There are how many pairs of positive integers (a,b) such that 1 <=a < b <=10?
(a) 24
(b) 36
(c) 45
(d) 64
(e) 81
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Marriage of Integers: Disregard other thread
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VP_Jim
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First, let's assume that B=10. That means that A is either 1, 2, 3, 4, 5, 6, 7, 8, or 9. Therefore, there are 9 different pairs we can make if B=10 (e.g., B=10 and A=9, or B=10 and A=8, etc).
What if B=9? Then, A must be 1, 2, 3, 4, 5, 6, 7, or 8. Thus, there are 8 possible pairs if B=9.
If B=8, there are 7 possible pairs. If B=7, there are 6 possible pairs, etc. All the way down to B=2, in which case A=1, so there is only 1 possible pair if B=2.
Therefore, the answer is:
9+8+7+6+5+4+3+2+1 = 45.
Hope this helps!
What if B=9? Then, A must be 1, 2, 3, 4, 5, 6, 7, or 8. Thus, there are 8 possible pairs if B=9.
If B=8, there are 7 possible pairs. If B=7, there are 6 possible pairs, etc. All the way down to B=2, in which case A=1, so there is only 1 possible pair if B=2.
Therefore, the answer is:
9+8+7+6+5+4+3+2+1 = 45.
Hope this helps!
Jim S. | GMAT Instructor | Veritas Prep
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sureshbala
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If I choose any two numbers from 1 to 10, definitely one of them will be less than the other.
Hence the total number of pairs = 10C2 = 45
Hence the total number of pairs = 10C2 = 45
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KICKGMATASS123
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Why Can't A = 10 when B = 10??VP_Jim wrote:First, let's assume that B=10. That means that A is either 1, 2, 3, 4, 5, 6, 7, 8, or 9. Therefore, there are 9 different pairs we can make if B=10 (e.g., B=10 and A=9, or B=10 and A=8, etc).
What if B=9? Then, A must be 1, 2, 3, 4, 5, 6, 7, or 8. Thus, there are 8 possible pairs if B=9.
If B=8, there are 7 possible pairs. If B=7, there are 6 possible pairs, etc. All the way down to B=2, in which case A=1, so there is only 1 possible pair if B=2.
Therefore, the answer is:
9+8+7+6+5+4+3+2+1 = 45.
Hope this helps!
dtweah wrote:There are how many pairs of positive integers (a,b) such that 1 <=a < b <=10?
(a) 24
(b) 36
(c) 45
(d) 64
(e) 81
c) For a = j, j = 1,2,…,9 there are 10 – j pairs. Thus the answer is 9 + 8 + 7+ … + 1 = 45
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KICKGMATASS123
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