-3x$$ => 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 question asks for the value of $$\frac{( x^2 + y^2 )}{( x^2 - y^2 )}= ( (\frac{x}{y})^2 + 1 ) / (\frac{x}{y})^2 – 1 ).$$ When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. Condition 1) Since $$|\frac{x}{y}|=\frac{1}{3}, \frac{x}{y} = ±(\frac{1}{3})$$, and $$\frac{( x^2 + y^2 )}{( x^2 - y^2 )}= ( (\frac{x}{y})^2 + 1 ) / ( (\frac{x}{y})^2 – 1 ) = ( (\frac{1}{3})^2 + 1 ) / ( (\frac{1}{3})^2 – 1) = (\frac{1}{9} + 1)/(\frac{1}{9}-1) = (\frac{10}{9})/(-\frac{8}{9}) = -\frac{10}{8} = -\frac{5}{4}.$$ Condition 1) is sufficient since it gives a unique solution. Condition 2) Since $$y = -3x, \frac{x}{y} = -\frac{1}{3}$$, and $$\frac{( x^2 + y^2 )}{( x^2 - y^2 )}= ( (\frac{x}{y})^2 + 1 ) / ( (\frac{x}{y})^2 – 1 ) = ( (-\frac{1}{3})^2 + 1 ) / ( (-\frac{1}{3})^2 – 1) = (\frac{1}{9} + 1)/(\frac{1}{9}-1) = (\frac{10}{9})/(-\frac{8}{9}) = -\frac{10}{8} = -\frac{5}{4}.$$ Condition 2) is sufficient since it gives a unique solution. Therefore, the answer is D. Answer: D 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. _________________ 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. "Only$149 for 3 month Online Course"
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27 Jan 2019, 17:25
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(exponents) $$m+n=?$$

$$1) (4^m)(2^n)=16$$
$$2) (2^{2m})(4^n)=64$$

=>

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.

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

Condition 2) is equivalent to $$m + n = 3$$ as shown below:
$$(2^{2m})(4^n)=64$$
$$=> (2^{2m})(2^{2n})=2^6$$
$$=> 2^{2m+2n}=2^6$$
$$=> 2m+2n = 6$$
$$=> m + n = 3$$
Condition 2) is sufficient.

Condition 1)
$$(4^m)(2^n)=16$$
$$=> (2^{2m})(2^n)=2^4$$
$$=> 2^{2m+n}=2^4$$
$$=> 2m+n = 4$$
If $$m = 1$$ and $$n =2$$, then $$m + n = 3$$.
If $$m = 0$$ and $$n = 4,$$ then $$m + n = 4.$$
Since it does not yield a unique solution, condition 1) is not sufficient.

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 28 Jan 2019, 00:37 [GMAT math practice question] (number properties) If $$n$$ is positive integer, is $$4^n+n^2+1$$ divisible by $$2$$? 1) $$n$$ is a multiple of $$4$$ 2) $$n$$ is a multiple of $$6$$ _________________ 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. "Only$149 for 3 month Online Course"
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29 Jan 2019, 00:00
[GMAT math practice question]

(function) If operation $$#$$ represents one of addition, subtraction, multiplication, and division, what is the value of $$0#1$$?

$$1) 2#1 = 2$$
$$2) 4#2 = 2$$
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Updated on: 29 Jan 2019, 05:13
MathRevolution wrote:
[GMAT math practice question]

(function) If operation $$#$$ represents one of addition, subtraction, multiplication, and division, what is the value of $$0#1$$?

$$1) 2#1 = 2$$
$$2) 4#2 = 2$$

#1
2#1=2
# can be multiplication or division so sufficient
as doing both operations we would get answer as 0 for $$0#1$$

#2
4#2 =2
# can be subtraction of division; in sufficient

IMO A
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Originally posted by Archit3110 on 29 Jan 2019, 02:07.
Last edited by Archit3110 on 29 Jan 2019, 05:13, edited 1 time in total.

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