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^m^ is equal to the digits in positive integer m in reverse
[#permalink]
19 Oct 2017, 22:43

1

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Question Stats:

^m^ is equal to the digits in positive integer m in reverse order, discounting the zeroes (e.g. ^41^ = 14 but ^3500^ = 53). Which of the following must be true? Select all that apply.

A. ^m^ < ^m+1^

B. m = ^(^m^)^

C. ^1000m^ = ^m^

D. (^m^)(^m^) > ^m^

Kudos for correct solution.

A. ^m^ < ^m+1^

B. m = ^(^m^)^

C. ^1000m^ = ^m^

D. (^m^)(^m^) > ^m^

Kudos for correct solution.

Re: ^m^ is equal to the digits in positive integer m in reverse
[#permalink]
20 Oct 2017, 07:19

1

A and D can be excluded because when the number is a 1-digit the sign would be an equal instead of a <.

B can be excluded too because when the number contains zeros, the equal sign does not hold. E.g. m = 100, ^m^ = 1 and ^^m^^ = 1 because the zeros do not reappear.

We are left with C that is our answer!

B can be excluded too because when the number contains zeros, the equal sign does not hold. E.g. m = 100, ^m^ = 1 and ^^m^^ = 1 because the zeros do not reappear.

We are left with C that is our answer!

Re: ^m^ is equal to the digits in positive integer m in reverse
[#permalink]
14 Jun 2019, 06:31

2

IlCreatore wrote:

A and D can be excluded because when the number is a 1-digit the sign would be an equal instead of a <.

B can be excluded too because when the number contains zeros, the equal sign does not hold. E.g. m = 100, ^m^ = 1 and ^^m^^ = 1 because the zeros do not reappear.

We are left with C that is our answer!

B can be excluded too because when the number contains zeros, the equal sign does not hold. E.g. m = 100, ^m^ = 1 and ^^m^^ = 1 because the zeros do not reappear.

We are left with C that is our answer!

For option a

^m^<^m+1^

if ^m^=1, then m=1

but ^m+1^= ^1+1^=2

or,

if ^m^=12, then m=21

but ^m+1^= ^21+1^=22.

How can we eliminate option a?

Please rectify me.Thanks

Re: ^m^ is equal to the digits in positive integer m in reverse
[#permalink]
21 Jul 2023, 06:46

1

^m^ is equal to the digits in positive integer m in reverse order, discounting the zeroes (e.g. ^41^ = 14 but ^3500^ = 53). Which of the following must be true? Select all that apply.

In this question seems better to plug in values to reach the correct answer, and since question asks for "must be true", we should work to falsify the options and the answer remaining will be our correct answer

A. ^m^ < ^m+1^

Lets consider m= 29 , thus m+1 = 30 , now ^m^ = 92 and ^m+1^ =3 , which means ^m^ > ^m+1^, thus this option is falsified.

B. m = ^(^m^)^

Easy one to eliminate , lets consider m=2500, thus ^m^ = 52 and ^(^m^)^ = 25 , thus m not equal ^(^m^)^ . Eliminate

C. ^1000m^ = ^m^ --> Here if we take any +ve integer , this condition satisfies , lets test with m=10, 1000m = 10000 and ^1000m^ = 1 and ^m^ = 1 , thus this condition will always hold true

D. (^m^)(^m^) > ^m^

Lets take m=10 , so ^m^ = 1 and (^m^)(^m^) = (1)(1) = 1 , thus this condition is also falsified, eliminate

Answer C.

In this question seems better to plug in values to reach the correct answer, and since question asks for "must be true", we should work to falsify the options and the answer remaining will be our correct answer

A. ^m^ < ^m+1^

Lets consider m= 29 , thus m+1 = 30 , now ^m^ = 92 and ^m+1^ =3 , which means ^m^ > ^m+1^, thus this option is falsified.

B. m = ^(^m^)^

Easy one to eliminate , lets consider m=2500, thus ^m^ = 52 and ^(^m^)^ = 25 , thus m not equal ^(^m^)^ . Eliminate

C. ^1000m^ = ^m^ --> Here if we take any +ve integer , this condition satisfies , lets test with m=10, 1000m = 10000 and ^1000m^ = 1 and ^m^ = 1 , thus this condition will always hold true

D. (^m^)(^m^) > ^m^

Lets take m=10 , so ^m^ = 1 and (^m^)(^m^) = (1)(1) = 1 , thus this condition is also falsified, eliminate

Answer C.

gmatclubot

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