If AB is divisible by 5 but not divisible by 2 and BA is divisible 3. Then which of the following is possible value of A and B?

(x-2)(x-5)= – 7x + 10

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(x+2) (x-2) = - 4

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A=7,B=5

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A=4,B=0

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Solution

The correct option is B
(x+2) (x-2) = - 4

AB is divisible by 5. Thus B should be either 0 or 5. But since AB is not divisible by 2, B is surely 5.
Since BA is divisible by 3, A+B should also be divisible by 3.
But B is 5. Thus A + 5 should also be divisible by 3.
Among the options, A+5 will be divisible by 3 only if A=4.

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Similar questions

If AB is divisible by 5 but not by 2 and BA is divisible 3. Then which of the following is possible value of A and B?

a.A=5,B=2

b.A=4,B=5

c.A=7,B=5

d.A=4,B=0

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Q. If n is a natural number, then 9²ⁿ − 4²ⁿ is always divisible by

(a) 5
(b) 13
(c) both 5 and 13
(d) None of these

[Hint : 9²ⁿ − 4²ⁿ is of the form a²ⁿ − b²ⁿ which is divisible by both a − b and a + b. So, 9²ⁿ − 4²ⁿ is divisible by both 9 − 4 = 5 and 9 + 4 = 13.]

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