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655-705 Level|   Arithmetic|      
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babusona
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What is the two-digit positive integer whose tens digit is a Updated on: 08 Mar 2012, 08:57
Originally posted by babusona on 08 Mar 2012, 07:30.
Last edited by Bunuel on 08 Mar 2012, 08:57, edited 1 time in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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65% (hard)

Question Stats:

61% (02:13) correct 39% (02:04) wrong based on 635 sessions

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What is the two-digit positive integer whose tens digit is a and whose units digit is b?

(1) 2a > 3b > 6
(2) a > 2b > 6
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B
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Bunuel
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What is the two-digit positive integer whose tens digit is a 08 Mar 2012, 08:56
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babusona
What is the 2 digit positive integer whose 1st digit is a and 2nd digit is b?
a) 2a > 3b > 6
b) a > 2b > 6
Show more

Original question reads:
What is the two-digit positive integer whose tens digit is a and whose units digit is b?

(1) 2a > 3b > 6 --> several cases are possible, for example b=3 and and a=5 or b=4 and and a=7. Not sufficient.

(2) a > 2b > 6 --> the least value of 2b is 8, for b=4 and since a is a single digit it can only be 9 (if b>4 then a won't be a single digit anymore). Sufficient.

Answer: B.

Similar questions to practice:
if-x-0-abcd-where-a-b-c-and-d-each-represent-a-nonzero-127399.html
if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html

Hope it helps.
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What is the two-digit positive integer whose tens digit is a 08 Mar 2012, 07:55
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a) 2a> 3b > 6

a=9, b=5 18> 15> 6
or
a=8, b=4 16> 12> 6

Insufficient

b) a > 2b > 6

a=9, b=4 9>8>6

This is the only possibility.

Sufficient.

B
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What is the two-digit positive integer whose tens digit is a 02 Oct 2017, 22:08
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in the statement B only 'a' is given hinting that most largest number should be 9, and 2b should be in this case is 8,
where as in statement a we have multiple answer.

So answer should be B
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What is the two-digit positive integer whose tens digit is a 17 Aug 2023, 07:56
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babusona
What is the two-digit positive integer whose tens digit is a and whose units digit is b?

(1) 2a > 3b > 6
(2) a > 2b > 6
Show more

Solution:
Pre Analysis:
  • Tens digit is a and the unit digit is b
  • We are asked the two-digit positive integer

Statement 1: \(2a > 3b > 6\)
  • According to this statement,
    • \(2a>6\) or \(a>3\)
    • \(3b>6\) or \(b>2\)
    • \(2a > 3b\) or \(a>1.5b\)
  • Multiple cases possible:
    • If \(b=3\), then \(a=5,6,7,8,9\)
    • If \(b=4\), then \(a=7,8,9\)
    • If \(b=5\), then \(a=8,9\)
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: \(a > 2b > 6\)
  • According to this statement,
    • \(a>6\)
    • \(2b>6\) or \(b>3\)
    • \(a > 2b\)
  • Only one possible case i.e., when \(b=4\) and \(a=9\)
  • statement 2 alone is sufficient

Hence the right answer is Option B
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What is the two-digit positive integer whose tens digit is a 28 Aug 2025, 09:14
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