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# two states have different rules for

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Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
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Location: India
GMAT 1: 640 Q43 V34
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two states have different rules for  [#permalink]

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06 Jan 2013, 04:10
Shouldn't the possible combination for state A be : 23*26*26*9*9*9*9

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Joined: 28 Dec 2011
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two states have different rules for  [#permalink]

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Updated on: 15 Feb 2017, 11:16
1
Dear Sachin9,

I'm happy to help with this.

This IR question is essentially a double "counting" problem. You may find this blog helpful:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/
That article discusses the FCP --- I will use this in both problems.

In State A, a license plate has 7 digits. The first 3 digits are letters, but the first letter cannot be an A, B, or C. The remaining digits are all numbers and zeros are not allowed.
First of all, here's my literal reading of the problem.
For the first slot has 23 possibilities (every letter except A, B, or C). Each of the next two has 26 possibilities --- there is no information forbidding repeat letters. MMM could be a legitimate choice for the first three letters. Then, for each of the remaining four slots, the number slots, there are 9 possibilities in each, every number except zero. This yields a total number of possibilities of
23*26*26*9*9*9*9 = 23*(26^2)*(9^4)

What you say in the spoiler section is 100% correct. We completely agree on this calculation.

I think the problem is the font or layout in this question box. Specifically, when they write
262*94*23
I think what they are trying to say is
(26^2)*(9^4)*23

Throughout the answer choices, wherever 263 appears, apparently they mean 26^3, and wherever 94 appears, apparently they mean 9^4. That the only thing that makes the OA make any sense as all.

You didn't specify a source for this question. I would say --- if they can't even print exponents correctly, I would consider this prep source about as valuable as elephant droppings. Run away. There are enough good prep sources that it doesn't make sense to waste time with junk that will just confuse you. That's my advice.

Let me know if you have any further questions involving these calculations.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Originally posted by mikemcgarry on 07 Jan 2013, 12:24.
Last edited by mikemcgarry on 15 Feb 2017, 11:16, edited 1 time in total.
Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 468
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: two states have different rules for  [#permalink]

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07 Jan 2013, 20:06
mikemcgarry wrote:
Dear Sachin9,

I'm happy to help with this.

This IR question is essentially a double "counting" problem. You may find this blog helpful:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/
That article discusses the FCP --- I will use this in both problems.

In State A, a license plate has 7 digits. The first 3 digits are letters, but the first letter cannot be an A, B, or C. The remaining digits are ll numbers and zeros are not allowed.
First of all, here's my literal reading of the problem.
For the first slot has 23 possibilities (every letter except A, B, or C). Each of the next two has 26 possibilities --- there is no information forbidding repeat letters. MMM could be a legitimate choice for the first three letters. Then, for each of the remaining four slots, the number slots, there are 9 possibilities in each, every number except zero. This yields a total number of possibilities of
23*26*26*9*9*9*9 = 23*(26^2)*(9^4)

What you say in the spoiler section is 100% correct. We completely agree on this calculation.

I think the problem is the font or layout in this question box. Specifically, when they write
262*94*23
I think what they are trying to say is
(26^2)*(9^4)*23

Throughout the answer choices, wherever 263 appears, apparently they mean 26^3, and wherever 94 appears, apparently they mean 9^4. That the only thing that makes the OA make any sense as all.

You didn't specify a source for this question. I would say --- if they can't even print exponents correctly, I would consider this prep source about as valuable as elephant droppings. Run away. There are enough good prep sources that it doesn't make sense to waste time with junk that will just confuse you. That's my advice.

Let me know if you have any further questions involving these calculations.

Mike

Thanks Mike for confirming.. Bad Question I would say or rather the formatting has been bad as pointed out by you.

Source is Veritas Prep Free CAT. I don't see any placeholder where I can tag the source now.
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

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Re: two states have different rules for  [#permalink]

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08 Jan 2013, 08:30
Thanks for the explanation...
I was wondering how this can be solved as my solution was not matching with the answers....
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Thanks
crazy4priya
GMATPrep 1 710/Q49/V38
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Joined: 28 Dec 2011
Posts: 4667
two states have different rules for  [#permalink]

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Updated on: 15 Feb 2017, 11:18
crazypriya wrote:
Thanks for the explanation...
I was wondering how this can be solved as my solution was not matching with the answers....

