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In the two-digit integers 3•

This topic has 1 expert reply and 1 member reply
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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In the two-digit integers 3•

Post Mon Aug 07, 2017 9:20 am
In the two-digit integers 3• and 2∆, the symbols • and ∆ represent different digits,and the product (3•)(2∆) is equal to 864. What digit does • represent ?

(1) The sum of • and ∆ is 10.
(2) The product of • and ∆ is 24

Official Guide question
Answer: D

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Colz Newbie | Next Rank: 10 Posts
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06 Nov 2017
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Post Mon Nov 06, 2017 10:05 am
I know this is a DS question, but I have a problem. What If in DS Question one solves the question without the need of either statements? Then what should one do? Is it D or E?

This question in point

Given two digits 3# & 2¢ gives product 864.

Now 864 is divisible by 9. Since last digit is 4 options to get 4 are

6,4 | 4,6| 8,3 | 3,8 | 4,1 | 1,4| 7,2 & 2,7

Out of all options I only can use ones with 6&4 and 7&2. As i need a multiple of 9 in one of these digits

So I started with 36 * 24 and I got answer as 864.


So what to do with the statements now?

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Post Mon Aug 07, 2017 10:10 am
With DIGIT questions like this, usually the only strategy is to TEST NUMBERS.

N.b. This can make these questions time-consuming, and it's hard to be sure if you tested everything. For many students, these questions are a good candidate for guessing.

When solving this one, don't dive straight into the answer choices. First, unpack the given information in the question stem. Since the two numbers multiply to 864, we should find the PRIME FACTORIZATION of 864:

ttps://postimg.org/image/ua1u11gl1/" target="_blank">

864 = (2^5)(3^3)

We now know that 3• and 2∆ must represent multiples of 2 and 3 only, so let's list the possibilities:

1. 32*27 ---> (2^5)(3^3)
2. 36*24 ---> ((2^2)(3^2))((2^3)(3^1))

32 and 36 are the only two numbers in the 30s that contain only 2 and/or 3 as factors, so these must be the only possibilities.

When evaluating the statements, see if you can narrow it down to a single possibility:

(1) The sum of • and ∆ is 10.
Case #1 would give us 2 + 7 = 9, so this doesn't fit the statement.
Case #2 gives us 6 + 4 = 10. So •=6 and ∆=4. Sufficient.

(2) The product of • and ∆ is 24
Case #1 would give us 2*7 = 14, so this doesn't fit the statement.
Case #2 gives us 6*4 = 24. So •=6 and ∆=4. Sufficient.

The answer is D.

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