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

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CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
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Kudos [?]: 389 [0], given: 4

Which of the following points is not on the line y=5x + 3? [#permalink]  14 Dec 2007, 10:33
Which of the following points is not on the line y=5x + 3?

1/2, 11/2
1/3, 14/3
sqrt8, 3+10sqrt2
sqrt4, 13
sqrt2, 31/3

Can someone please explain the shortcut?
Senior Manager
Joined: 06 Mar 2006
Posts: 497
Followers: 7

Kudos [?]: 92 [0], given: 1

Re: points not on a line [#permalink]  14 Dec 2007, 10:41
bmwhype2 wrote:
Which of the following points is not on the line y=5x + 3?

1/2, 11/2
1/3, 14/3
sqrt8, 3+10sqrt2
sqrt4, 13
sqrt2, 31/3

Can someone please explain the shortcut?

The shortcut is you don't need to even calculate this problem to be able to recognize that choice E is the answer.

If x is sqrt2, then y should be a number with sqrt2 in it. The question did not ask you to approximate or anything, obviously 31/3 for y is not possible. You can be confident that E is the answer in maybe 5 seconds.
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

Re: points not on a line [#permalink]  14 Dec 2007, 10:46
eileen1017 wrote:
bmwhype2 wrote:
Which of the following points is not on the line y=5x + 3?

1/2, 11/2
1/3, 14/3
sqrt8, 3+10sqrt2
sqrt4, 13
sqrt2, 31/3

Can someone please explain the shortcut?

The shortcut is you don't need to even calculate this problem to be able to recognize that choice E is the answer.

If x is sqrt2, then y should be a number with sqrt2 in it. The question did not ask you to approximate or anything, obviously 31/3 for y is not possible. You can be confident that E is the answer in maybe 5 seconds.

I dont follow. A coordinate is on a given line if we can plug in the coordinates and the equation nets out on both sides equally.

Why "If x is sqrt2, then y should be a number with sqrt2 in it. "?
Intern
Joined: 08 Dec 2007
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 0

Put the values of x and y in the equation and solve it. There is no other shortcut. Also, the point are very simple even though it looks difficult at first. Answer is 'e'
Senior Manager
Joined: 06 Mar 2006
Posts: 497
Followers: 7

Kudos [?]: 92 [0], given: 1

Re: points not on a line [#permalink]  14 Dec 2007, 10:51
bmwhype2 wrote:
eileen1017 wrote:
bmwhype2 wrote:
Which of the following points is not on the line y=5x + 3?

1/2, 11/2
1/3, 14/3
sqrt8, 3+10sqrt2
sqrt4, 13
sqrt2, 31/3

Can someone please explain the shortcut?

The shortcut is you don't need to even calculate this problem to be able to recognize that choice E is the answer.

If x is sqrt2, then y should be a number with sqrt2 in it. The question did not ask you to approximate or anything, obviously 31/3 for y is not possible. You can be confident that E is the answer in maybe 5 seconds.

I dont follow. A coordinate is on a given line if we can plug in the coordinates and the equation nets out on both sides equally.

Why "If x is sqrt2, then y should be a number with sqrt2 in it. "?

This is simple, you plug in the sqrt2 to the original equation of line y=5x+3; since x is sqrt2, y has to be 5sqrt2 +3, not 31/3. This is what I mean "If x is sqrt2, then y should be a number with sqrt2 in it."
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
in other words, a rational number gives a rational number, a irrational number gives a irrational one. really 10sec shortcut.
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

alright figured it out.

asked an engineering buddy and he said the line is linear, so the input of the x coordinate expression must be the same as the y coordinate expression.
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