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# What is the two-digit number whose first digit is a and whose second

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Math Expert
Joined: 02 Sep 2009
Posts: 49267
What is the two-digit number whose first digit is a and whose second  [#permalink]

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05 Nov 2017, 01:41
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Difficulty:

45% (medium)

Question Stats:

61% (01:06) correct 39% (01:21) wrong based on 41 sessions

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What is the two-digit number whose first digit is a and whose second digit is b ? The number is greater than 9.

(1) 2a + 3b = 11a + 2b
(2) The two-digit number is a multiple of 19.

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Math Expert
Joined: 02 Aug 2009
Posts: 6789
Re: What is the two-digit number whose first digit is a and whose second  [#permalink]

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05 Nov 2017, 01:48
Bunuel wrote:
What is the two-digit number whose first digit is a and whose second digit is b ? The number is greater than 9.

(1) 2a + 3b = 11a + 2b
(2) The two-digit number is a multiple of 19.

the two-digit number whose first digit is a and whose second digit is b ? The number is greater than 9.
this tells us that a>0

lets see the statements

(1) 2a + 3b = 11a + 2b

$$11a-2a=3b-2b.........9a=b$$
for b to be a digit a can take ONLY one value 1, otherwise b will become 2-digit number
so a=1, b = 9a=9
number = 19
suff

(2) The two-digit number is a multiple of 19
it can be 19,38 etc
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the two-digit number whose first digit is a and whose second &nbs [#permalink] 05 Nov 2017, 01:48
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