If x and y are positive integers such that (x + y)

Question

If x and y are positive integers such that (x + y) < 10, then which of the following must be true?

A) x < 8

B) x > 3

C) x >y

D) x + y = 5

E) x - y <= 7

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OneLazyBum · Answer

(E)
Since 1<=x<=8 and 1<=y<=8
Therefore,
-7<=x-y<=7
which will be option (E) x-y<=7

ravi1522 · Answer

Hello,
If x and y are positive integers such that (x + y) < 10, then which of the following must be true?
so 1<=X<=8 and 1<=y<=8

so X-y<=7 always

Hence E is correct answer

Nitish03 · Answer

If X and Y are positive integers then Max of X - Min of Y will satisfy the condition.
X-Y = Max of X i.e. 8 - Min of Y i.e. 1 
 = 7 (satisfies the condition as 8+1 > 10)
 
Hence E.

Legallyblond · Answer

ABCD are not must be true so E is the only one left

notyarb · Answer

A) x<8
x<8
Counterexample: x=8, y = 1 → x + y = 9 < 10
x+y=9<10.
So not always true.

B) x > 3
Counterexample: x = 1, y = 1
So not always true.

C) x > y
Counterexample: x = 1, y = 2
So not always true.

D) x + y = 5
Many possibilities do not sum to 5.
So not true.

E) x − y ≤ 7
Largest possible value of x − y occurs when x is largest and y is smallest:

Max x is 8
Min y is 1.

Then x − y = 8 − 1 = 7

Correct answer: E

Dereno · Answer

It’s given that x,y are positive integers ( greater than 0). X >= 1 Y>=1 More over it’s given that (x+y) < 10 ( x+y) minimum = (1+1) = 2 (x+y) maximum = 9 Let’s look into the options : A) x < 8 This means x can take the values 7,6,5,4,3,2,1. But, as per question x can also take the value 8. Hence, Wrong. B) x > 3 x is a positive integer , and x can take values greater than 0. So, 1,2 also exists. Hence, Wrong. C) x >y (x+y) <10. Lets for time being take (x+y) = 9 y=8 and x = 1 . (y>x) This contradicts the option. Hence, wrong. D) x + y = 5 This can be true, but not must be true. Hence, wrong. E) x - y <= 7 (x+y) can take the minimum value of (1+1) = 2 (x+y) < 10 , which means the max value either x or y can take is (1,8) or (8,1). x- y = 8-1 = 7 if y increases, the value of (x-y) falls below 7. Hence, correct. Option E

If x and y are positive integers such that (x + y) < 10, then which of

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