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# m10 q18

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29 Dec 2008, 22:01
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) $$(\sqrt{2}, \frac{31}{3})$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?
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29 Dec 2008, 22:40
1
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georgechanhc wrote:
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 $$(\sqrt{2}, \frac{31}{3})$$

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?

agree with E for the reason given above.

$$\sqrt{2}$$ is an irrational number i.e a non-terminating value.
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29 Dec 2008, 23:02
1
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Ah ok... Thx.

At first glance i thought C was the choice as it also has sqrt2.

Only realize now that sqrt2 will be canceled out later on.
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30 Dec 2008, 16:29
1
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Expert's post
GMAT TIGER wrote:
agree with E for the reason given above.

$$\sqrt{2}$$ is an irrational number i.e a non-terminating value.

Ah, there's a difference between 'irrational' and 'non-terminating'. 1/3 = 0.33333.... is 'non-terminating', but it is also certainly a rational number. Rational numbers are those that can be written as fractions using only integers. As decimals, rational numbers can be terminating or non-terminating, but when rational numbers produce non-terminating decimals, they *always* produce repeating (sometimes called recurring) decimals; a certain pattern of digits repeats forever. Irrational numbers are those numbers like $$\Pi$$ and $$\sqrt{2}$$ which cannot be written as fractions involving integers. As decimals, irrational numbers have no pattern of digits that repeats forever.
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09 Apr 2010, 09:15
1
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Either both number are rational or irrational

E is the only choice with one irrational and one rational.
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17 Apr 2011, 11:48
2\sqrt{2} is irrational too?(and transcendental number too ... )
I did not get the explanation about it being sqrt{2}irrational number ..so not an option
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17 Apr 2012, 05:36
georgechanhc wrote:
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) $$(\sqrt{2}, \frac{31}{3})$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?

i am going to follow substitution method...

A: 1/2, 11/2 which is in the form of x,y

if substituting these values in y = 5x + 3 makes LHS = RHS then thats the answer

11/2 = 5*1/2 + 3 = 5/2 + 3 = (5+6)/3 = 11/3 so NO

B: 1/3, 14/3

14/3 = 5*1/3 + 3 = 5/3 + 3 = (5+9)/3 = 14/3

so YES

C:(\sqrt{8}, 3 + 10*\sqrt{2})

3 + 10*\sqrt{2} = 5 * \sqrt{8} + 3 = 5 * 2 * \sqrt{2} + 3 = 10\sqrt{2} + 3 so YES

D: (\sqrt{4}, 13)

13 = 5 * \sqrt{4} + 3 = 5 * 2 + 3 = 13 so YES

E: (\sqrt{2}, \frac{31}{3})

\frac{31}{3} = 5 * \sqrt{2} + 3 = 5 * 1.41 + 3 approximately 10 so may be YES

i am getting YES for most of the substitution...am i doing anything wrong?

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17 Apr 2012, 05:50
1
KUDOS
Expert's post
harshavmrg wrote:
georgechanhc wrote:
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) $$(\sqrt{2}, \frac{31}{3})$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?

i am going to follow substitution method...

A: 1/2, 11/2 which is in the form of x,y

if substituting these values in y = 5x + 3 makes LHS = RHS then thats the answer

11/2 = 5*1/2 + 3 = 5/2 + 3 = (5+6)/3 = 11/3 so NO

B: 1/3, 14/3

14/3 = 5*1/3 + 3 = 5/3 + 3 = (5+9)/3 = 14/3

so YES

C:(\sqrt{8}, 3 + 10*\sqrt{2})

3 + 10*\sqrt{2} = 5 * \sqrt{8} + 3 = 5 * 2 * \sqrt{2} + 3 = 10\sqrt{2} + 3 so YES

D: (\sqrt{4}, 13)

13 = 5 * \sqrt{4} + 3 = 5 * 2 + 3 = 13 so YES

E: (\sqrt{2}, \frac{31}{3})

\frac{31}{3} = 5 * \sqrt{2} + 3 = 5 * 1.41 + 3 approximately 10 so may be YES

i am getting YES for most of the substitution...am i doing anything wrong?

Substituting values is not the best way to solve this question but anyway: if you go this way then when you substitute the values of x and y, LHS and RHS must be equal without any approximation.

For $$(\sqrt{2}, \frac{31}{3})$$ --> $$LHS=y=\frac{31}{3}=rational$$ and $$RHS=5x + 3=5\sqrt{2}+3=irrational$$ --> $$rational\neq{irrational}$$, so line $$y=5x+3$$ does not pass through point $$(\sqrt{2}, \frac{31}{3})$$

P.S. To format the formulas correctly please mark them and push [ m] button.
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18 Apr 2012, 02:09
kapac wrote:
At which difficulty level is this question supposed to occur ?

I'd say that the difficulty level of this question is around 600.
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18 Apr 2013, 07:43
Bunuel wrote:
harshavmrg wrote:
georgechanhc wrote:
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) $$(\sqrt{2}, \frac{31}{3})$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?

i am going to follow substitution method...

