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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
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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06 Apr 2020, 02:51
1
MathRevolution wrote:
[GMAT math practice question]

(Function) What is the value of $$f(2019)$$?

1) $$f(3) = 5$$

2) $$f(x+2) = \frac{f(x) - 1}{f(x) + 1}$$

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Since we have many variables to determine the function f(x), E is most likely 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)
Since $$f(3) = 5$$, we have:

$$f(5) = \frac{(f(3) - 1) }{ (f(3) + 1)}$$

$$f(5) = \frac{(5 - 1) }{ (5 + 1)}$$

$$f(5) = \frac{4}{6} = \frac{2}{3}.$$

Then we have:
$$f(7) = \frac{(f(5) - 1) }{ (f(5) + 1) }$$

$$f(7) = ((\frac{2}{3}) - 1) / ((\frac{2}{3}) + 1)$$

$$f(7) = -(\frac{1}{3}) / (\frac{5}{3}) = -(\frac{1}{5}).$$

We have:
$$f(9) = \frac{(f(7) - 1) }{ (f(7) + 1)}$$

$$f(9) = (-(\frac{1}{5}) - 1)/(-(\frac{1}{5}) + 1)$$

$$f(9) = -(\frac{6}{5}) / (\frac{4}{5}) = -(\frac{3}{2}).$$

We have:
$$f(11) = \frac{(f(9) - 1) }{ (f(9) + 1)}$$

$$f(11) = (-(\frac{3}{2}) - 1)) / (-(\frac{3}{2}) + 1)$$

$$f(11) = -(\frac{5}{2}) / -(\frac{1}{2}) = 5.$$

Since $$f(3) = f(11)$$, we have $$f(8k - 5) = 5.$$

Then we have:
$$f(8k-3) = \frac{2}{3}$$, $$f(8k-1) = -(\frac{1}{5})$$ and $$f(8k+1) = -(\frac{3}{2}).$$

$$f(2007) = f(8*251-1) = -(\frac{1}{5}).$$

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
_________________
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 $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 06 Apr 2020, 02:52 1 MathRevolution wrote: [GMAT math practice question] (Statistics) x1, x2, …, x10 are real numbers. a1 = x1, a2 is defined as the average of {x1, x2}, a3 as the average of {x1, x2, x3}, ….., a10 as the average of {x1, x2,…,x10}. What is the value of x10? 1) a1 = 5 2) an+1 = an+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. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Since we have 10 variables (x1, x2,…,x10) and 0 equations, E is most likely 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) a10 = (x1 + x2 + … + x10) / 10 and a9 = (x1 + x2 + … + x9) / 9 x10 = 10a10 – 9a9 a10 = a1 + 9*2 = 5 + 18 = 23. a9 = a1 + 8*2 = 5 + 16 = 21. x10 = 10a10 – 9a9 = 10*23 – 9*21 = 230 – 189 = 41. Since both conditions together yield a unique solution, they 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. However, each condition alone does not provide enough information on its own, and therefore neither condition alone is sufficient. Therefore, C is the answer. Answer: C 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$79 for 1 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: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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06 Apr 2020, 02:53
1
[GMAT math practice question]

(Number Properties) What is the solution of ($$x, y$$)’s satisfying $$\sqrt{500} = \sqrt{x} +\sqrt{y}$$ and $$x < y$$?

1) $$x$$ and $$y$$ are positive integers.
2) $$x = 5t^2$$ with $$0 < t < 5.$$
_________________
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 $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 07 Apr 2020, 03:27 1 [GMAT math practice question] (Inequalities) What is the summation of the maximum and the minimum values of $$6x - 37$$? 1) $$x$$ satisfies $$2 < \sqrt{3(x-4)} ≤ 5$$. 2) $$x$$ is an 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$79 for 1 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: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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09 Apr 2020, 18:08
1
MathRevolution wrote:
[GMAT math practice question]

(Inequalities) What is the summation of the maximum and the minimum values of $$6x - 37$$?

1) $$x$$ satisfies $$2 < \sqrt{3(x-4)} ≤ 5$$.

2) $$x$$ is an 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Condition 1)

$$2 < \sqrt{3(x-4)} ≤ 5$$

$$=> 4 < 3(x - 4) ≤ 25$$ (squaring)

$$=> \frac{4}{3} < x - 4 ≤ \frac{25}{3}$$ (dividing by $$3$$)

$$=> \frac{16}{3} < x ≤ \frac{37}{3}$$ (adding $$4$$)

Then even though x has a maximum value, x doesn’t have a minimum value.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)

Since condition 2) does not yield a unique solution; obviously, it is not sufficient.

