For every positive even integer n, the function h(n)

[RonPurewal]

... so you only know that the smallest prime factor is at least 23. no easy way to tell if it's over 40.

[chetan86]

Hi Ron,

I am trying to understand how these concepts will be applicable.

In the question, if we had h(40)+1 rather than h(100)+1, then calculation would have been as follows?

h(40)+1 = 2^40*40!+1

As 2^40*40! and 2^40*40!+1 are consecutive number, they are co-prime and will no share any prime factor.

So the smallest prime factor for h(40)+1 would be greater than 40.
Am I correct?

Thanks!!!

not quite right.

don't skip steps!
write stuff out!

using the definition given here, h(40) is
2 • 4 • 6 • ... • 38 • 40
which is
(2•1) • (2•2) • (2•3) • ... • (2•19) • (2•20)

so, as you can see, this is actually 20! • 2^20. your 40's should actually be 20's.

(incidentally, that last sentence is also pretty good advice for how to live once you turn 40.)

Hi Ron,

Thanks a lot for clarifying my doubt and identifying the mistake.
Now I have understood how these concepts work, and I would definitely be able to crack this kind of question.

Thanks a lot for below tip. :)

don't skip steps!
write stuff out!

Thanks!!
Chetan

[RonPurewal]

a surprisingly large proportion of your success on this exam will boil down to things like "write stuff down! answer the right question, and don't answer the wrong question!"

in other words, your first-grade teacher would absolutely adore this exam.

[chetan86]

a surprisingly large proportion of your success on this exam will boil down to things like "write stuff down! answer the right question, and don't answer the wrong question!"

in other words, your first-grade teacher would absolutely adore this exam.

Yeah, actually few months back I had gone through your below post on beatthegmat.

http://www.beatthegmat.com/strategies-for-preventing-careless-mistakes-t17044.html#73619

After writing stuffs down, I am making fewer calculation and silly mistakes, and my timing has also improved.
Thanks a lot for awesome suggestion :)

Thanks!!
Chetan

[tim]

Glad to hear you're making progress!

[RonPurewal]

Thanks a lot for awesome suggestion :)

sure.

by the way, you're looking at one of the reasons why many people don't improve on this exam: they desperately want the quant section to be "a math test".
problem is ... it isn't, really (except for people scoring toward the lower end of the quant scale).
in reality, it's a test of all the stuff surrounding the math-- stuff like organization, due diligence, careful reading, understanding goals, and so on.

a lot of people just don't want to study those things; they just cling to studying math, in the same way a baby might cling to a blanket.
... but those are the things that you should study.

[chetan86]

Thanks a lot for awesome suggestion :)

sure.

by the way, you're looking at one of the reasons why many people don't improve on this exam: they desperately want the quant section to be "a math test".
problem is ... it isn't, really (except for people scoring toward the lower end of the quant scale).
in reality, it's a test of all the stuff surrounding the math-- stuff like organization, due diligence, careful reading, understanding goals, and so on.

a lot of people just don't want to study those things; they just cling to studying math, in the same way a baby might cling to a blanket.
... but those are the things that you should study.

Yeah, you are absolutely correct.
Whenever I get any question wrong, it is because of one of the reasons you have cited. Thanks a lot for your help.

Yesterday I encountered your another precious post available on below link.

p104280

My GMAT is on 26th Feb, and my main target is to become extra careful to silly mistakes and reading the question and slow down while reading the verbal questions. If I can do these things, I would definitely score very high score. :)

I think without your help, my GMAT journey would have been incomplete. I have learned a lot from you and your posts. Thanks a lot for sharing vast knowledge. :)

Regards,
Chetan

[RonPurewal]

you're welcome and good luck.

[chetan86]

you're welcome and good luck.

Thanks you :)

[RonPurewal]

yep.