Baton wrote:If a, b, and c are integers, what's the value of a?
1. (a-7)(b-7)(c-7)=0
2. bc=18
None of the statements is sufficient on it's own so here is how I am solving it after realizing it can't be solved algebraically.
From statement 2, I let b=2 and c=9. (taking negative numbers will yield the same result)
(a-7)(2-7)(9-7)=0
(a-7)(-5)(2)=0
a=7
It's good that you tested some values, but testing only 1 pair does not mean that we can safely say that a must equal 7.
If it weren't for the given information that says a, b and c are integers, the answer would be E.
So, testing one set of values isn't enough.
You must recognize that, because b and c are integers, it's impossible for either b or c to equal 7, which means a must equal 7.
Cheers,
Brent
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Plugging in numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question.
Conversely, if the statement is SUFFICIENT, then plugging in values will only HINT at whether or not the statement is sufficient, but you won't be able to make any definitive conclusions.
For example, let's say we have the following target question:
If n is a positive integer, is (2^n) - 1 prime?
Let's say statement 1 says:
n is a prime number:
Now let's plug in some prime values of n:
If n = 2, then
(2^n) - 1 = 2² - 1 = 3, and 3 IS prime
If n = 3, then case
(2^n) - 1 = 2³ - 1 = 7, and 7 IS prime
If n = 5, then
(2^n) - 1 = 2� - 1 = 31, and 31 IS prime
At this point, it certainly APPEARS that statement guarantees that (2^n) - 1 is prime? Let's try one more prime value of n.
If n = 7, then
(2^n) - 1 = 2� - 1 = 127, and 127 IS prime
So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let's examine the possibility that n = 11
If n = 11, then
(2^n) - 1 = (2^11) - 1 = 2047, and 2047 is NOT prime
Here's a different example:
Target question:
Is x > 0?
Let's say statement 1 says: 5x > 4x
Now let's plug in some values of x that satisfy the condition that 5x > 4x.
x = 3, in which case
x > 0
x = 0.5, in which case
x > 0
x = 15, in which case
x > 0
x = 1000, in which case
x > 0
Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers (as was the case in the first example). Perhaps there's a number that we could have plugged in such that
x < 0
If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in.
Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA - we can now answer the target question with absolute certainty.
So, statement 1 is SUFFICIENT.
TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can STRONGLY HINT at sufficiency, but the results are not 100% conclusive.
For more on this, you can watch our free video titled "Choosing Good Numbers:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1102 or you can read an article I wrote for BTG about it:
https://www.beatthegmat.com/mba/2013/10/ ... -in-values
Or you can read my article:
https://www.beatthegmat.com/mba/2013/10/ ... -in-values[/i]
