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# The Ultimate Q51 Guide [Expert Level]

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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07 Oct 2016, 05:31
u=?
1) |u|≤0
2) u2+v2=0

==> In the original condition, there are 2 variables (u,v), so C is highly likely to be the answer. In the case of 1), u=0 and in the case of 2), u=v=0, then u=0 all the time, hence unique and sufficient. The answer is D.
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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 11 Oct 2016, 04:46 As always, there are more and more problems like CMT 3,4 types recently. Take a look at below, and you will exactly the type of a question which falls under CMT 4(B), a 5051 level problem. You should be prepared for this type of questions. You must know the relation between the variable approaches and the CMT. If x and y are integers, is x+y an odd? 1) (x^2+y^2)(x-y)=odd 2) x^2+y^2 is not divisible by 2 ==> C is the answer, and D is also the answer, hence a typical CMT. This is a common 5051-level problem. CMT 4(B) Answer: 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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13 Oct 2016, 07:37
When the average (arithmetic mean) of a, b, and c is 5, what is the median of them?
1) The average (arithmetic mean) of a and b is 5
2) c=5

==> In the original condition, there are 3 variables (a,b,c), and 1 equation (a+b+c=15), and you need 2 more of them, so C is highly likely to be the answer. If you do 1) & 2), you get 1)=2, so D 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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 17 Oct 2016, 00:24 The question below is a typical statistics problem that is 5051-level. (statistics) What is the median number of cloths sold in the last 15 days? 1) 21 cloths are sold every day in the last 8 days 2) The total number of clothes sold was 600 in the last 15 days. ==>If you change the condition and the problem, the median of the number of all the clothes sold for 15 days is the 8th number when all figures are arranged in an ascending order. In the case of 1), 21 clothes were sold each day for the last 8 days, hence median=21, and sufficient. The answer is A. This kind of questions(integer and statistics) is the current 5051-question. 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$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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19 Oct 2016, 01:38
Also, If a≠-b, √[(a+2b)/(a+b)]=?

1) a=3
2) b/a=2/3

==>In the original condition, there are 2 variables (a,b), so C is the answer. However, if you modify the problem, and divide the numerator and denominator of √[(a+2b)/(a+b)] by a, you get sqrt[1+2(b/a)][1+(b/a)], so you only need to know b/a. B is the answer. In general, if one condition is a number, and the other condition is a ratio, the answer is highly likely to be the ratio.

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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 21 Oct 2016, 08:16 Also, CMT 4(A) is still a common type of questions If 23,ab2 is 5-digit positive integers, what is the remainder when 23,ab2 is divided by 25? 1) a=9 2) b=5 ==>If you modify the condition and the problem, in general, the remainder of a certain integer,n, divided by 25 is the same as the value when divided by 25 to the nearest hundreds digit. That is because 100=25*4. 2,3,a do not have any influence when you divide 23,ab2 by 25 like b2, so you only need to know what b is. The answer is B. 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
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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23 Oct 2016, 06:34
If |a|>|b|, is a>b?

1) a>0
2) b<0

==>If you look at the original condition, there are 2 variables (a,b) and 1 equation (|a|>|b|), so in order for them to match with the number of equations there has to be 1 more equation. Hence D is the answer.
In the case of 1), you get a>|b|≥b, then a>b, hence always yes, and sufficient.
In the case of 2), you get |a|>|b|=-b>b, then a>b, hence always yes, and sufficient. The answer is D.
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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 24 Oct 2016, 01:20 The question below is also a 5051-level problem. If r and s are positive integers is r/s a terminating decimal? 1) r is a factor of 100 2) s is a factor of 200 ==>If you modify the original condition and the problem, in order for r/s to become a terminating decimal, prime factors of s, the denominator, should be only 2 or 5. However, in the case of 2), in order for s to be a factor of 200, you always get 200=2352, hence yes, and sufficient. The answer is B. 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
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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27 Oct 2016, 08:31
If |m-n|=3, is m>n?
1) mn<0
2) The distance between m and 0 is 2

==>In the original condition, there are 2 variables(m,n) and 1 equation(|m-n|=3), so D is highly likely to be the answer. In the case of 1), (m,n)=(2,-1),(-2,1), so yes and no coexist, hence not sufficient. In the case of 2), you get |m-0|=|m|=2, m=±2, then (m,n)=(2,-1),(-2,1), hence yes/no, so not sufficient.
Through 1) & 2), you get (m,n)=(2,-1),(-2,1), so yes/no, hence not sufficient. The answer is E.

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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 31 Oct 2016, 06:25 It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x? A. 50 B. 100 C. 150 D. 250 E. 400 ==>In general, from y=ax^2+bx+c, the value of y from symmetric axis, x=-b/2a is the least or the greatest. For the profit has to be the greatest, x=-20,000/2(-25) = 400, hence the greatest profit. The answer is E. 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$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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03 Nov 2016, 02:21
On the coordinate planes system there are line L and line M, y=3x+2 and y=kx, respectively. For which of the following value of k did the line L intersect with the line M?
I. -3 II.-1 III.3

A.none B.I only C. IIIonly D.I & II E.II & III

==>For the two straight lines to intersect with each other, the slope has to be different. Hence, from y=kx, it has to be k≠3, so I & II is the answer. The answer is D.

