If Whitney wrote the decimal representations for the first 300 positiv

hi BrentGMATPrepNow

i m bit confused by term " decimal representation of integer" is 55 = 5*10+5 just like 125 = 1*100+2*10+1*5

can you please provide your solution

BrentGMATPrepNow thanks but now i got totally confused cause my imagination is ulimited so i better stick to what is implied in the question

what does this mean ? If Whitney wrote the decimal representations for the first 300 positive integer multiples of 5

for example 55 = 5*10 +5 (here we write 5 two times) 15 = 10*1+5*1 (here 5 is written one time) is it correct how i should approach the problem?

is it how how should understand the highlighted part
chetan2u

"decimal representation" just means expressing the number in the form XXXX.XXX
For example, all of the following are decimal representations of the number 5: 5, 5.0, 5.00, 5.000, 5.0000, ....etc

So, this definition rules out representing 5 as 5 + 15 - 10, etc
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Can any GMAT expert explain what decimal representations is?

Does it mean digital representations.

All the numbers is integer so not sure why there is the reference of decimal representations.

Thanks in advance.

Please read the whole thread before posting a question. Check posts just above yours. Hope it hleps.
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From 1 to 100 Whitney will write 5 12 times ( units and tens place)
so for first 300 multiples 12 x 15 = 180 (units and tens place)
for multiples of 5 at hundreds place starting from 500 -- ( 595-500/ 5 ) + 1 = 20
and one at hundreds place on 1500
total 180 + 20 + 1 = 201

Let's further explore the awkward term "decimal representation" in this question, whose wording implies that the numbers in question should be written in some sort of fractional / decimal form, when in fact they are simply regular integers.

You're better off ignoring the term "decimal representation" in this particular case. This question is using the broader definition of the word "decimal," which is the adjective part of speech: "relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten." In other words: despite the deceptive wording, a "decimal representation" can in fact be any number, even integers.

Please note that the word "decimal" almost always indicates a real decimal on today's GMAT. This question is a rare exception — possibly because of the advanced age of the question. Unfortunately, many of the so-called "GMAT Advanced Questions" (the book was published in 2019) are in fact quite old — in fact, some go all the way back to 1990s editions of the Official Guide, way back when it was written by ETS, not GMAC.
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I dont think you should blindly follow the answer.
The question ask how many digit, not how many unit digit of 5.

55 is counted as 2 times.
5,15,25,35,45,55,65,75,85,95 =12
12x 15 = 180
500,505,510........= 20 times
180 +20 + 1 =201

This is how I got it finally!
Range of Number: 5*I to 300*I

1.For Units Place:
Possible Numbers = {5,10,15,20.....................,1500}
The last digit can be either 0 or 5 i.e. 2 options are available.
so for units place total choices = 300/2 = 150

2. For Tens Place:
Possible Number = {50,55,150,155,...........,1450,1455}
Consider 50,55 as 1; 150,155 as 2; 250,255 as 3; so 1450,1455 will be 15
Therefore, number of choices = 2*15 = 30

3. For Hundreds Place:
Possible Numbers = {500,505,515,.......550,555,..........595}
Using Concept of Permutation and Combination:
Hundreds place has to be 5 so we have 1 option.
Tens place can be any number from 0 to 9, so we have 10 options
Units place can be either 0 or 5 in order to satisfy the confition of being a multiple of 5.

so 1*10*2= 20

Answer:
150+30+20+1 = 201

In 150 numbers that you counted for units digit part. Doesn't this include numbers like 155, 55. Which you have also considered in ten's digit part.

There are 150 multiples of 5 that end with 5. Now to make things simple, find the ratio of number of 5's in units place and number of 5's in tens place . In the range 5 to 95, the ratio is 5:1. So over the complete range, there are 150/5 = 30 fives in tens place. Similarly the ratio of 5's in hundreds place to tens and units place in the range 500 to 595 is 1:1 and 1:1 resp. So there are 20 5s in hundreds place. Then we have the 5 in 1500, for a total of 150+30+20+1= 201.
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Thanks for the response , actually my question. How do you know that the 150 multiples that end with 5 don't have 5 at tens place or hundreds place. I could not find any explanation regarding this on the thread .

5 can repeat in the tens and the hundreds place. The question is how many times 5 is written.
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Hi Experts, ThatDudeKnows, KarishmaB,

Can you please share your approach to this question?

Thanks in advance.
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Exactly what Chetan has done here:
https://gmatclub.com/forum/if-whitney-w ... l#p2392437
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