124k views
4 votes
Using all the digits from 1 to 9 inclusive, Shahb wrote down a fraction which had four digits in the numerator and five digits in the denominator. He then noticed that the fraction simplified to give exactly one half. Which of the following could have been the numerator of Shahb’s fraction?

1 Answer

3 votes

The numerator of Shahb's fraction, which includes four digits from 1 to 9 inclusive, is B. 6729.

The numerator is the number taken out of a whole number. It represents the fractional part of the whole value.

How option B is chosen:

To make the numerator and denominator result in one-half, the denominator must be two times the numerator:

A) 5314/(5314 x 2) = 5314/10628 ... one digit (1) is repeated while others (7 and 9) are not included in either the numerator or the denominator.

B) 6729/(6729 x 2) = 6729/13458 ... no digit is repeated in both the numerator and the denominator, and there is no omission of any digits from 1 to 9.

C) 7341/( 7341 x 2) = 7341/14682 ...one digit (1) is repeated while others (5 and 9) are not included in either the numerator or the denominator.

D) 7629/(7629 x 2) = 7629/15258...two digits (2 and 5) are repeated while others (3 and 4) are not included in either the numerator or the denominator.

E) 8359/(8359 x 2) = 8359/16,718...two digits (1 and 8) are repeated while others (2 and 4) are not included in either the numerator or the denominator.

Simplifying 6729/13458 = 1/2.

Thus, the correct option is B.

Complete Question:

Using all of the digits from 1 to 9 inclusive, Shahb wrote down a fraction that had four digits in the numerator and five digits in the denominator. He then noticed that was the fraction simplified to give exactly one-half.

Which of the following could have been the numerator of Shahb's fraction?

A. 5314 B. 6729 C. 7341 D. 7629 E. 8359

User Miquelvir
by
7.5k points