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In a certain two-digit integer, the ratio of the units

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In a certain two-digit integer, the ratio of the units

by BTGmoderatorLU » Fri Nov 16, 2018 2:19 pm

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Source: GMAT Paper Tests

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 OA D
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by fskilnik@GMATH » Sat Nov 17, 2018 3:11 pm

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BTGmoderatorLU wrote:Source: GMAT Paper Tests

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.
\[N = \left\langle {AB} \right\rangle \,\,,\,\,\,\left\{ \begin{gathered}
\,A = 3k \hfill \\
\,B = 2k \hfill \\
\end{gathered} \right.\,\,\,\,\left( {k \in \left\{ {1,2,3} \right\}\,\,\left( * \right)\,} \right)\]
\[? = N\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{\,? = k\,}\]
\[\left( 1 \right)\,\,3 = A - B = k\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]
\[\left( 2 \right)\,\,54 = A \cdot B = 6{k^2}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,k = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Jay@ManhattanReview » Mon Nov 19, 2018 10:25 pm

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BTGmoderatorLU wrote:Source: GMAT Paper Tests

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 OA D
Given for the two-digit integer, the ratio of the units digit to the tens digit is 2 to 3, there are three possibilities.

The number can be one of the following: 32; 64; and 96.

Let's take each statement one by one.

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

Only 96 qualifies. Sufficient.

2) The product of the two digits is 54.

Only 96 qualifies. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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