How many distinct positive integers\(d\) exist such that, when 48 is divided by\(d\) , the remainder is\( d -4\)?
A. Two
B. Three
C. Four
D. Five
E. Six
Dividing 48 by\(d\) and obtaining a remainder of\( d -4\) can be expressed as\( 48 = qd + (d -4)\) . Note that since the remainder must be non-negative, we have\( d - 4 \geq0\) , which implies\( d \geq4\) .
Rewriting\( 48 = qd + (d -4)\) leads to\( q + 1= \frac{52}{d}\) . Here, since\( q +1\) is an integer,\(\frac{52}{d}\) must also be an integer, meaning\(d\) is a factor of 52. The factors of 52 are 1, 2, 4, 13, 26, and 52. Given that\( d \geq4\) , the valid values for\(d\) are 4, 13, 26, and 52.
Therefore, there are four possible values for\(d\) .
Answer: C
...
A. Two
B. Three
C. Four
D. Five
E. Six
Dividing 48 by\(d\) and obtaining a remainder of\( d -4\) can be expressed as\( 48 = qd + (d -4)\) . Note that since the remainder must be non-negative, we have\( d - 4 \geq0\) , which implies\( d \geq4\) .
Rewriting\( 48 = qd + (d -4)\) leads to\( q + 1= \frac{52}{d}\) . Here, since\( q +1\) is an integer,\(\frac{52}{d}\) must also be an integer, meaning\(d\) is a factor of 52. The factors of 52 are 1, 2, 4, 13, 26, and 52. Given that\( d \geq4\) , the valid values for\(d\) are 4, 13, 26, and 52.
Therefore, there are four possible values for\(d\) .
Answer: C
...
Statistics : Posted by Bunuel • on 21 May 2022, 09:32 • Replies 3 • Views 2195