Question: 1/10 and 1/2

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Comment on 1/10 and 1/2

We can also solve for 1) as follow, instead of using all values and make calculation
we can rewrite expression in 1) as

10>4x+2>2, this means, 4x+2 can be 3,4,5,6,7,8 or 9
if we solve above, we get
8>4x>0
divide by 4
2>x>0,
that leave us option: x=1.

Can we do following?
1/x<1/y<1/z then x>y>z, i think so.
gmat-admin's picture

Fantastic!

Your suggested rule (if 1/x <1/y < 1/z then x > y > z) is true AS LONG AS x, y, and z are all positive or all negative.

For example, 1/(-2) < 1/(-3) < 1/2, however we can't say that -2 > -3 > 2

Thank you so much.

I really liked your videos. The way that you solves and explains little facts are really amazing as these little facts can trick in simple questions.

Cheers
Atul

Great video. Question: on test day, would we have to go through each of the integers from 3-9 to figure something like this out? Or is there a way we can identify a shortcut when we see something like this? If not, I guess just knowing this question type beforehand will save us time so we can get right to it.
gmat-admin's picture

Once we know that 4x+2 equals one of the integers from 3 to 9, we can automatically eliminate all of the ODD integers, since 4x will be EVEN and when we add 2, the result is EVEN.

This leaves us with 4, 6 or 8 top test.

Thank you!

Brent,

Please help me, I solved the first stated as below.

1/10 < 1/4x+2 < 1/2

0.1 < 1/4x+2 < 0.5

Since there is no integer that lies between 0.1 & 0.5, I declared this statement to be insufficient.
gmat-admin's picture

Be careful. We are told that x is an integer. We are not told that 1/(4x+2) is an integer.

For example, ix x = 1, then 1/(4x+2) = 1/6 = 0.166...

Brent,

Exercise 224 (Problem Solving - OG 2017)
Could you explain me in a different way from OG 2017 answer solution?

Thank you in advance.

Cheers,
Pedro
gmat-admin's picture

At the risk of appearing to "pass the buck," I'd like to direct you to a very rich discussion of this question here: http://www.beatthegmat.com/og-13-ps-218-is-this-prob-really-doable-withi...

In particular, Mitch (GMATGuruNY) provides a concise solution.
Also, Ceilidh (from Manhattan Prep) explains why this might be a great candidate for guessing and moving on.

If you have any questions about those various solutions, I'm happy to respond. I just don't think I'd do much better than Mitch's solution.

Hey Brent, on statement 2, when I got (x+6)(x-1), I concluded that x must be -6 or 1, and then made the mistake of checking for extraneous roots, which took extra time. How do you know when to check for extraneous roots?
gmat-admin's picture

You only need check for extraneous roots when dealing with equations with square roots and equations with absolute value.

Cheers,
Brent

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