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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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.

Therefore, the answer is B.
Answer: B


MathRevolution

QUOTING YOUR LINE :
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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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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[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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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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

Originally posted by MathRevolution on 23 Jan 2019, 01:06.
Last edited by MathRevolution on 13 Aug 2021, 03:17, edited 1 time in total.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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[Math Revolution GMAT math practice question]

(algebra) \(x=\)?

\(1) x^3-x=0\)
\(2) x=-x\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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

Originally posted by MathRevolution on 24 Jan 2019, 06:24.
Last edited by MathRevolution on 26 Jan 2022, 03:46, edited 1 time in total.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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[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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Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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

Originally posted by MathRevolution on 25 Jan 2019, 02:28.
Last edited by MathRevolution on 26 Jan 2022, 03:47, edited 1 time in total.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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[Math Revolution GMAT math practice question]

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

\(1) (4^m)(2^n)=16\)
\(2) (2^{2m})(4^n)=64\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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.

Originally posted by MathRevolution on 27 Jan 2019, 18:23.
Last edited by MathRevolution on 04 Feb 2022, 01:22, edited 1 time in total.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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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.

Therefore, the answer is B.
Answer: B

Originally posted by MathRevolution on 27 Jan 2019, 18:25.
Last edited by MathRevolution on 04 Feb 2022, 01:22, edited 1 time in total.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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[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 \(6\)
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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[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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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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

Originally posted by Archit3110 on 29 Jan 2019, 03:07.
Last edited by Archit3110 on 29 Jan 2019, 06:13, edited 1 time in total.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
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