QR problem

[sacjumpman]

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At a summer camp, counselors are instructed to read a code off of a flagpole. On each of 5 different pennants on the flagpole is a different integer from 0 to 9, and when read from top to bottom, the 5 digits represent the code. The 0 pennant can never be on top and the sum of the pennants must be a multiple of 9.

What are the number of possible different codes?

Answer: 9830

Any decent explanations. I kinda sorta follow the one in the book.

I'm hoping they aren't this difficult on the real thing.

Thanks

 

[z3u2]

At a summer camp, counselors are instructed to read a code off of a flagpole. On each of 5 different pennants on the flagpole is a different integer from 0 to 9, and when read from top to bottom, the 5 digits represent the code. The 0 pennant can never be on top and the sum of the pennants must be a multiple of 9.

What are the number of possible different codes?

Answer: 9830

Any decent explanations. I kinda sorta follow the one in the book.

I'm hoping they aren't this difficult on the real thing.

Thanks

if i didn't interpret ur question wrong, i think ur answer is incorrect.
let me know if u agree on how i interpret the question:
Between the integers of 10000 and 99999, inclusive, the total number of the integers such that the sum of each individual digit is a multiple of 9

if above is correct, then you can interpret the question as:
Between the integers of 10000 and 99999, inclusive, the total number of integers that is multiples of 9

because for number to be divisible by 9, the sum of it's digits must be multiple of 9

so:
99999-10000+1=90000
90000 / 9 = 10000

answer should be 10000

 

[Streetwolf]

if i didn't interpret ur question wrong, i think ur answer is incorrect.
let me know if u agree on how i interpret the question:
Between the integers of 10000 and 99999, inclusive, the total number of the integers such that the sum of each individual digit is a multiple of 9

if above is correct, then you can interpret the question as:
Between the integers of 10000 and 99999, inclusive, the total number of integers that is multiples of 9

because for number to be divisible by 9, the sum of it's digits must be multiple of 9

so:
99999-10000+1=90000
90000 / 9 = 10000

answer should be 10000

Negative, the integers have to be different on each of the poles. I will tackle this today, seems interesting.

 

[z3u2]

Negative, the integers have to be different on each of the poles. I will tackle this today, seems interesting.

If change the question to: Between the integers of 10000 and 99999, inclusive, the total number of integers that is multiples of 9 AND non of the digits within the integer are the same
the answer is 3024

I couldn't figure out how to do it mathematically though. Got the answer from a small program i wrote🙂

 

[jfitzpat]

I'd say that the correct answer is "C" and move onto the next question.

 

[sacjumpman]

Negative, the integers have to be different on each of the poles. I will tackle this today, seems interesting.

I know you will figure out Streetwolf.

I'm guessing, since you hesitated, that this must be much tougher than what we need to know for QR.

They give a full explanation in the book it is from.... and the answer does make some sense, but it was kinda confusing and tricky.

I think the answer makes sense though.

The one thing about the question stem that is confusing though is that when it says "the sum of the pennants must be a multiple of 9"

It means that if the pennants are 12345, then the number 12,345 must be a multiple of 9...

not 1+2+3+4+5.... which confused me at first.... and I still think it is worded poorly.

 

[Streetwolf]

Same thing, if the sum of the digits of a number is a multiple of 9 then the number itself is divisible by 9.

 

[sacjumpman]

Same thing, if the sum of the digits of a number is a multiple of 9 then the number itself is divisible by 9.

Nice. I knew that, but it never clicks when it needs to. 🙂

Like I have all the Pythagorean triples memorized, but can never recognize them come crunch time. lol....

 

[Streetwolf]

Can you post their solution? I'm obviously interpreting the problem incorrectly and would like to see what they have to say about it. Maybe I can help you figure out what they're doing.

 

[sacjumpman]

The three conditions to be satisfied by a code number are that each of the 5 digits is different, the first digit cannot be 0, and the code number must be a multiple of 9. In order to determine the number of possible different codes, we should create the smallest and largest possible code numbers that satisfy all three conditions.

Without considering the code number to be a multiple of 9, the smallest possible number is 10,234. When divided by 9, the number 10,234 has a remainder of 1. We can now list the multiples of 9 greater than 10,234 and stop when we have a code that has 5 different digits. That is,

10,242 10,251 10,260 10269

Hence, the smallest code number that satisfies all three conditions is 10,269.

The LARGEST possible code number without considering it to be a multiple of 9 is 98,765. This leaves a remainder of 8 when divided by 9. We can list the multiples of 9 in descending order and stop when we have a code with 5 different digits. That is,

98,757 98,748 98,739 98,730........n

Hence, the largest code number that satisfies all three conditions is 98,730:

10,269 = 9 x 1,141 and 98,730= 9 x 10,970

Therefore, eliminating the first 1,140 multiples of 9, there are 10,970 -1,140 = 9,830 mulitples of 9 between and including these numbers. That is, the number of possible codes is 9,830.


Don't sweat it too much SW.... This is problem too much for me regardless. This explanation makes sense, I guess. Just very involved, for me.

