If You Know That the Remainder of and Integer B Divided by 7 Is 5

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If ten is divided by 7, the remainder is five. What is the rest if 4x [#permalink] 31 Oct 2016, 03:00

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If x is divided by 7, the remainder is 5. What is the residue if 4x is divided past 7?

A. 1
B. two
C. 4
D. 6
Due east. 8

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Re: If x is divided by seven, the remainder is 5. What is the remainder if 4x [#permalink] 31 Oct 2016, 03:13

10 = 7y + 5

So, 4x = 4(7y + v) = 4*7y + 20

When this is divided by 7 4*7y will be multiple of 7, and on dividing 20 by 7 we will be left with remainder 6.

So selection D

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Re: If x is divided by 7, the remainder is v. What is the remainder if 4x [#permalink] 31 October 2016, 06:49

Bunuel wrote:

If x is divided past seven, the remainder is 5. What is the residual if 4x is divided past 7?

A. ane
B. 2
C. iv
D. 6
E. viii

Lets attempt -

Quote:

If x is divided by 7, the rest is five.

Least Possible value of x = 5

Quote:

What is the remainder if 4x is divided by vii?

four*5/vii = remainder 6

Hence , right answer must be (D) 6
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Re: If x is divided past 7, the residuum is five. What is the rest if 4x [#permalink] 03 Nov 2016, 01:39

x=7q+5

4x=seven*4q+20

4x=vii*4q+7*2+half-dozen

4x=seven(4q+2)+vi

4x=7k+6 (k=4q+2)

Answer D
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Re: If x is divided by 7, the remainder is five. What is the remainder if 4x [#permalink] 03 Nov 2016, 02:09

Bunuel wrote:

If 10 is divided past 7, the balance is 5. What is the residue if 4x is divided by 7?

A. 1
B. two
C. 4
D. 6
East. eight

ten=7k+5
4x=4*7k+20
hence balance =6
Choice D

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Re: If x is divided by seven, the remainder is 5. What is the rest if 4x [#permalink] 04 Nov 2016, 15:20

Bunuel wrote:

If x is divided by vii, the remainder is 5. What is the balance if 4x is divided by 7?

A. 1
B. 2
C. four
D. 6
East. 8

Since when x is divided by vii, the residual is 5, we tin create the following equations in which the caliber = Q:

x/7 = Q + 5/7

x = 7Q + 5

Since we demand to determine the remainder when 4x is divided by 7, we tin multiply both sides of the equation x = 7Q + v past 4 and nosotros have:

4x = 28Q + 20

Finally, we can split 28Q + 20 past 7:

(28Q + xx)/seven

28Q/vii + 20/7

Since 7 divides into 28Q, we are only concerned with the residue of the division of 20 by seven, which is 6.

Alternate solution:

We are given that when x is divided by 7, the remainder is 5. We can see that a possible number for x is 12. Therefore, nosotros need to determine the remainder when 4x, or in this case, 48, is divided by seven. Since 48/7 = half dozen, R 6, the remainder is half dozen.

Respond: D
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Re: If x is divided by seven, the remainder is 5. What is the residuum if 4x [#permalink] 04 Nov 2016, 21:twenty

Bunuel wrote:

If x is divided by vii, the remainder is 5. What is the remainder if 4x is divided by 7?

A. one
B. ii
C. 4
D. half-dozen
E. 8

If x is divided by 7, the residual is 5
i.east. x may exist = 12, xix, 26, 33 etc
i.eastward. 4x may be = 48, 76, 104, 312 etc

i.eastward. Balance (4x/7) = 6, 6, 6, half dozen, etc

Respond: Option D
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Re: If x is divided by 7, the residual is 5. What is the residual if 4x [#permalink] x Feb 2018, 07:35

Bunuel wrote:

If ten is divided by 7, the residue is five. What is the residuum if 4x is divided by 7?

A. 1
B. 2
C. iv
D. half-dozen
E. eight

When information technology comes to remainders, we take a overnice rule that says:

If North divided by D leaves remainder R, and then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if thousand divided by 5 leaves a residue of i, and so the possible values of thousand are: i, 1+5, i+(2)(5), ane+(3)(5), 1+(4)(5), . . . etc.

If ten is divided by 7, the remainder is 5
So, some possible values of x are: 5, 5+vii, five+(2)(vii), v+(iii)(seven), . . . etc
The easiest number to work with is the smallest, 5.

So, let's see what happens when ten = 5

What is the remainder if 4x is divided by 7?
4x = 4(5) = 20
xx divided past vii equals two with residuum 6

Answer: D