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# If x and y are positive integers such that the product of x

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Senior Manager
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If x and y are positive integers such that the product of x [#permalink]

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01 Nov 2006, 11:58
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If x and y are positive integers such that the product of x and y is prime, what is the unitsâ€™ digit of 7xx + 9y?

(1) 24 < y < 32
(2) x = 1

--> Here, i'm not sure if 7xx means (7)(x)(x) or xx are the last two digits of a 3 digit number 7_ _
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Impossible is nothing

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Re: DS: Variables - Difficult [#permalink]

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01 Nov 2006, 12:43
Hermione wrote:
If x and y are positive integers such that the product of x and y is prime, what is the unitsâ€™ digit of 7xx + 9y?

(1) 24 < y < 32
(2) x = 1

--> Here, i'm not sure if 7xx means (7)(x)(x) or xx are the last two digits of a 3 digit number 7_ _

In either case, I get 2 sets of diff units digits.

St 2 is redundant. If product of 2 nbrs is prime, then one of them has to be 1 and the other prime. S1 resolves that by saying y is between 24 and 32 which gives us 2 primes, 29 and 31 for the value of y.

For 7XX +9Y, I get 972 and 990
For 7X^2+9Y, I get 268 and 286

Hence E.
(Hope I havent made any calc mistakes)
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01 Nov 2006, 12:45
should be the 2 digits, otherwise it would be x^2

upadate: calculated - also E, same numbers
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01 Nov 2006, 13:10
St 1 insuuf info abt y
st2 info abt x only so insuff

Combining we get y must be prime.
but within the specified we get 2 values for y i.e 29 and 31
so insuff

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01 Nov 2006, 15:33
Peter Green wrote:
should be the 2 digits, otherwise it would be x^2

upadate: calculated - also E, same numbers

It makes no difference Either way.
01 Nov 2006, 15:33
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