A: 1/2, 11/2 which is in the form of x,y

if substituting these values in y = 5x + 3 makes LHS = RHS then thats the answer

11/2 = 5*1/2 + 3 = 5/2 + 3 = (5+6)/3 = 11/3 so NO

B: 1/3, 14/3

14/3 = 5*1/3 + 3 = 5/3 + 3 = (5+9)/3 = 14/3

so YES

C:(\sqrt{8}, 3 + 10*\sqrt{2})

3 + 10*\sqrt{2} = 5 * \sqrt{8} + 3 = 5 * 2 * \sqrt{2} + 3 = 10\sqrt{2} + 3 so YES

D: (\sqrt{4}, 13)

13 = 5 * \sqrt{4} + 3 = 5 * 2 + 3 = 13 so YES

E: (\sqrt{2}, \frac{31}{3})

\frac{31}{3} = 5 * \sqrt{2} + 3 = 5 * 1.41 + 3 approximately 10 so may be YES

i am getting YES for most of the substitution...am i doing anything wrong?

Substituting values is not the best way to solve this question but anyway: if you go this way then when you substitute the values of x and y, LHS and RHS must be equal without any approximation.

For $$(\sqrt{2}, \frac{31}{3})$$ --> $$LHS=y=\frac{31}{3}=rational$$ and $$RHS=5x + 3=5\sqrt{2}+3=irrational$$ --> $$rational\neq{irrational}$$, so line $$y=5x+3$$ does not pass through point $$(\sqrt{2}, \frac{31}{3})$$

P.S. To format the formulas correctly please mark them and push [ m] button.

In Option C, whether Sqrt8 is not irrational?
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18 Apr 2013, 09:13
Bunuel wrote:
harshavmrg wrote:
georgechanhc wrote:
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) $$(\sqrt{2}, \frac{31}{3})$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?

i am going to follow substitution method...

A: 1/2, 11/2 which is in the form of x,y

if substituting these values in y = 5x + 3 makes LHS = RHS then thats the answer

11/2 = 5*1/2 + 3 = 5/2 + 3 = (5+6)/3 = 11/3 so NO

B: 1/3, 14/3

14/3 = 5*1/3 + 3 = 5/3 + 3 = (5+9)/3 = 14/3

so YES

C:(\sqrt{8}, 3 + 10*\sqrt{2})

3 + 10*\sqrt{2} = 5 * \sqrt{8} + 3 = 5 * 2 * \sqrt{2} + 3 = 10\sqrt{2} + 3 so YES

D: (\sqrt{4}, 13)

13 = 5 * \sqrt{4} + 3 = 5 * 2 + 3 = 13 so YES

E: (\sqrt{2}, \frac{31}{3})

\frac{31}{3} = 5 * \sqrt{2} + 3 = 5 * 1.41 + 3 approximately 10 so may be YES

i am getting YES for most of the substitution...am i doing anything wrong?

Substituting values is not the best way to solve this question but anyway: if you go this way then when you substitute the values of x and y, LHS and RHS must be equal without any approximation.

For $$(\sqrt{2}, \frac{31}{3})$$ --> $$LHS=y=\frac{31}{3}=rational$$ and $$RHS=5x + 3=5\sqrt{2}+3=irrational$$ --> $$rational\neq{irrational}$$, so line $$y=5x+3$$ does not pass through point $$(\sqrt{2}, \frac{31}{3})$$

P.S. To format the formulas correctly please mark them and push [ m] button.

How are you supposed to know that this is testing rational/irrational. When you look at this problem, what does one think to crack it open? What about for similar problems that ultimately aren't testing rational/irrational?
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18 Apr 2013, 09:22
ranjeet75 wrote:
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) $$(\sqrt{2}, \frac{31}{3})$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Even without calculations it is clear that ( $$\sqrt{2}$$ , $$\frac{31}{3}$$ ) cannot lie on the line $$y = 5x + 3$$ . If x is irrational, y must also be irrational.

What do they mean by $$(\sqrt{2}, \frac{31}{3})$$ is irrational?

i am going to follow substitution method...

A: 1/2, 11/2 which is in the form of x,y

if substituting these values in y = 5x + 3 makes LHS = RHS then thats the answer

11/2 = 5*1/2 + 3 = 5/2 + 3 = (5+6)/3 (5+6)/2 = 11/3 11/2 so NO YES

I dont think the test wants to check ur equation solving powers with this question. So they would try stumping you with the options.
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20 Jul 2013, 06:54
CAN someone explain me the concept behind solving this question .I dont find any proper explaination
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20 Jul 2013, 06:57
skamal7 wrote:
CAN someone explain me the concept behind solving this question .I dont find any proper explaination

Please specify what didn't you understand (for example, here: m10-q18-74349.html#p1074872). Thank you.
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20 Jul 2013, 07:08
Can you help us in understanding the concept of rational and irrational and also tell us why if rational not equal to irratonal the line wont pass.. Am not able to grasp the concept
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21 Jul 2013, 01:31
skamal7 wrote:
Can you help us in understanding the concept of rational and irrational and also tell us why if rational not equal to irratonal the line wont pass.. Am not able to grasp the concept

Some point (a, b) is on line y=5x+3 means that, when you replace x and y with a and b, the equation should hold.

For $$(\sqrt{2}, \frac{31}{3})$$ the left hand side is $$\frac{31}{3}=rational$$ and the right hand side is $$5\sqrt{2}+3=irrational$$. Does LHS equal to RHS? No, $$rational\neq{irrational}$$, so line $$y=5x+3$$ does not pass through point $$(\sqrt{2}, \frac{31}{3})$$.

Hope it's clear.
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04 Apr 2014, 04:17
very simple ques...

just plugin the values of x from options into the given equation...
All, except the last option satisfies the value of y...

Hence E is the OA
Re: m10 q18   [#permalink] 04 Apr 2014, 04:17
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