Dear Crazy Priya,

First of all, did you read my post about how the formatting is incorrect in the question slide, so that what appears as "263" really should be 26^3"? That's a big different.

If you understand what the answers are supposed to say, then
(1) the correct answer for State A is $$(26^2)*(9^4)*23$$
(2) the correct answer for State B is $$(26^2)*(9^4)$$
If that's what you got, your correct.
If you didn't get these answers, then one would get these using the Fundamental Counting Principle, explained in this blog article:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/

If, after reading that blog, you still have questions, let me know, and I'll demonstrate a full solution for this problem.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Originally posted by mikemcgarry on 08 Jan 2013, 10:35.
Last edited by mikemcgarry on 15 Feb 2017, 11:18, edited 1 time in total.
Intern
Joined: 19 May 2012
Posts: 31
Location: India
GMAT Date: 03-03-2014
WE: Information Technology (Computer Software)
Re: two states have different rules for  [#permalink]

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08 Jan 2013, 21:27
mikemcgarry wrote:
crazypriya wrote:
Thanks for the explanation...
I was wondering how this can be solved as my solution was not matching with the answers....

Dear Crazy Priya,

First of all, did you read my post about how the formatting is incorrect in the question slide, so that what appears as "263" really should be 26^3"? That's a big different.

If you understand what the answers are supposed to say, then
(1) the correct answer for State A is (26^2)*(9^4)*23
(2) the correct answer for State B is (26^2)*(9^4)/26, which also can be written as 26*25*(9^4)
If that's what you got, your correct.
If you didn't get these answers, then one would get these using the Fundamental Counting Principle, explained in this blog article:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/

If, after reading that blog, you still have questions, let me know, and I'll demonstrate a full solution for this problem.

Mike

Hi Mike,

Yeah i understood your explanation...I was correct with my solution but just got confused with answer choices....bt nw I have understood it...
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Joined: 27 May 2012
Posts: 573
Re: two states have different rules for  [#permalink]

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15 Feb 2017, 08:33
mikemcgarry wrote:
crazypriya wrote:
Thanks for the explanation...
I was wondering how this can be solved as my solution was not matching with the answers....

Dear Crazy Priya,

First of all, did you read my post about how the formatting is incorrect in the question slide, so that what appears as "263" really should be 26^3"? That's a big different.

If you understand what the answers are supposed to say, then
(1) the correct answer for State A is (26^2)*(9^4)*23
(2) the correct answer for State B is (26^2)*(9^4)/26, which also can be written as 26*25*(9^4)
If that's what you got, your correct.
If you didn't get these answers, then one would get these using the Fundamental Counting Principle, explained in this blog article:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/

If, after reading that blog, you still have questions, let me know, and I'll demonstrate a full solution for this problem.

Mike

Hi Mike,

Thanks for the solution.
However shouldn't the answer for state B be 26*26* 9*9*9*9
Seems as though there is a small typo above, has gotten me confused.
if you could please have a look.
Thank you.
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- Stne

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Joined: 28 Dec 2011
Posts: 4667
Re: two states have different rules for  [#permalink]

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15 Feb 2017, 11:19
stne wrote:
Hi Mike,

Thanks for the solution.
However shouldn't the answer for state B be 26*26* 9*9*9*9
Seems as though there is a small typo above, has gotten me confused.
if you could please have a look.
Thank you.

Dear stne,

Yes, you're perfectly correct. I changed it in the above post. Thanks for pointing out the mistake.

Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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Re: two states have different rules for  [#permalink]

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27 Mar 2017, 03:58
for STATE A

ways in which we can get the values are

23*26*26*9*9*9*9 = 23*26^2*9^4

for STATE B

ways in which we can get the values are

26*26*9*9*9*9 = 26^2*9^4

Hence Column 1 last option and column 2 second option
Re: two states have different rules for &nbs [#permalink] 27 Mar 2017, 03:58
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