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