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

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Manager
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If x and y are positive integers such that the product of x [#permalink]  23 Jul 2008, 06:22
If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7x + 9y?

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

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient
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Re: Units' digit [#permalink]  23 Jul 2008, 06:37
Capthan wrote:
If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7x + 9y?

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

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient

Product of two numbers prime means that one number is 1 and other number is prime number itself

Statement 1) tells that y is prime number since it is not 1 and prime number will be 29 in this case. Therefore 7x + 9y = 7*1 + 9*29. Sufficient

Statement 2) is not sufficient since it does not tell any way of finding value of y.

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Re: Units' digit [#permalink]  23 Jul 2008, 07:09
nmohindru wrote:
Capthan wrote:
If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7x + 9y?

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

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient

Product of two numbers prime means that one number is 1 and other number is prime number itself

Statement 1) tells that y is prime number since it is not 1 and prime number will be 29 in this case. Therefore 7x + 9y = 7*1 + 9*29. Sufficient

Statement 2) is not sufficient since it does not tell any way of finding value of y.

E, y could be 29 or 31.
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Re: Units' digit [#permalink]  23 Jul 2008, 07:31
A

y = 31 or 29

the unit digit of 9y is going to be 1 for both cases

7 + 1 = 8
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Re: Units' digit [#permalink]  23 Jul 2008, 07:54
gmatnub wrote:
A

y = 31 or 29

the unit digit of 9y is going to be 1 for both cases

7 + 1 = 8

Oops!
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Re: Units' digit [#permalink]  23 Jul 2008, 15:15
31 x 9 = 279
29 x 9 = 261

Did I miss something?

young_gun wrote:
gmatnub wrote:
A

y = 31 or 29

the unit digit of 9y is going to be 1 for both cases

7 + 1 = 8

Oops!
Senior Manager
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Re: Units' digit [#permalink]  25 Jul 2008, 06:50
xy= prime
one of x or y is 1 and the other is prime

(1) 24 < y < 32
so y is not 1
y can be 29 or 31
Not sufficient

(2) x = 1
no information on y
Not sufficient

(1) & (2)
we cannot get the exact info on y
not sufficient
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Re: Units' digit [#permalink]  26 Jul 2008, 02:52
E

from 1 and from the combination of 1 and 2 we know:
y could be 29 or 31

7*x=7

9*y= 9*31 or 9*29

the unit digit would therefore be 9 or 1

9+7=16, so unit 6

1+7=8, so unit 8

so ins
Re: Units' digit   [#permalink] 26 Jul 2008, 02:52
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