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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 04 Nov 2016, 21:52 It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x? A. 50 B. 100 C. 150 D. 250 E. 400 ==>In general, from y=ax^2+bx+c, the value of y from symmetric axis, x=-b/2a is the least or the greatest. For the profit has to be the greatest, x=-20,000/2(-25) = 400, hence the greatest profit. The answer is E. 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$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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08 Nov 2016, 02:24
It is well known that the ratio of hydrogen’s mass to oxygen’s mass is 1 to 16. If the moving speed rates of hydrogen atoms and oxygen atoms are inversely proportional to square root of its mass, what is the ratio of the moving speed rate of hydrogen to that of oxygen?
A. 1:4 B. 4:1 C. 1:16 D. 16:1 E. 1:2

==>From v=k/√m, (v: moving speed and m: mass), if hydrogen=a, oxygen=16a If you substitute this, the rate of the speed of hydrogen atoms to that of oxygen atoms is k/√a : k/√16a =1:1/4=4:1. Hence the answer is 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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 11 Nov 2016, 01:29 The revenue increased by 10 percent from March to April and then the revenue decreased by 10 percent from April to May. By what percent is increased (or decreased) the revenue from March to May? A. 10% less B. 10% more C. 1% less D. 1% more E. 0.9% less ==>If the revenue increases by 10% from March to April, R -->R(1+10%)=1.1R, and if this decreases by 10% from April to May, 1.1R  1.1R(1-10%)=1.1R(0.9)=0.99R. If so, the revenue from March to May is R  0.99R, hence 1% decrease. The answer is C. 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$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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15 Nov 2016, 02:34
When a positive integer n has 6 different factors, n=?
1) n has 2 prime factors
2) n<18

==> In the original condition, in case of standard deviation questions, there is 1(n) variable, and therefore D is most likely to become the answer.
In case of con 1), you get n=2231, 2132, hence it is not unique and not sufficient.
In case of con 2), you get only n=2231, hence it is unique and sufficient.

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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 18 Nov 2016, 03:36 Is x<0? 1) x^5<0 2) x^5+x+1=0 ==> In the original condition, there is 1 variable, and therefore D is most likely to be the answer. In case of con 1), from x^5<0, if you divide both sides by x^4, you get x<0, hence yes, it is sufficient. In case of con 2), it cannot be factored, and this is when you use CMT 4 (B). In other words, if you get A and B too easily, then consider D. Since x^5+x=-1, x(x^4+1)=-1, and x=-1/(x^4+1) always agree with x^4+1>0, and hence yes, it is sufficient. Therefore, the answer is D. Answer: 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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21 Nov 2016, 02:09
If a^3*b^4*c^5<0, is abc<0?

1) c<0
2) b>0

==> If you modify the original condition and the question, when you divide both sides of a^3*b^4*c^5<0 by a^2*b^4*c^4, you get ac<0, and the question abc<0? becomes b>0?. From con 2) b>0, it becomes yes, hence it is sufficient.

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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 24 Nov 2016, 02:57 As always, more developed questions that combine both CMT 3 and 4 are being released. As shown below, this question, which was recently released, is a 5051 level question that also corresponds to the CMT 4 (A). You must be aware of this type of questions. You need to know the relationship between variable approach and CMT. Number of pets Number of People 0 4 1 5 2 6 A 7 5 B In the above list, what is the median number of pets? 1) A=3 2) B=2 ==> In the original condition, there are 2 variables (A, B), and therefore c is most likely to be the answer. By solving con 1) and con 2), C becomes the answer, but since it is a statistical question, one of the key questions, when you apply CMT 4 (A) and look at con 2), the median becomes (2+2) /2=2, and hence it is sufficient. Therefore, the answer is B. 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
Posts: 8257
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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29 Nov 2016, 04:28
Also, integer questions constantly appear recently.

If m and n are positive integers, is $$n^m-n$$ divisible by 6?

1) m=3
2) n=2

==> In the original condition, there are 2 variables (m,n), and in order to match the number of variables to the number of equations, there must be 2 equations. Therefore, C is most likely to be the answer. By solving con 1) and con 2), from $$2^3-2=6$$, you get yes, and hence it is sufficient. The answer is C. However, this question is an integer question, one of the key questions, so you need to apply CMT 4. For con 1), from $$n^3-n$$=(n-1)n(n+1), it is the multiple of the three consecutive integers, which always becomes the multiple of 6, hence yes, it is sufficient. For con 2), from n=2 and m=3 yes, m=2 no, and hence it is not sufficient. Therefore, the answer is A.

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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: 8257 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 02 Dec 2016, 02:01 |a-b|=b-a? 1) a<b 2) ab<0 and $$a^2b$$=1 ==> If you modify the original condition and question, to get |A|=-A, you need to get A≤0?, so it becomes |a-b|=b-a=-(a-b)?, a-b<0?, a<b?. Thus, for con 1), it is always yes, hence sufficient, and for con 2), if you apply CMT 4 (B), it also becomes a<b, hence yes, it is sufficient. Therefore, the answer is D. Answer: 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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Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 02 Dec 2016, 02:01

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# The Ultimate Q51 Guide [Expert Level]

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