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# D represents a single digit number from 1 to 9. What is the value of D

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Math Expert
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D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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28 Jul 2017, 01:23
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45% (medium)

Question Stats:

70% (01:27) correct 30% (01:43) wrong based on 229 sessions

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D represents a single digit number from 1 to 9. What is the value of D?

(1) D.D + DD = D.D × DD
(2) D is not a prime number.

The dot (.) represents a decimal point.

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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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28 Jul 2017, 01:48
1
Bunuel wrote:
D represents a single digit number from 1 to 9. What is the value of D?

(1) D.D + DD = D.D × DD
(2) D is not a prime number.

The dot (.) represents a decimal point.

(1) D.D + DD = D.D × DD
1.1 + 11 = 1.1 * 11 Yes
2.2 + 22 = 2.2 * 22 No

9.9 + 99 = 9.9 * 99 No (Only D=1 can hold)

Sufficient

(2) D can represent 2, 3, 5, 7...Not Sufficient

A
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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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30 Jul 2017, 11:09
(1)Sufficient
D +D/10 + 11D = (D+D/10)*11D
-> 121D = 121D^2
-> D(D-1) = 0
D is from 1-9 so D =1
(2) Not
D can be 1,4,6,8,9
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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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24 Aug 2017, 01:15
2
My approach:

1- Let 2 digit number DD is a, then D.D = a/10

a/10 + a = a/10 x a
11a/10 = a^2 /10
11 = a (a is positive so we can get rid of a/10 on both side)

so D = 1 => SUFF

2- D not prime, so D can be 4, 6, 8 => INSUFF

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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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14 Sep 2017, 14:40
Tried plugging in, which worked:
1) 22*2.2 = 22+2.2 not possible
11*1.1 = 11+ 1.1 --> possible
Suff
2) D not prime -- multiple values possible then. Not suff

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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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17 Dec 2017, 15:17
Hi All,

This question can be solved with a little math and a bit of 'brute force.'

We're told that D is a positive DIGIT (meaning 1-9, inclusive). We're asked for the value of D.

1) D.D + DD = (D.D)(DD)

While this might look complex, if you substitute in a value for D, you'll find that math to be rather straight-forward....

IF.... D = 1, we have...
1.1 + 11 = (1.1)(11)

Does that equation 'balance out?'
1.1 + 11 = 12.1
(1.1)(11) = 12.1
So YES, D could equal 1.

What about D = 2? Does....
2.2 + 22 = (2.2)(22)

You should be able to answer that question WITHOUT actually doing the math. On the left side, you're ADDING 10% of 22 to 22 and on the right side you're MULTIPLYING those values. The right side will clearly be a lot bigger than the left side. This means that D CANNOT equal 2.

Now how about D=3? D=4? Etc. You should see that you run into the same issue that you did when we worked through D=2: the right side is much bigger than the left side, so there's really no need to check all of those values. This means that D=1 is the ONLY possible solution.
Fact 1 is SUFFICIENT.

2) D is not a prime number

This tells us that D cannot be 2, 3, 5 or 7.... but that still leaves us with 5 other possibilities (1, 4, 6, 8 and 9)
Fact 2 is INSUFFICIENT.

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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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08 Apr 2018, 06:11
Bunuel wrote:
D represents a single digit number from 1 to 9. What is the value of D?

(1) D.D + DD = D.D × DD
(2) D is not a prime number.

The dot (.) represents a decimal point.

by statement 1,

D.D + DD = (D.D) (DD)
$$\frac{DD}{10}+ DD = \frac{DD}{10} (DD)$$
DD + 10DD = (DD) (DD)
11DD = (DD) (DD)
DD = 11

therefore, statement 1 is sufficient.

Statement 2 gives no proper information.

Please correct me if my solution is wrong.
Thanks
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Re: D represents a single digit number from 1 to 9. What is the value of D  [#permalink]

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08 Apr 2018, 09:44
(1) DD+D.D=DD*D.D
=DD(1+1/10)=(DD^2)/10
=11/10=DD/10
DD=11
SUFFICIENT

(2) D can represent 2, 3, 5, 7...NOT SUFFICIENT
Re: D represents a single digit number from 1 to 9. What is the value of D &nbs [#permalink] 08 Apr 2018, 09:44
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