Ximena lists the whole numbers 1 through 30 once. Emilio copies Ximena

Question

Ximena lists the whole numbers 1 through 30 once. Emilio copies Ximena's numbers, replacing each occurrence of the digit 2 by the digit 1. Ximena adds her numbers and Emilio adds his numbers. How much larger is Ximena's sum than Emilio's?

(A) 13
(B) 26
(C) 102
(D) 103
(E) 110

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paragw · Answer

Every digit 2 is replaced by 1

-When number 2 is replaced by 1, it gives difference of 1 in the sum
-Unit digit of the number 12 is replaced by 1, it gives difference of 1 in the sum
-When unit digit of the numbers from 20 to 29 is replaced by 1, it gives difference of 10*10 = 100 in the sum
 note that in numbers from 20 to 29, a number (22) is also there which contains 2 at its unit place, it'll also give a difference of 1

Therefore, total difference in the sum will be  103 .

vjhawar84 · Answer

The answer is 102 
Replacing 12 with 11 - Difference of 1 
Replacing 22 with 11 - Difference of 11
Replacing 2 of these numbers - 20,21,23,24,25,26,27,28,29= 9*10= 90 
Total difference =  102

architectodicta · Answer

You missed the 2.

It's 2 (-1) , 12 (-1) , 20,21,22,23,24,25,26,27,28,29 (-90 - 11)

CareerLauncherCL · Answer

Here is the solution of the question:-

The numbers from one to thirty containing the digit two are two, twelve, and twenty through twenty-nine. Replacing each digit two with one reduces each number as follows:

Two reduces by 1, twelve by 1, twenty by 10, twenty-one by 10, twenty-two by 11, twenty-three by 10, twenty-four by 10, twenty-five by 10, twenty-six by 10, twenty-seven by 10, twenty-eight by 10, twenty-nine by 10.

Summing these reductions gives 103.

Therefore, Ximena’s sum is 103 greater than Emilio’s.
 
Final Answer: Option(D) 103

Ximena lists the whole numbers 1 through 30 once. Emilio copies Ximena

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Ximena lists the whole numbers 1 through 30 once. Emilio copies Ximena

Prep Toolkit

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