Follow table of 7

9 comes at units digit only when multiplied by 7

Therefore ans has to be the one which has 7 as units place.

Ans is E (irrespective of first two digits)

The key to answering this question is the knowledge that we get 9 as the unit's digit if we multiply a number with unit's digit 7 with another number ending in 7 as well . There is no other combination giving a 9 when ----7 is multiplied by ----X (where x=0 to 9 excluding 7).

Thus per the question---> abcd9 = ef7*gh7 ----> Thus E is the correct answer.
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This question is a classic example which emphasizes on the importance of Concept of Unit digit. Looking at the calculation of unit digit is not only required to solve questions like this but also to eliminate wrong options in many other Problem solving questions

As we Know,

\(\frac{Dividend}{Divisor} = Quotient\)

i.e. \(Dividend = Divisor * Quotient\)

Here, \(\frac{abcd9}{ef7} = Quotient\)

i.e. \(abcd9 = Quotient * ef7\)

And the Quotient is available among the options

So, when Unit digit of ef7 is multiplied with Unit digit of Correct option should result in the Unit Digit of abcd9

Option E: 7 * 7 = 9

i.e. Answer: Option E
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\(\frac{abcd9}{ef7} = x\) (\(x\) is integer)

since the units digit of the numerator and the denominator are 9 and 7 respectively, the quotient's units digit must be 7. For instance 49/7 = 7. Only option E satisfies this condition. Hence, Ans (E).
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Given:

abcd9 / ef7 = x
=> abcd9 = x * ef7

Since we know that the units digit of the given five digit number is 9, and ef7 * 7 = ****9. We need an answer option with unit digit 7.
Hence option E.

Suppose there are two options which has unit digit as 7, is there a way to find the answer?

It will be very difficult to choose one of the 2 options, but lets say you do get such a question, I believe there will be 1 more condition with which you will be able to eliminate 1 of the 2 options. If not, there can be very many possibilities to choose from and definitely not possible within 2 minutes that are given to you for solving 1 GMAT Quant question.
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There are generally three things to be looked at in all such questions

1) The unit digit calculation
2) No. of digits in the final result as product of two numbers with their specific number of digits
3) Digits referred by similar alphabets (i.e. same digits) among the numbers to be multiplied and the result of multiplication

Just keep an eye on all three things and certainly the question can be solved if it has been made for GMAT

I hope it helps!
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looking at the last digits ...7*..7=..9..
only 7*7 have last digit as 9, so the quotient has to have last digit as 7..
ans E
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800score Official Solution:

(To understand units and tens, in 75 7 is tens and 5 is units.) This question is testing your knowledge of the fact that when you multiply multi-digit integers, the units digit of the result is the same as the units digit on the product of the units digits of the original integers. For example, the units digit of the result of 1,237 × 653 is 1, because the units digit on the result of 7 × 3 is 1.

So if abcd9 is divisible by ef7, we know that:
(abcd9) / (ef7) = some integer.

Rearranging this equation, we have:
ef7 × (some integer) = abcd9.

Let’s think about possibilities for the units digit of this unknown integer, given the rule above:
7 × 1 = 7
7 × 2 = 14
7 × 3 = 21
…
7 × 7 = 49.

We can see that if the unknown integer has a units digit of 7, then abcd9 may be divisible by ef7.
gh7 is the only answer with a units digit of 7.

The correct answer is choice (E).
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