If x and y are integers each with absolute value less than 5 and 7x -

Question

If x and y are integers each with absolute value less than 5 and 7x - 6y = 3, how many values of x are there?

A. 1
B. 2
C. 3
D. 4
E. 5

nailin16 · Answer

7x-6y=3
7x=6y+3
Only x= -3 and x=3 satisfy the equation 
So
Ands is B ie 2

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chetan2u · Answer

Hi,

A way to do such Qs..
7x-6y=3...
7x=6y+3=3(2y+1)....
We can see from this that x HAS to be a multiple of 3..
Possible values are 3&-3..

But remember to check:-
 if these values have y as an integer..
2y+1 can take any ODD values
And for X=3, y=3..
X=-3, y is -4..
So both are OK...
B

Sirakri · Answer

Hi  chetan2u , nice explanation, thank you.

Can you explain this part again if you don't mind?

and this

I've a sort of weakness with this type of questions :/ Any theory you can suggest in this regard?

chetan2u · Answer

Hi 
If we have co-prime numbers and x and y are integers then those variables x and y will be multiple of those PRIME numbers..
Say 7x = 8y...Here x will be multiple of 8 and y will be multiple of 7

Similarly here when you say 7x=3(2y+1)....
In 7x, there has to be a multiple of 3 as RHS is a multiple of 3... So x is a multiple of 3

RMD007 · Answer

I solved it in this way.

We know that x and y are integers such that -5<= x,y<=5
For the equation to hold true 7x - 6y = 3. 
1. x and y can not be equal.
2. 6y will always be even so to get the overall difference as odd number 7x should be odd number. Hence x should be odd number. So |x| = 1,3,5

By plug n play we can figure out that 1 and 5 are not possible. Only 3 makes sense. So 2 values 3,-3.

Hope it helps..

hoang221 · Answer

I used a more brute-force approach, but it's plausible for such question:

7*x - 6*y = 3 => x = (6*y + 3)/7

since both x and y are integers, 6*y + 3 must be a multiple of 7
trying the first 4 multiple of 7 on both positive and negative spectrum, we found that only x = 3 and x = -3 satisfy the condition

Hence the answer (B)

bumpbot · Answer

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If x and y are integers each with absolute value less than 5 and 7x -

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