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Bunuel
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

(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)
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Bunuel
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

Hit & Trial: (x,y)
11
12
21
31
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can someone help to solve this one in a more efficient way?
somehow I m not comfortable with the Hit & Trail way
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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







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


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

Total 4 pairs are possible

IMO D
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Bunuel
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


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

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Answer is D.

(3,1)
(2,1)
(1,1) (1,2)
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In Ordered pair, the order of the solution matters.
For example- (1,2) and (2,1) will be counted as 2 different solutions.


jackfr2
Bunuel
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


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

Posted from my mobile device
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Doesn't (x,y) indicate that they have to be different numbers???
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