In a certain two-digit integer, the ratio of the units digit : GMAT Data Sufficiency (DS)
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# In a certain two-digit integer, the ratio of the units digit

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In a certain two-digit integer, the ratio of the units digit [#permalink]

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07 Jan 2013, 21:46
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In a certain two-digit integer, the ratio of the units digit to the tens digit is 2 to 3. What is the integer?

(1) The tens digit is 3 more than the units digit.

(2) The product of the two digits is 54.
[Reveal] Spoiler: OA
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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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07 Jan 2013, 21:54
(1)I get more than one possibilities therefore I think BCE

(2) i get 96 so B is a possibility

so I think the answer is C because 96 appears in both but OG says D?

How is statement one sufficient when more than once possibility can be derived from stmt 1
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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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07 Jan 2013, 22:13
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There are only three possibilities with ratio 3:2 -> 32, 64, and 96.

(1) The tens digit is 3 more than the units digit.
SUFFICIENT: Only number that satisfies is 96. (6+3=9)

(2) The product of the two digits is 54.
SUFFICIENT: Only number that satisfies is 96. (9 * 6=54)

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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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07 Jan 2013, 22:18
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jsphcal wrote:
In a certain two-digit integer, the ratio of the units digit to the tens digit is 2 to 3. What is the integer?

(1) The tens digit is 3 more than the units digit.

(2) The product of the two digits is 54.

The possible integers are 32, 64 and 96.

1) 3-2 = 1, 6-4 = 2, 9-6 = 3. Only 96 satisfies the statement. Sufficient.

2) 3*2 = 6, 6*4 = 24, 9*6 = 54. Only 96 satisfies the statement. Sufficient.

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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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01 Jun 2014, 01:32
the two digits be -9 and -6 in that case "B" option would yield 54 so the digits can be 9 & 6 as well as -9 & -6
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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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02 Jun 2014, 00:28
Given:

units to tens = 2:3

Meaning it could be:

32
63
96

(It cannot be negative as the ratio given is positive.) Although we could say it's "-6 and -9" it does not make sense as these numbers together make up a two-digit integer.

Leaving us with the numbers above.

The first statement gives us that the digit in the tens place is 3 times larger than the one in the units place. As we've already worked out the three possibilities, we can rule out 32 and 63.

Statement 1 is sufficient.

Statement two gives us the product between the two numbers that make up the integer. We can simply find that the products are, respectively, 6, 18 and 54.

54 matches 96(9*6). Statement 2 is therefore sufficient.

Hence, D.
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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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07 Jun 2014, 08:50
SaudKhan wrote:
the two digits be -9 and -6 in that case "B" option would yield 54 so the digits can be 9 & 6 as well as -9 & -6

Why cant the two digits both be -9 and -6 ? I am still confused on this ...
Option A will fail , but B will hold ?
Can any one clarify this ....
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In a certain two-digit integer, the ratio of the units digit [#permalink]

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18 Oct 2014, 12:07
U/T = 2/3, what is UT?

From 1, T = U + 3 => we know that 3U = 2T that means U is multiple of 2 and T is multiple of 3.
T => -9,-6,-3,3,6,9, negatives are not possible, when T=3 not possible, T=6 then U = 5 not possible, T=9 then U=6 and ratio is intact, UT = 96 in both cases. Sufficient.

From 2, UT=54 and U/T=2/3 => \sqrt{T} = \sqrt{9x9} => T = +-9 =>
if T = -9, U = -6 => Not possible ==> -9-6 ???
if T = +9, U = 6, =>UT = 96 yes

jsphcal wrote:
In a certain two-digit integer, the ratio of the units digit to the tens digit is 2 to 3. What is the integer?

(1) The tens digit is 3 more than the units digit.

(2) The product of the two digits is 54.

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[Reveal] Spoiler:

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Re: In a certain two-digit integer, the ratio of the units digit [#permalink]

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18 Oct 2014, 12:11
Question is asking what is UT and not what is U*T. Test maker confuse you with giving you information that stick to your mind, like in st2. Watch this trap!

U and T cannot be negative at all. So the UT can only be 96 in this case.

SaudKhan wrote:
the two digits be -9 and -6 in that case "B" option would yield 54 so the digits can be 9 & 6 as well as -9 & -6

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Re: In a certain two-digit integer, the ratio of the units digit   [#permalink] 18 Oct 2014, 12:11
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