Conditions 1) & 2)

Since we have $$\frac{16}{3} < x ≤ \frac{37}{3}$$ from condition 1), the possible values of $$x$$ are $$6, 7, 8, …, 12.$$

Then the maximum and minimum values of $$x$$ are $$6$$ and $$12$$, respectively.

Thus, their sum is $$6 + 12 = 18.$$

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.

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.
_________________
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 $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 09 Apr 2020, 18:09 1 [GMAT math practice question] (Inequalities) $$M$$ denotes the maximum of $$x$$ and m the minimum of $$x$$. What is the integer part of $$\sqrt{M-m}?$$ 1) The integer part of $$\sqrt{3x-2}$$ is $$9.$$ 2) $$x$$ is a positive 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$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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10 Apr 2020, 16:11
1
MathRevolution wrote:
[GMAT math practice question]

(Inequalities) What is the value of ($$x, y$$) satisfying $$\sqrt{x^2+4y}$$, with the integer portion equaling $$5$$.

1) $$x$$ and $$y$$ are the numbers of eyes on two dice.

2) $$x$$ and $$y$$ are positive integers.

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Since the integer part of $$\sqrt{x^2+4y},$$ we have

$$5≤\sqrt{x^2+4y} < 6$$

=> $$25≤\sqrt{x^2 + 4y} < 36$$

$$X = 1, y = 6$$ and $$x = 2, y = 6$$ are possible solutions.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
_________________
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 $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 10 Apr 2020, 16:12 1 [GMAT math practice question] (Number Properties) $$a, b,$$and $$c$$ are $$3$$ different unit numbers. What is the $$3$$-digit number $$abc$$? 1) The $$5$$-digit number $$ababc$$ is a multiple of $$12$$. 2) The $$2$$-digit number $$ab$$ is equal to $$c^2$$. _________________ 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$79 for 1 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: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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17 Apr 2020, 18:39
1
MathRevolution wrote:
[GMAT math practice question]

(Statistics) The standard deviation of the salaries of the workers in company $$A$$ is $$\sqrt{5}$$ and that of the workers in company $$B$$ is $$\sqrt{30}.$$ What is the standard deviation of the salary of company $$A$$ and B’s workers together?

1) The number of workers in company $$A$$ is $$20$$ and that of company $$B$$ is $$30$$.
2) The averages of the salaries of the workers in companies $$A$$ and $$B$$ are the same.

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we don’t know how many workers companies A and B have, we have many variables and 0 equations, and E is most likely 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)
Let $$m$$ be the average of the salaries of $$A$$ and $$B.$$

Assume a1, a2, …, a20 are the salaries of the workers in A and b1, b2, …, b30 are those of the workers in B.
Since the standard deviation of the company A is $$\sqrt{5}$$, we have
[(a1-m)^2+(a2-m)^2 + … + (a20-m)^2] / 20 = 5 or (a1-m)^2+(a2-m)^2 + … + (a20-m)^2 = 100.
Since the standard deviation of the company B is $$\sqrt{30}$$, we have
[(b1-m)^2+(b2-m)^2 + … + (b30-m)^2] / 30 = 30 or (b1-m)^2+(b2-m)^2 + … + (b30-m)^2 = 900.
Then, we have
[(a1-m)^2+(a2-m)^2 + … + (a20-m)^2 + (b1-m)^2+(b2-m)^2 + … + (b30-m)^2] / 50
= (100 + 900) / (20 + 30) = 1000/50 = 20.
The standard deviation of the combined set of A and B is $$\sqrt{20}=2\sqrt{5}.$$

Since both conditions together yield a unique solution, they 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 there is no relation between the number of data and the standard deviation, condition 1) is not sufficient.

Condition 2)
Since there is no relation between the average and the standard deviation, condition 2) is not sufficient.

Therefore, C is the answer.

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 $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 01 May 2020, 02:51 1 MathRevolution wrote: [GMAT math practice question] (Absolute Value) What is the value of $$x + y$$? 1) $$|x - 2| = 4.$$ 2) $$|x – y + 3| = 4.$$ => 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. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have $$2$$ variables ($$x$$ and $$y$$) and $$0$$ equations, C is most likely 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 have $$x = 6$$ or $$x = -2$$, since $$|x - 2| = 4 ⇔ x - 2 = ±4 ⇔ x = 2 ± 4 ⇔ x = 6$$ or $$x = -2$$ from condition 1). We have $$x – y = 1$$ or $$x – y = -7$$, since $$|x – y + 3| = 4 ⇔ x – y + 3 = ±4 ⇔ x - y = -3 ± 4 ⇔ x - y = 1$$ or $$x – y = -7$$ from condition 2). If $$x = 6$$ and $$x – y = 1$$, then we have $$x = 6, y = 5$$ and $$x + y = 11.$$ If $$x = 6$$ and $$x – y = -7,$$ then we have $$x = 6, y = 13$$ and $$x + y = 19.$$ Since both conditions together do not yield a unique solution, they are not sufficient. Therefore, E is the answer. 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. _________________ 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$79 for 1 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: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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01 May 2020, 02:52
1
[GMAT math practice question]

