When a certain number is multiplied by 13, the product consists entire

Question

When a certain number is multiplied by 13, the product consists entirely of fives. What is the smallest such number ?

A. 41625
B. 42135
C. 42515
D. 42735
E. 44735

stne · Answer

Using the options, starting from the smallest one:

13*41625 = 541125  does not give all 5's 
 13*42135= 547755  does not give all 5's 
 13*42515 = 552695  does not give all 5's 
 13*42735= 555555  All 5's

Ans D

hope it helps.

pratiksha1998 · Answer

Any short method for this question?

Yoaerez · Answer

Let me have a crack at it:

A. 41625
B. 42135
C. 42515
D. 42735
E. 44735

You see that B,D,E have 3 as their 4th digit, so let's look at those:

let's start with 42135:

42135
13
-------
xxx05
xxx50

by only calculating the two last digit you can see that the number has to have 3 as its fourth number.  ELIMINATE A AND C

let's continue:

42135
13
-------
xx405
xx355

third digit is 7, so  B is eliminated.  only D and E remain. let's do D:

42735
13
-------
128205
427350

128205+427350=555555

Answer choice D is the correct answer.

This way you only had to calculate 1.5 choices. calculating half of B eliminated A, B, and C, and calculating D will eliminate either D (if it doesn't add up to 555555) or eliminate E (if it does add up to 555555)

yinan · Answer

Yes, you can just start dividing 5s by 13 to get the digits of the right answer, since the multiplication of the correct answer choice by 13 will result in a number that consists of only 5s. By doing this, you are not calculating with the answer choices themselves and instead are able to eliminate the choices as you go.

For example, start by dividing 555 by 13. You will get 42 as quotient with remainders. That immediately eliminates options A and E. Continue dividing the remainders by adding another digit 5 to the division. So, when you manually divide 555 by 13, you will get 42 at the quotients place and 9 as remainder. Add a 5 digit to the end of the remainder, so it becomes 95 divided by 13. With that, your quotient becomes 427 with remainder 4. Look at the options, because you do not have to continue dividing. You are only left with option D. So all in all, you only did two divisions and got the answer.

This is much faster than it looks when you actually do it, and its much more intuitive and you only calculate as you eliminate the options until you are left with a single option.

When a certain number is multiplied by 13, the product consists entire

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When a certain number is multiplied by 13, the product consists entire

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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