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# M10-18

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Math Expert
Joined: 02 Sep 2009
Posts: 51215

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15 Sep 2014, 23:42
4
5
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:14) correct 37% (00:53) wrong based on 81 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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Joined: 02 Sep 2009
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15 Sep 2014, 23:42
1
1
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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12 Apr 2016, 08:05
D does not work either
Math Expert
Joined: 02 Aug 2009
Posts: 7106

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12 Apr 2016, 08:44
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

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28 Jul 2016, 10:15
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?
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Joined: 27 Jan 2015
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Concentration: Marketing, Economics
GMAT Date: 03-26-2015

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03 Aug 2016, 09:34
letter C, the value is for x or y?
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Joined: 28 Apr 2016
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08 Apr 2017, 01:03
fla162 wrote:
letter C, the value is for x or y?

First one is always X. In this case X= \sqrt{8}
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Joined: 06 Jun 2018
Posts: 46
GMAT 1: 590 Q44 V27
GMAT 2: 540 Q42 V22

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26 Aug 2018, 17:30
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.
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26 Aug 2018, 17:40
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
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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

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02 Oct 2018, 19:31
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 ?
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02 Oct 2018, 22:07
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
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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

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Re: M10-18 &nbs [#permalink] 02 Oct 2018, 22:07
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# M10-18

Moderators: chetan2u, Bunuel

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