# SAT Question

• July 30th 2011, 05:37 PM
RK29
Inequality question
For how many ordered pairs of positive integers (x,y) is 2x+3y<6

1
2
3
5
7
• July 30th 2011, 05:51 PM
rdtedm
Re: Inequality question
Quote:

Originally Posted by RK29
For how many ordered pairs of positive integers (x,y) is 2x+3y<6

1
2
3
5
7

(0, 0)
(0, 1)
(1, 0)
(1, 1)
(2, 0)

I count 5.
• July 30th 2011, 05:56 PM
RK29
Re: Linear equation question
Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
• July 30th 2011, 05:57 PM
RK29
Re: Inequality question
Quote:

Originally Posted by rdtedm
(0, 0)
(0, 1)
(1, 0)
(1, 1)
(2, 0)

I count 5.

so did I but the answer key is it's 1
• July 30th 2011, 05:58 PM
rdtedm
Re: Inequality question
Quote:

Originally Posted by RK29
so did I but the answer key is it's 1

Answer key is wrong - I have seen many errors in test prep books when I tutor confused students.. Answer has to be five unless it was transcribed wrong
• July 30th 2011, 06:07 PM
RK29
Re: Inequality question
okay thanks

Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
• July 30th 2011, 06:07 PM
rdtedm
Re: Linear equation question
Quote:

Originally Posted by RK29
Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?

Passes through origin means line has form y= mx, where m is some real number.

Rearranging the perpendicular line, we get y = -4x + k, so this line has a slope of -4, so the inverse reciprocal slope is 1/4.
Which means, Line 1 has an equation of y = (1/4)x

Line 1: y = (1/4)x
Line 2: y = -4x + k

Since we know they intersect at (t, t+1), this must be a solution to both equations. Since Line 2 would have infinite solutions (since k is unknown), we choose Line 1 to solve for t.

t+1 = (1/4)t
1 = (-3/4)t
(-4/3) = t

So, t = -4/3
• July 31st 2011, 02:48 AM
Plato
Re: Inequality question
Quote:

Originally Posted by RK29
For how many ordered pairs of positive integers (x,y) is 2x+3y<6
1, 2, 3, 5, 7
the answer key is it's 1

Quote:

Originally Posted by rdtedm
Answer key is wrong - I have seen many errors in test prep books when I tutor confused students.. Answer has to be five unless it was transcribed wrong

The answer key is correct.
There is only one pair of positive integers that works: (1,1).
@ rdtedm, you should that 0 is not a positive integer.
• July 31st 2011, 04:07 AM
Soroban
Re: Inequality question
Hello, RK29;669895!

Quote:

$\text{For how many ordered pairs of }positive\text{ integers }(x,y)\text{ is }2x+3y \,<\, 6$

. . $(a)\,1 \qquad (b)\;2 \qquad (c)\;3 \qquad(d)\;5 \qquad (e) 7$

For positive integers, there is one pair: $(1,1)$

Code:

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Ah, Plato beat me to it . . .