How many ordered pairs of positive integers (x,y) satisfy the inequali

Question

How many ordered pairs of positive integers (x,y) satisfy the inequality 2x + 3y < 10 ?

A. One

B. Two

C. Three

D. Four

E. Five

Archit3110 · Answer

2x + 3y < 10 would hold true for values of + ve integers at , (1,1), ( 2,1),(1,2) ,(3,1)so total 4 .. IMO D..

Archit3110 · Answer

2x + 3y < 10 would hold true for values of + ve integers at ( 0,0), (1,1), ( 2,1),(1,2) so total 4 .. IMO D..

KarishmaB · Answer

(x, y) can take integer values from 1 onwards since they must be positive integers.

So smallest sum of 2x + 3y = 2*1 + 3*1 = 5
(x, y) = (1, 1)

x and y can each increase by 1 and the sum will stay less than 10. 
(x, y) = (1, 2), (2, 1),

The moment (x, y) becomes (2, 2), the sum becomes 10 which is not acceptable.

Check for (3, 1) - the sum is 9 which is fine. (4, 1) does not work so no further values will work. 
(1, 3) is not acceptable since the sum becomes 11. So no further values will work.

So in all, we have 4 pairs: (1, 1), (1, 2), (2, 1), (3, 1)

Answer (D)

LeoN88 · Answer

Hit & Trial: (x,y)
11
12
21
31

mdsaddamforgmat · Answer

can someone help to solve this one in a more efficient way?
somehow I m not comfortable with the Hit & Trail way

nick1816 · Answer

2x + 3y < 10
We need the positive integral solutions. We can infer that y<4, as 3*4>10.

There are 3 possible cases.

1. y=1

2x+3<10
x<3.5

3 positive integral values of x (1,2 and 3) are possible.

2. y=2 
2x+6<10
x<2

1 positive integral value of x(1) is possible.

3. y=3 
2x+9<10
x<0.5

0 positive integral value of x is possible.

Total possible solutions= 3+1=4

Kinshook · Answer

(x,y) = {(1,1),(1,2),(2,1),(3,1)}

Total 4 pairs are possible

IMO D

jackfr2 · Answer

what does ordered pair means? and what is the difference between ordered and simple pair ?

Posted from my mobile device

fireagablast · Answer

Answer is D.

(3,1)
(2,1)
(1,1) (1,2)

nick1816 · Answer

In Ordered pair, the order of the solution matters. 
For example- (1,2) and (2,1) will be counted as 2 different solutions.

Keismith · Answer

Doesn't (x,y) indicate that they have to be different numbers???

How many ordered pairs of positive integers (x,y) satisfy the inequali

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GMAT Problem Solving (PS) Questions

How many ordered pairs of positive integers (x,y) satisfy the inequali

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards