If d represents a digit from 0 through 9, what is the remainder when

Question

If d represents a digit from 0 through 9, what is the remainder when the number d,340 is divided by 8 ? A. 7 B. 4 C. 2 D. 0 E. Cannot be determined from the given information 2024-01-27_14-52-30.png

Bunuel · Accepted Answer

For divisibility and remainders concerning powers of 2, specific last digits of the number are crucial.

When dividing by 2, only the  last digit  matters. If it's odd, the remainder is 1, if even, the remainder is 0.

When dividing by 4, the  last two digits  determine the remainder. For example, any number ending in ...13 will always leave a remainder of 1 when divided by 4, regardless of the preceding digits.

Similarly, when dividing by 8, the  last three digits  of the number are significant. The remainder of a number ending in ...340 when divided by 8 can be determined by simply dividing 340 by 8.

340 divided by 8 gives the remainder of 4. So, regardless of what digit 'd' represents, the remainder when d,340 is divided by 8 is always 4.

Answer: B.

Bunuel · Answer

Remainder rule when dividing by  2^n :

The remainder when an integer is divided by 2 is determined by its last digit. If the last digit is even, the remainder is 0, if odd, it's 1.

The remainder when an integer is divided by 4 is determined by its last two digits. This pair of digits, considered as a separate number, will give the remainder upon division by 4.

The remainder when an integer is divided by 8 is determined by its last three digits. These three digits, as a standalone number, will give the remainder when divided by 8.

...

Generally, the remainder when an integer is divided by  2^n  is determined by its last  n  digits. These  n  digits, treated as a separate number, will yield the remainder upon division by  2^n .

Hope it helps.

gmatophobia · Answer

d,340 = 1000*d + 340

Remainder( \frac{	ext{d,340}}{8} ) = Remainder( \frac{	ext{1000*d}}{8} ) + Remainder( \frac{	ext{340}}{8} )

Remainder( \frac{	ext{d,340}}{8} ) = 0 + Remainder( \frac{	ext{340}}{8} )

Remainder( \frac{	ext{d,340}}{8} ) = 0 + Remainder( \frac{	ext{336 + 4}}{8} )

Remainder( \frac{	ext{d,340}}{8} ) = Remainder( \frac{336}{8})  + Remainder( \frac{4}{8} )

Remainder( \frac{	ext{d,340}}{8} ) = 0 + Remainder( \frac{4}{8} = 4 )

Option C

vasu1104 · Answer

to find the remainder of num when divided by 8, we need to consider only last 3 digits of the particular num.

so here we consider only 340.
when divided by 8, 340 will have 4 as remainder.

so we really dont care about what d could be.

choice B

If d represents a digit from 0 through 9, what is the remainder when

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If d represents a digit from 0 through 9, what is the remainder when

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

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