Problem Solving

BTGmoderatorDC wrote: ↑

Wed Apr 08, 2020 2:58 am

If a and b are positive integers such that a/b = 82.024, which of the following can be the value of b?

(A) 100
(B) 150
(C) 200
(D) 250
(E) 550

OA D

Source: Veritas Prep

Notice that we can rewrite 82.024 as 82 + 24/1000
So, 82.024 = 82 + 24/1000
Simplify to get: 82.024 = 82 + 3/125
Rewritten as an ENTIRE fraction, we get: 82.024 = [(82)(125) + 3]/125

a/b = [(82)(125) + 3]/125, so b COULD equal 125.
When we check the answer choices, we don't see 125.
That's okay, because we can rewrite [(82)(125) + 3]/125 as an EQUIVALENT fraction, just like we can rewrite 3/7 as 6/14 or 9/21 or 12/28 etc.

Likewise, if we rewrite [(82)(125) + 3]/125 as an EQUIVALENT fraction, the denominator (b) can be ANY MULTIPLE of 125
Checking the answer choices, only 250 is a multiple of 125

Answer: D

Cheers,
Brent

BTGmoderatorDC wrote: ↑

Wed Apr 08, 2020 2:58 am

If a and b are positive integers such that a/b = 82.024, which of the following can be the value of b?

(A) 100
(B) 150
(C) 200
(D) 250
(E) 550

OA D

Source: Veritas Prep

Solution:

a/b = 82 + 0.024

a = 82b + 0.024b

Notice that 0.024b is the remainder when a is divided by b and it must be an integer. We see that b must be 250 since only 0.024 x 250 = 6 is an integer (note: all the other values of b will have 0.024b as a non-integer).

Alternate Solution:

Since a/b = 82.024, the quotient from the division of a by b is 82. Let R be the remainder from the division of a by b. Then, we have:

a = 82b + R

a/b = 82 + R/b

82.024 = 82 + R/b

R/b = 0.024 = 24/1000 = 3/125

Since R and b are integers, b must be a multiple of 125. The only multiple of 125 among the answer choices is 250.

Answer: D