If a, b and c are positive, is ac 5?

Question

If a, b and c are positive, is ac > 5?

(1) a + b = 3
(2) 4 = c - b

pushpitkc · Answer

(1) a + b = 3 
Without knowing the value of c, we cannot determine if the expression(ac) is greater than 5.
Hence, insufficient
 (2) 4 = c - b 
Without knowinth the value of a, we cannot determine if the expression(ac) is greater than 5.
Hence, insufficient.

On combining the information from both the statements, 
b = 3 - a and b = c - 4
Therefore  a + c = 7
 
Though the sum of a and c is 7, it is possible that the expression (ac) is greater/lesser than 5
Case 1: a = 6.2,c = 0.8. Here ac = 4.96 < 5
Case 2: a = 4, b = 3. Here ac = 12 > 5  (Insufficient)(Option E)

ksanchay92 · Answer

a, b, and c are positive.
Ok.

1. a + b = 3 Cant say, without knowing the value of c.

2. 4 = c - b Cant say, without knowing the value of a.

1&2. b = 3 - a, b = c - 4 which gives, a + c = 7.
Now, assume a=1, c=6, ac=6>5.
Now, assume a=0.5, c=6.5, ac=3.25<5.

Not sufficient.
Option E. :shock:

I just selected the wrong answer myself. :cry:

I just selected the wrong answer myself. :cry:

VeritasPrepBrian · Answer

I love this problem as an example of how some of the simplest testmaker "tricks" - like "did you remember to think about nonintegers?" -can appear on the hardest problems when you're not looking for them. Here the statements are really cleverly set up to get you thinking about integers: all provided values are integers, and when you start playing with the statements it's a pretty clever problem if you're just using integers (4 = c - b makes you think that c has to be at least 5 on its own, if you assume that b has to be at least 1).

So what does the testmaker do while you're satisfying your intellect playing with the various integer options? The whole time it allows for a to be a really small fraction/decimal that makes the product ac super small leading to an "obvious" no for "is ac > 5?" It's just that when our intellect is piqued with interesting math, the "page one" mistakes (don't assume integer, don't assume positive, etc.) are their most powerful. That's why I'm a big fan of writing really quickly on your scarchpad a quick checklist of things to always check for (fractions, negatives, 0, infinity) to make sure you're not falling for one of these traps because your mind got so occupied with something interesting in the problem that you forgot to check the common pitfalls.

LeoN88 · Answer

a,b,c>0
Statement 1.
a= 3-b
So, a<3

Statement 2.
c= b+4
c>4

Now, both 1 and 2 are independently insufficient.
ac can be 1*5, ac=5
ac can be 1*10, ac>5. Insufficient.  E

bumpbot · Answer

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If a, b and c are positive, is ac > 5?

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