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

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

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05 Feb 2019, 16:08
1
MathRevolution wrote:
[GMAT math practice question]

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

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

$$a > b > c > d > 0\,\,\,\,\, \Rightarrow \,\,\,\,0 < {1 \over a} < {1 \over b} < {1 \over c} < {1 \over d}\,\,\,\,\left( * \right)$$

$$d\,\,\mathop < \limits^? \,\,4$$

$$\left( 1 \right)\,\,{1 \over c} + {1 \over d} > {1 \over 2}\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\left\langle {{\rm{YES}}} \right\rangle$$

$$\left( {**} \right)\,\,\,d \ge 4\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,c > 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{1 \over c} + {1 \over d} < {1 \over 4} + {1 \over 4} = {1 \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{impossible}}$$

$$\left( 2 \right)\,\,\,1 = {1 \over a} + {1 \over b} + {1 \over c} + {1 \over d}\,\,\mathop < \limits^{\left( * \right)} \,\,4\left( {{1 \over d}} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,d\, > \,0} \,\,\,\,\,1 \cdot d < 4\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$

The correct answer is therefore (D).

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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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13 Mar 2019, 08:42
1
AjjayKannan wrote:
How many DS questions will be there in the test?

There is no actual count on how much DS questons one might face on the test day. It might range from 13-15. Totally depends.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8583
GMAT 1: 760 Q51 V42
GPA: 3.82

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01 Apr 2019, 20:19
1
Sandeepanisha wrote:
(ratio) All of the households used a total of x watts for 24 hours and one household used y watts per hour. What is the total number of all the households, in terms of x and y?

A. x/y B. 24x/y C. x/24y D. 24xy E. 24/xy

Let n be the number of households.
Then we have 24y*n = x, which is the total waats they use.
Thus n = x/(24y).

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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: 8583 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 14 May 2019, 23:47 1 [GMAT math practice question] (number properties) What is the value of $$n$$? 1) $$n$$ is the product of $$2$$ different prime numbers less than $$15$$ 2) $$n$$ and $$210$$ are relatively prime _________________ 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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03 Oct 2019, 23:40
1
MathRevolution wrote:
[GMAT math practice question]

(functions) $$f(x)○f(y)$$ is defined as $$f(x+y+2xy)$$. What is the value of $$1○(-1)$$?

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

$$2) f(x)=2x+1$$

=>

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 many variables to determine a function and $$0$$ equations, E is most likely to be the answer. However, by Tip 1) of the VA method, D is most likely to be the answer if condition 1) gives the same information as condition 2).

Condition 1)
$$1○(-1) = f(0)○f(-1)=f(0+(-1)+0)=f(-1)=-1.$$

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since we have $$f(0)=1$$ and $$f(-1)=-1,$$ we have $$1○(-1) = f(0)○f(-1)=f(0+(-1)+0)=f(-1)=-1.$$

Since condition 2) yields a unique solution, it is sufficient.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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: 8583 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 03 Nov 2019, 18:24 1 MathRevolution wrote: [GMAT math practice question] (number properties) $$x, y$$, and $$z$$ are positive integers. What is the value of $$xyz$$? $$1) xy + yz = 24$$ $$2) xz + yz = 13$$ => 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 $$3$$ variables ($$x, y,$$ and $$z$$) 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) Since we have $$(x+y)z = 13$$ from condition 2), we have $$x+y=13$$ and $$z = 1.$$ We have $$(x+z)y = (x+1)y = 24$$ from condition 1) since $$z = 1.$$ If $$x = 1, y = 12, z = 1$$, then $$xyz = 12.$$ If $$x = 11, y = 2, z = 1$$, then $$xyz = 22.$$ 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"
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Joined: 16 Aug 2015
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03 Feb 2020, 00:31
1
[GMAT math practice question]

(Geometry) The figure below shows the dimensions of the right triangle $$ABC$$ with $$AB = 13, BC = 12, CA = 5$$ and $$I$$ is a point inside triangle $$ABC.$$ Angle $$C$$ is $$90^o.$$ What is the minimum distance from the point $$I$$ to sides $$AB, BC$$ and $$CA$$?

Attachment:

2.3ds.png [ 12.43 KiB | Viewed 168 times ]

1) Point $$I$$ is the incenter of $$△ABC.$$

2) Line $$AI$$ bisects angle $$A$$, and line $$BI$$ bisects angle $$B$$.
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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: 8583 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"
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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.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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: 8583 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 GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82

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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.

_________________
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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: 8583 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
Posts: 8583
GMAT 1: 760 Q51 V42
GPA: 3.82

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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 $$ac ≤ 0.$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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: 8583 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8583
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GPA: 3.82

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25 Oct 2018, 23:52
MathRevolution wrote:
[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 $$x$$?

$$1) x△1 = 4$$
$$2) 1△x = 4$$

=>

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 of the conditions on their own first.

Condition 1)
$$x△1 = (x-1)^2 + (1+1)^2 = (x-1)^2 + 2^2 = 4.$$
Thus, $$(x-1)^2 = 0$$ and $$x = 1.$$
Since we have a unique solution, condition 1) is sufficient.

Condition 2)
$$1△x = (1-1)^2 + (x+1)^2 = (x+1)^2 = 4.$$
So, $$x+1 = ±2$$ or $$x = -1 ± 2.$$
Thus, $$x = -3$$ or $$x = 1$$.
Since we don’t have a unique solution, condition 2) is not sufficient.

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
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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: 8583 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, 23:53 [Math Revolution GMAT math practice question] (number property) $$n$$ is an integer. Is $$n(n+2)$$ a multiple of $$8$$? 1) $$n$$ is an even integer 2) $$n$$ is a multiple of $$4$$ _________________ 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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28 Oct 2018, 18:17
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number property) $$n$$ is an integer. Is $$n(n+2)$$ a multiple of $$8$$?

1) $$n$$ is an even integer
2) $$n$$ is a multiple of $$4$$

=>

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.

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 the product of two consecutive even integers is a multiple of 8 since one of them is a multiple of 4 and the other is an even integer.

Thus, each of conditions is sufficient since each implies that n and n+2 are two consecutive even integers.

_________________
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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: 8583 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 28 Oct 2018, 23:57 [Math Revolution GMAT math practice question] (algebra) $$(x^2-3x+2)(y^2-5y+6)=?$$ $$1) x=1$$ $$2) y=1$$ _________________ 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"
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30 Oct 2018, 17:34
[Math Revolution GMAT math practice question]

(sequence) The terms of $$a$$ sequence are defined by an=an-2+3. Is 411 a term of the sequence?

1) a1=111
2) a2=112
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30 Oct 2018, 18:02
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(sequence) The terms of $$a$$ sequence are defined by an=an-2+3. Is 411 a term of the sequence?

1) a1=111
2) a2=112

From statement 1:

$$a_1$$ = 111.

$$a_3 = a_1$$ + 3 = 114

$$a_5 = a_3$$ + 3 = 117.

The series becomes 111, 114, 117....

the terms are 1, 3, 5, 7....

The common difference between the terms 1,3,5... is 3.

Let's consider 411 as the last term. then 411 = 111 +(n-1)3.
Then 411 becomes 101th term.

A is sufficient.

From statement 2:

We get $$a_2$$, $$a_4$$ and $$a_6$$ and so on..
But first term is unknown.
B is sinsufficient.

Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 30 Oct 2018, 18:02

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