Numbers

Question

How many times the digits of a computer keyboard will be required to be pressed in typing 1st 100 natural numbers ?

Brent@GMATPrepNow · Answer

sukhman wrote:How many times the digits of a computer keyboard will be required to be pressed in typing 1st 100 natural numbers ?

In other words, how many digits are in the integers from 1 to 100 inclusive.

1-digit numbers: from 1 to 9 inclusive
There are such 9 integers, and each has 1 digit, for a total of 9 digits

3-digit numbers: 100
There is 1 such integer with 3 digits, for a total of 3 digits

2-digit numbers: from 10 to 99 inclusive
There are 90 such integers, and each has 2 digits, for a total of 180 digits

TOTAL number of digits = 9 + 3 + 180 = 192

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Mathsbuddy · Answer

Brent@GMATPrepNow wrote:sukhman wrote:How many times the digits of a computer keyboard will be required to be pressed in typing 1st 100 natural numbers ? In other words, how many digits are in the integers from 1 to 100 inclusive. 1-digit numbers: from 1 to 9 inclusive There are such 9 integers, and each has 1 digit, for a total of 9 digits 3-digit numbers: 100 There is 1 such integer with 3 digits, for a total of 3 digits 2-digit numbers: from 10 to 99 inclusive There are 90 such integers, and each has 2 digits, for a total of 180 digits TOTAL number of digits = 9 + 3 + 180 = 192 Cheers, Brent Exactly how I would answer it. However there are 2 accepted definitions of "natural number", (reference https://mathworld.wolfram.com/NaturalNumber.html) the second of which includes zero - which means that an alternative solution would look at the integers 0 to 99, yielding a total of (192 - 1) = 191 I believe we are both correct: 191 or 192, both acceptable. However, the question states "how many times will be required" and as 192 exceeds necessity, then 191 should be the overall winner! In other words, 191 will be required for either methiod. PS: This is based on your answer of 192 being correct.

Brent@GMATPrepNow · Answer

Mathsbuddy wrote: Exactly how I would answer it. However there are 2 accepted definitions of "natural number", (reference https://mathworld.wolfram.com/NaturalNumber.html) the second of which includes zero - which means that an alternative solution would look at the integers 0 to 99, yielding a total of (192 - 1) = 191

I believe we are both correct: 191 or 192, both acceptable.

However, the question states "how many times will be required" and as 192 exceeds necessity, then 191 should be the overall winner! In other words, 191 will be required for either methiod.

PS: This is based on your answer of 192 being correct.

Fortunately, the GMAT test-writers would never require us to know the definition of "natural numbers." In fact, this term does not appear anywhere in the Official Guide.

Instead, they'd say something like ". . . the integers from 1 to 100 inclusive" or perhaps ". . . the first 100 positive integers"

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Rich.C@EMPOWERgmat.com · Answer

Hi All,

A few things worth noting with this type of question:

1) IF we were interested in 0 to 99, inclusive, the total number of digits would be 190, NOT 191 (Replacing "100" with "0" removes 2 digits).

2) As Brent has already pointed out, Official GMAT questions are meticulously and very carefully worded, so that there is no ambiguity in what is being asked.

3) If there is any conceivable ambiguity in your mind about the question, then it's worth noting that the writers have likely written the answer choices with 4 easy-to-define "wrong" answers, so that if you have chosen an answer based on an ambiguity, then that answer WON'T BE THERE. This will allow you to re-work the question and catch the "mistake" in your thinking.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Mathsbuddy · Answer

Rich.C@EMPOWERgmat.com wrote:Hi All, A few things worth noting with this type of question: 1) IF we were interested in 0 to 99, inclusive, the total number of digits would be 190, NOT 191 (Replacing "100" with "0" removes 2 digits). 2) As Brent has already pointed out, Official GMAT questions are meticulously and very carefully worded, so that there is no ambiguity in what is being asked. 3) If there is any conceivable ambiguity in your mind about the question, then it's worth noting that the writers have likely written the answer choices with 4 easy-to-define "wrong" answers, so that if you have chosen an answer based on an ambiguity, then that answer WON'T BE THERE. This will allow you to re-work the question and catch the "mistake" in your thinking. GMAT assassins aren't born, they're made, Rich Thanks for that. I realised the error afterwards while driving.

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