 

[z3u2]

The three conditions to be satisfied by a code number are that each of the 5 digits is different, the first digit cannot be 0, and the code number must be a multiple of 9. In order to determine the number of possible different codes, we should create the smallest and largest possible code numbers that satisfy all three conditions.

Without considering the code number to be a multiple of 9, the smallest possible number is 10,234. When divided by 9, the number 10,234 has a remainder of 1. We can now list the multiples of 9 greater than 10,234 and stop when we have a code that has 5 different digits. That is,

10,242 10,251 10,260 10269

Hence, the smallest code number without considering it to be a multiple of 9 is 98,765. This leaves a remainder of 8 when divided by 9. We can list the multiples of 9 in descending order and stop when we have a code with 5 different digits. That is,

98,757 98,748 98,739 98,730........n

Hence, the largest code number that satisfies all three conditions is 98,730:

10,269 = 9 x 1,141 and 98,730= 9 x 10,970

Therefore, eliminating the first 1,140 multiples of 9, there are 10,970 -1,140 = 9,830 mulitples of 9 between and including these numbers. That is, the number of possible codes is 9,830.


Don't sweat it too much SW.... This is problem too much for me regardless. This explanation makes sense, I guess. Just very involved, for me.

you probably left out some of the explanations between that part.
but it's still understandable

however what the solution is saying is that ANY NUMBER between 10269 and 98730 that is divisible by 9 DOES NOT have repeating digit, which is clearly impossible.

counter-ex: 10269 + 900 = 11169 is divisible by 9, but first three digits are the same.

I still think the first interpretation i had with the question was the intended, at least for the studying purpose, because it's a reasonable question on the DAT and calculation is limited, good luck studying.

 

[sacjumpman]

The three conditions to be satisfied by a code number are that each of the 5 digits is different, the first digit cannot be 0, and the code number must be a multiple of 9. In order to determine the number of possible different codes, we should create the smallest and largest possible code numbers that satisfy all three conditions.

Without considering the code number to be a multiple of 9, the smallest possible number is 10,234. When divided by 9, the number 10,234 has a remainder of 1. We can now list the multiples of 9 greater than 10,234 and stop when we have a code that has 5 different digits. That is,

10,242 10,251 10,260 10269


Hence, the smallest code number that satisfies all three conditions is 10,269.

The LARGEST possible code number without considering it to be a multiple of 9 is 98,765. This leaves a remainder of 8 when divided by 9. We can list the multiples of 9 in descending order and stop when we have a code with 5 different digits. That is,

98,757 98,748 98,739 98,730........n

Hence, the largest code number that satisfies all three conditions is 98,730:

10,269 = 9 x 1,141 and 98,730= 9 x 10,970

Therefore, eliminating the first 1,140 multiples of 9, there are 10,970 -1,140 = 9,830 mulitples of 9 between and including these numbers. That is, the number of possible codes is 9,830.


Don't sweat it too much SW.... This is problem too much for me regardless. This explanation makes sense, I guess. Just very involved, for me.

Damn. My bad. You were exactly right. I lost track of the passage as I copied it. My mistake. 😳

I guess I don't think there is any possible way I will be able to do a problem of this sort in a minute... I'll have to focus my energy on other things that I can learn to do efficiently.

 

[sacjumpman]

you probably left out some of the explanations between that part.
but it's still understandable

however what the solution is saying is that ANY NUMBER between 10269 and 98730 that is divisible by 9 DOES NOT have repeating digit, which is clearly impossible.

counter-ex: 10269 + 900 = 11169 is divisible by 9, but first three digits are the same.

I still think the first interpretation i had with the question was the intended, at least for the studying purpose, because it's a reasonable question on the DAT and calculation is limited, good luck studying.

Ahhh... I just read this again.

Yes, perhaps the first interpretation you had would be do-able on actual test for me.

I'm curious, did you take your DAT already.

You've been very solid as far as answers to QR to myself and other people's questions.... I'm curious as to how you did.

Thanks for the help thus far.

 

[Streetwolf]

That solution makes no sense. It just found the smallest number with no repeating digits and the largest number with no repeating digits and assumed all numbers in the middle worked.

 

[sacjumpman]

That solution makes no sense. It just found the smallest number with no repeating digits and the largest number with no repeating digits and assumed all numbers in the middle worked.

Thanks again.

Maybe that's why it seemed weird to me. I looked at it again this morning and was confused again.

Oh well, moving on. Thanks for all the help. 🙂

 

[z3u2]

Ahhh... I just read this again.

Yes, perhaps the first interpretation you had would be do-able on actual test for me.

I'm curious, did you take your DAT already.

You've been very solid as far as answers to QR to myself and other people's questions.... I'm curious as to how you did.

Thanks for the help thus far.

np
i have a little bit more foundation in math than bio/chem/ochem, so to help answering questions i choose the ones i'm more confidient in.

i took my dat in march, 23 on QR, every section is fine except a 17RC score 🙁

for math, i used kaplan book and practiced topscore.