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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6398
GMAT 1: 760 Q51 V42
GPA: 3.82

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03 Oct 2018, 18:30

Hello, I am Max Lee, Founder and Lead Math Tutor at Math Revolution.

My other discussions you may be interested in:

Thank you all - good luck on the GMAT and look forward to seeing you in the DS forum!
- Max Lee.

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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 $99 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 Discount Codes Veritas Prep GMAT Discount Codes Optimus Prep Discount Codes Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6398 GMAT 1: 760 Q51 V42 GPA: 3.82 Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] Show Tags Updated on: 16 Oct 2018, 00:29 [Math Revolution GMAT math practice question] (absolute value) If $$|x+1|=2|x-1|, x=?$$ $$1) x<1$$ $$2) x>0$$ _________________ 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$99 for 3 month Online Course"
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Originally posted by MathRevolution on 15 Oct 2018, 01:40.
Last edited by MathRevolution on 16 Oct 2018, 00:29, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6398
GMAT 1: 760 Q51 V42
GPA: 3.82

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16 Oct 2018, 00:29
[Math Revolution GMAT math practice question]

Is the sum of $$7$$ different positive integers greater than or equal to $$48$$?

1) Their median is $$9$$
2) The largest number is $$12$$
_________________

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 $99 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: 6398 GMAT 1: 760 Q51 V42 GPA: 3.82 Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] Show Tags 17 Oct 2018, 00:35 MathRevolution wrote: [Math Revolution GMAT math practice question] (absolute value) If $$|x+1|=2|x-1|, x=?$$ $$1) x<1$$ $$2) x>0$$ => 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. 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 $$|x+1|=2|x-1|$$ is equivalent to $$x=\frac{1}{3}$$ or $$x=3$$ as shown below: $$|x+1|=2|x-1|$$ $$=> |x+1|^2=(2|x-1|)^2$$ $$=> (x+1)^2=4(x-1)^2$$ $$=> x^2+2x+1=4(x^2-2x+1)$$ $$=> x^2+2x+1=4x^2-8x+4$$ $$=> 3x^2-10x+3 = 0$$ $$=> (3x-1)(x-3) = 0$$ $$=> 3x-1=0$$ or $$x-3 = 0$$ $$=> x=\frac{1}{3}$$ or $$x=3$$ Thus, condition 1) is sufficient since it gives a unique solution. Condition 2) is not sufficient, since it allows both possible solutions. Therefore, A is the answer. Answer: A _________________ 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6398
GMAT 1: 760 Q51 V42
GPA: 3.82

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17 Oct 2018, 00:37
[Math Revolution GMAT math practice question]

(set) If $$|X|$$ is the number of elements in set $$X$$, and $$“∪”$$ is the union and $$“∩”$$ is the intersection of $$2$$ sets, what is the value of $$|A∩B|$$?

$$1) |A∪B|＝50$$
$$2) |B|=40$$
_________________

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 $99 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: 6398 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] Show Tags 18 Oct 2018, 01:10 MathRevolution wrote: [Math Revolution GMAT math practice question] Is the sum of $$7$$ different positive integers greater than or equal to $$48$$? 1) Their median is $$9$$ 2) The largest number is $$12$$ => 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. Since we have many variables (x1, x2, …, x7) 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) & 2) We write the numbers as x1≤x2≤x3≤x4≤x5≤x6≤x7. Then x4 is their median. From condition 1), x4 = 9 and the smallest possible number is 1 + 2 + 3 + 9 + 10 + 11 + 12 = 48. Therefore, the answer is ‘yes’. Both conditions 1) & 2) together are sufficient. 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) Since we didn’t use condition 2) in the above argument, condition 1) is sufficient on its own. By condition 1), x4 = 9 and the smallest possible number is 1 + 2 + 3 + 9 + 10 + 11 + 12 = 48. Therefore, the answer is ‘yes’. Condition 2) When the numbers are 6,7,8,9,10,11,12, their sum is 6 + 7 + 8 + 9 + 10 + 11 + 12 = 63 > 48, and the answer is ‘yes’. When the numbers are 6,7,8,9,10,11,12, their sum is 1 + 2 + 3 + 4 + 5 + 6 + 12 = 33 < 48, and the answer is ‘no’. Since we don’t obtain a unique answer, condition 2) is not sufficient. Therefore, A is the answer. Answer: A 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. _________________ 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6398
GMAT 1: 760 Q51 V42
GPA: 3.82

