Number System Question - please assist

Question

If their HCF is 22, the two numbers x and y can be written as 22x and 22y where x and y are co-primes

Now 22x * 22y = 9680

So xy = 20

Now we need to find co-prime pairs whose product is 20

20 = 2 * 5 * 2 = 2^2 * 5

So only two such pairs are possible.

And the numbers possible are -> (22*1, 22 * 20) (22*4, 22*5)

Answer - D

Are you sure the OA is B ?

jamifahad · Answer

i think it should be 3 pairs.
As subhashghosh did, except 20 will have 3 pairs.
20 = 2,10
20= 4,5
20, 20,1

OA A.

fluke · Answer

Can you please tell me what are the three pairs?

I see two pairs at least just as Subhashghosh did:
22*1, 22*20
22*5, 22*4

I can't see the other two.

scbguy · Answer

subhash hi, were getting the same answer "D", but using different methods

The prime factors of 9680 are the following

9680= 2*2*2*2*5*11*11

HCF= 22, hence through the venn diagram, the overlapping set should have 11*2.

This would effectively mean that the two numbers x and y should have a 11 and 2 in common in their prime factors.

The only two possible scenarios would be

Scenario 1
5*2*11
2*2*2*11

Scenario 2
2*11
5*11*2*2*2

every other combination would be redundant hence D

jamifahad · Answer

22*2=44
22*10=220
Product is 9680 but HCF is not 22. so pair (2,10) is not valid.
Ah! indeed it is two pairs. Need co-primes.

fluke · Answer

I guess it can be 4 by flipping the numbers.
x=22; y=440
x=440; y=22
x=110; y=88
x=88; y=110

Still, I'd say the question is open to multiple interpretations.

subhashghosh · Answer

It can't be more than 2, because :

1) we need co-primes

2) Flipping the pairs is not a sensible thing to do, how does it make a difference in the "number of pairs" ?

puneetj · Answer

i used the method that scbguy used but its kinda time consuming..

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