a is the hundreds digit of the three digit integer x,

BTGModeratorVI wrote: ↑

Sun Feb 23, 2020 6:58 am

a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. a = 2b = 4c, and a > 0.
What is the difference between the two greatest possible values of x?

A. 124
B. 297
C. 394
D. 421
E. 842

Source: Veritas
Answer: D

Our 3-digit number looks like this: abc

If a = 4c, then c cannot be greater than 2. Otherwise, a will not be a digit.
For example, if we let c = 3, then a = 12, and 12 is not a digit.

So, there are ONLY TWO possible values for c.
Case a: c = 1
If a = 2b = 4c, the a = 4, b = 2 and c = 1
So, the resulting 3-digit number (aka x) is 421

Case b: c = 2
If a = 2b = 4c, the a = 8, b = 4 and c = 2
So, the resulting 3-digit number (aka x) is 842

What is the difference between the two greatest possible values of x?
There are only 2 possible values of x.
Their DIFFERENCE = 842 - 421 = 421

Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sun Feb 23, 2020 6:58 am

a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. a = 2b = 4c, and a > 0.
What is the difference between the two greatest possible values of x?

A. 124
B. 297
C. 394
D. 421
E. 842

Source: Veritas
Answer: D

We see that the value of c is the smallest. Since a > 0, b and c are also greater than 0; therefore,

If c = 1, we have a = 4, b = 2, and hence x = 421.

If c = 2, we have a = 8, b = 4, and hence x = 842.

Since c can’t be 3 or more (otherwise a would be a two-digit number), there are only 2 possible values of x, and their difference is 842 - 421 = 421.

Answer: D