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Math Expert V
Joined: 02 Sep 2009
Posts: 53768

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4
5 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:14) correct 37% (00:55) wrong based on 83 sessions

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Which of the following points is not on the line $$y = 5x + 3$$?

A. $$(\frac{1}{2}, \frac{11}{2})$$
B. $$(\frac{1}{3}, \frac{14}{3})$$
C. $$(\sqrt{8}, 3 + 10*\sqrt{2})$$
D. $$(\sqrt{4}, 13)$$
E. $$(\sqrt{2}, \frac{31}{3})$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 53768

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Official Solution:

Which of the following points is not on the line $$y = 5x + 3$$?

A. $$(\frac{1}{2}, \frac{11}{2})$$
B. $$(\frac{1}{3}, \frac{14}{3})$$
C. $$(\sqrt{8}, 3 + 10*\sqrt{2})$$
D. $$(\sqrt{4}, 13)$$
E. $$(\sqrt{2}, \frac{31}{3})$$

For $$(\sqrt{2}, \frac{31}{3})$$, the left hand side (LHS) becomes $$LHS=y=\frac{31}{3}=\text{rational}$$ and $$RHS=5x + 3=5\sqrt{2}+3=\text{irrational}$$ and since $$\text{rational} \ne \text{irrational}$$, then line $$y=5x+3$$ does not pass through point $$(\sqrt{2}, \frac{31}{3})$$.

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Intern  Joined: 03 Nov 2015
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D does not work either
Math Expert V
Joined: 02 Aug 2009
Posts: 7424

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1
forsellingonline1 wrote:
D does not work either

Hi,
D does fit in..
D. $$(\sqrt{4},13)$$
y=5x+3..
substitute x= $$\sqrt{4}$$ = 2 and y as 13..
13=5*2+3..
13=13..
OK
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi, I have the following doubts please clarify:
1. In D can't square root of 4 be + or -2?
.
2. I did not understand your explanation for E. Square root if 2 is approximately 1.41. so LHS is approximately 10.33. RHS = 5 * 1.41 + 3 which is approximately 10.08. Does this negligible difference be attributed to the reason that it does not lie on the line?
Intern  Joined: 27 Jan 2015
Posts: 6
Concentration: Marketing, Economics
GMAT Date: 03-26-2015

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letter C, the value is for x or y?
Intern  B
Joined: 28 Apr 2016
Posts: 19

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fla162 wrote:
letter C, the value is for x or y?

First one is always X. In this case X= \sqrt{8}
Intern  B
Joined: 06 Jun 2018
Posts: 45
Location: India
Schools: IIMA PGPX"20 (D)
GMAT 1: 640 Q47 V30 GMAT 2: 540 Q42 V22 GPA: 3.7

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Bunuel, chetan2u, thanks for your explanation. I have question on rational vs irrational point here. 31/3 also turns out to be irrational because 31/3 = 10.333333 which continues. So how 31/3 is rational.
Math Expert V
Joined: 02 Aug 2009
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NAvinash wrote:
Bunuel, chetan2u, thanks for your explanation. I have question on rational vs irrational point here. 31/3 also turns out to be irrational because 31/3 = 10.333333 which continues. So how 31/3 is rational.

Rational numbers are numbers that can be written in a fraction form. So they can be terminating decimal or can ALSO be non-terminating where the sequence repeats endlessly.. here too 31/3 =10.333333....
But in the right side √2 is non terminating and there is no sequence. Thus it is irrational

Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Intern  B
Joined: 06 Jun 2018
Posts: 45
Location: India
Schools: IIMA PGPX"20 (D)
GMAT 1: 640 Q47 V30 GMAT 2: 540 Q42 V22 GPA: 3.7

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chetan2u , thanks this helps. Then can I assume any number in fraction form in given question is rational and any number like root 2 , root 3 for which square root is not integer is irrational number ?
Math Expert V
Joined: 02 Aug 2009
Posts: 7424

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NAvinash wrote:
chetan2u , thanks this helps. Then can I assume any number in fraction form in given question is rational and any number like root 2 , root 3 for which square root is not integer is irrational number ?

yes, you can
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert Re: M10-18   [#permalink] 02 Oct 2018, 23:07
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# M10-18

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