(Algebra) $$a, b$$ and $$X$$ are positive numbers where $$a > b$$ and $$n$$ is a positive integer. What is the value of $$(\sqrt{X}-\sqrt{X-1})^{\frac{1}{n}}$$?

1) $$X=(\frac{a^n+b^n}{2})^2.$$

2) $$ab = 1.$$
_________________
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 $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 03 May 2020, 19:33 1 MathRevolution wrote: [GMAT math practice question] (Algebra) $$abc ≠ 0$$. What is the value of $$a^2+b^2+c^2$$? 1) $$a+b+c=3.$$ 2) $$a^3+b^3+c^3=27.$$ => 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. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have $$3$$ variables ($$a, b$$, and $$c$$) and $$0$$ equations, E is most likely 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) If $$a = 1, b = -1, c = 3$$, then we have $$a^2 + b^2 + c^2 = 1 + 1 + 9 = 11.$$ If $$a = 2, b = -2, c = 3$$, then we have $$a^2 + b^2 + c^2 = 4 + 4 + 9 = 17.$$ Since both conditions together do not yield a unique solution, they are not sufficient. Therefore, E is the answer. Answer: E 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$79 for 1 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: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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03 May 2020, 19:34
1
MathRevolution wrote:
[GMAT math practice question]

(Algebra) $$a, b$$ and $$X$$ are positive numbers where $$a > b$$ and $$n$$ is a positive integer. What is the value of $$(\sqrt{X}-\sqrt{X-1})^{\frac{1}{n}}$$?

1) $$X=(\frac{a^n+b^n}{2})^2.$$

2) $$ab = 1.$$

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have $$4$$ variables ($$a, b, X$$, and $$n$$) and $$0$$ equations, E is most likely 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)

Attachment:

5.1DS(A).png [ 24.73 KiB | Viewed 288 times ]

Since there many possible values of b, both conditions together do not yield a unique solution, and they are not sufficient.

Therefore, E is the answer.

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 $79 for 1 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: 9006 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, 00:11 [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$79 for 1 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: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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19 Oct 2018, 00:03
1
1
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.
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"Only $79 for 1 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: 9006 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, 17:51 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$79 for 1 month Online Course"
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Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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21 Oct 2018, 17:53
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.

Therefore, C is the answer.
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"Only $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 24 Oct 2018, 00:17 [Math Revolution GMAT math practice question] (algebra) For integers $$m$$ and $$n$$, the operation $$△$$ is defined by $$m△n = (m-1)^2 + (n+1)^2$$. What is the value of the integer $$x$$? $$1) x△1 = 4$$ $$2) 1△x = 4$$ _________________ 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$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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25 Oct 2018, 00:20
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(function) In the xy-plane, does the graph of $$y=ax^2+c$$ intersect the x-axis?

$$1) a>0$$
$$2) c>0$$

=>

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 question “does the graph of $$y=ax^2+c$$ intersect the x-axis” is equivalent to asking “does the equation $$ax^2+c = 0$$ have a root”.
Note that the statement “$$ax^2 + bx + c = 0$$ has a root” is equivalent to $$b^2-4ac ≥ 0.$$
Thus, the question asks if $$-4ac ≥ 0,$$ or $$ac ≤ 0$$, since $$b = 0$$ in this problem.

When we consider both conditions together, we obtain $$ac > 0$$ and the answer is “no”, since $$a > 0$$ and $$c > 0.$$
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions together are sufficient.

Note: Neither condition on its own provides enough information for us to determine whether $$ac ≤ 0.$$

Therefore, C is the answer.
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"Only $79 for 1 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: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 25 Oct 2018, 00:20 [Math Revolution GMAT math practice question] (statistics) If the average (arithmetic mean) of $$5$$ numbers is $$20$$, what is their standard deviation? 1) Their minimum is $$20$$. 2) Their maximum is $$20$$. _________________ 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$79 for 1 month Online Course"
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 25 Oct 2018, 00:20

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