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18 Oct 2018, 01:11
[Math Revolution GMAT math practice question]

(number property) If $$a$$ and $$b$$ are positive integers such that when $$a$$ is divided by $$b$$, the remainder is $$10$$, what is the value of $$b$$?

$$1) b>10$$
$$2) b<12$$
_________________

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 $99 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: 6398 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] Show Tags 19 Oct 2018, 01:03 MathRevolution wrote: [Math Revolution GMAT math practice question] (set) If $$|X|$$ is the number of elements in set $$X$$, and $$“∪”$$ is the union and $$“∩”$$ is the intersection of $$2$$ sets, what is the value of $$|A∩B|$$? $$1) |A∪B|＝50$$ $$2) |B|=40$$ => 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. Note that $$|A∪B| = |A| + |B| - |A∩B|$$ and $$|A∩B| = |A| + |B| - |A∪B|$$. Since we have $$4$$ variables$$(|A∩B|, |A|, |B|, |A∪B|)$$ and $$1$$ equation $$(|A∩B| = |A| + |B| - |A∪B|)$$, 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) & 2) Suppose $$A$$ and $$B$$ are disjoint sets, $$|A∪B| = 50, |A| = 10,$$ and $$|B| = 40.$$ Then $$|A∩B| = |A| + |B| - |A∪B| = 0.$$ Suppose $$A$$ contains $$B, |A∪B| = 50, |A| = 50,$$ and $$|B| = 40.$$ Then $$|A∩B| = |A| + |B| - |A∪B| = 40.$$ Since we don’t have a unique solution, both conditions together are not sufficient. Therefore, E is the answer. Answer: 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. "Only$99 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: 6398
GMAT 1: 760 Q51 V42
GPA: 3.82

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19 Oct 2018, 01:04
[Math Revolution GMAT math practice question]

(inequality) Is $$1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}$$?

$$1) x>0$$
$$2) x<1$$
_________________

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 $99 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: 6398 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] Show Tags 21 Oct 2018, 18:51 MathRevolution wrote: [Math Revolution GMAT math practice question] (number property) If $$a$$ and $$b$$ are positive integers such that when $$a$$ is divided by $$b$$, the remainder is $$10$$, what is the value of $$b$$? $$1) b>10$$ $$2) b<12$$ => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. By the quotient-remainder theorem, we can write $$a = b * q + 10$$, where the remainder $$10$$ is less than $$b$$, that is, $$b > 10$$. Thus, condition 2) $$“b<12”$$ is sufficient since it gives the unique solution $$b = 11$$. Note: Condition 1) does not give a unique solution. For example, we might have $$b = 11$$ or $$b = 12$$. Thus, it 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$99 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: 6398
GMAT 1: 760 Q51 V42
GPA: 3.82

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21 Oct 2018, 18:53
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(inequality) Is $$1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}$$?

$$1) x>0$$
$$2) x<1$$

=>

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.

The question $$1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}$$ is equivalent to $$0 < x < 1$$ as shown below:

For $$x ≠1$$,
=>$$1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}$$
$$=> (1+x+x^2+x^3+x^4+x^5+x^6)(1-x)^2< (1-x)$$
$$=> (1 - x^7)(1 - x) < 1 – x$$
$$=> 1 - x^7 – x +x^8 < 1 - x$$
$$=> - x^7 + x^8 < 0$$
$$=> x^7( x – 1 ) < 0$$
$$=> x( x – 1 ) < 0$$
$$=> 0 < x < 1$$

Since both conditions must be applied together to obtain this inequality, both conditions 1) & 2) are sufficient, when applied together.

_________________

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 $99 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: 6398 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] Show Tags 22 Oct 2018, 01:30 [Math Revolution GMAT math practice question] (inequality) Is $$x^3-y^>x^2+xy+y^2$$? $$1) x > y + 1$$ $$2) 0 < y < x$$ _________________ 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS &nbs [#permalink] 22 Oct 2018, 01:30
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