If n is divided by 7 the remainder is 5. what is the remainder when (n+3) is divided by 7

This quotient and remainder calculator helps you divide any number by an integer and calculate the result in the form of integers. In this article, we will explain to you how to use this tool and what are its limitations. We will also provide you with an example that will better illustrate its purpose.

When you perform division, you can typically write down this operation in the following way:

where:

• a — Initial number you want to divide, called the dividend;
• n — Number you divide by; it is called the divisor;
• q — Result of division rounded down to the nearest integer; it is called the quotient; and
• r — Remainder of this mathematical operation.

When performing division with our calculator with remainders, it is important to remember that all of these values must be integers. Otherwise, the result will be correct in the terms of formulas, but will not make mathematical sense.

Make sure to check our modulo calculator for a practical application of the calculator with remainders.

🔎 If the remainder is zero, then we say that a is divisible by n. To learn more about this concept, check out Omni's divisibility test calculator.

1. Begin with writing down your problem. For example, you want to divide 346 by 7.
2. Decide on which of the numbers is the dividend, and which is the divisor. The dividend is the number that the operation is performed on – in this case, 346. The divisor is the number that actually "does the work" – in this case, 7.
3. Perform the division – you can use any calculator you want. You will get a result that most probably is not an integer – in this example, 49.4285714.
4. Round this number down. In our example, you will get 49.
5. Multiply the number you obtained in the previous step by the divisor. In our case, 49 * 7 = 343.
6. Subtract the number from the previous step from your dividend to get the remainder: 346 - 343 = 3.
7. You can always use our calculator with remainders instead and save yourself some time 😀

1. Make sure you have an unknown equal to two or more different modulos, e.g., x = d mod a, e mod b & f mod c.
2. Check that all modulos have the same greatest common divisor.
3. Multiply each modulo by all but one other modulo, until all combinations are found. For the above moduli, this would be: b*c, a*c, a*b.
4. Divide each number by the modulo that it is missing. If it equals the remainder for that modulo, e.g., (b*c)/a = d, leave the number as is.
5. If the remainder is not that for the modulo, use trial and error to find a positive integer to multiply the number by so that step 4 becomes true.
6. Add all numbers together once step 4 is true for all combinations.

It's useful to remember some remainder shortcuts to save you time in the future. First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder. Lastly, you can multiply the decimal of the quotient by the divisor to get the remainder.

Learning how to calculate the remainder has many real-world uses and is something that school teaches you that you will definitely use in your everyday life. Let’s say you bought 18 doughnuts for your friend, but only 15 of them showed up, you’d have 3 left. Or how much money did you have left after buying the doughnuts? If the maximum number of monkeys in a barrel is 150, and there are 183 monkeys in an area, how many monkeys will be in the smaller group?

1. Set up your division, adding a decimal place followed by a zero after the dividend’s one’s column (if your dividend is already a decimal, add an additional zero to the end).
2. Perform the division as usual until you are left with the remainder.
3. Instead of writing the remainder after the quotient, move the remainder above the additional zero you placed.
4. If there is a remainder from this division, add another zero to the dividend and add the remainder to that.
5. Continue in this fashion until there is either: no remainder, the digit or digits repeat themselves endlessly, or you reach the desired degree of accuracy (3 decimal places is usually okay).
6. The result after the decimal place is the remainder as a decimal.

The quotient is the number of times a division is completed fully, while the remainder is the amount left that doesn’t entirely go into the divisor. For example, 127 divided by 3 is 42 R 1, so 42 is the quotient, and 1 is the remainder.

Once you have found the remainder of a division, instead of writing R followed by the remainder after the quotient, simply write a fraction where the remainder is divided by the divisor of the original equation. It's that easy!

There are 3 ways of writing a remainder: with an R, as a fraction, and as a decimal. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second, and 205.25 in the third.

The remainder is 2. To work this out, find the largest multiple of 6 that is less than 26. In this case, it’s 24. Then subtract the 24 from 26 to get the remainder, which is 2.

The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.

1. Subtract 7 from 24 repeatedly until the result is less than 7.
2. 24 minus 3 times 7 is 3.
3. The number that is left, 3, is the remainder.
4. This can be expressed as 3/7 in fractional form, or as 0.42857 in decimal form.

Math Expert

Joined: 02 Sep 2009

Posts: 86861

If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

00:00

Difficulty:

Question Stats:

Hide Show timer Statistics

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?A. 1B. 2C. 4D. 6

E. 8

Manager

Joined: 29 Aug 2008

Posts: 93

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

x = 7y + 5So, 4x = 4(7y + 5) = 4*7y + 20When 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 option D

Board of Directors

Joined: 11 Jun 2011

Status:QA & VA Forum Moderator

Posts: 5684

Location: India

GPA: 3.5

WE:Business Development (Commercial Banking)

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

Bunuel wrote:

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?A. 1B. 2C. 4D. 6

E. 8

Quote:

If x is divided by 7, the remainder is 5.

Quote:

What is the remainder if 4x is divided by 7?

Hence , correct answer must be (D) 6

Manager

Joined: 02 Aug 2014

Status:Quant Expert Q51

Posts: 90

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

x=7q+5

4x=7*4q+20

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

Manager

Joined: 06 Jun 2016

Posts: 242

Location: India

Concentration: Operations, Strategy

Schools: ISB '18 (D)

GMAT 1: 600 Q49 V23

GMAT 2: 680 Q49 V34

GPA: 3.9

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

Bunuel wrote:

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?A. 1B. 2C. 4D. 6

E. 8

Option D

Target Test Prep Representative

Joined: 14 Oct 2015

Status:Founder & CEO

Affiliations: Target Test Prep

Posts: 16286

Location: United States (CA)

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

Bunuel wrote:

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?A. 1B. 2C. 4D. 6

E. 8

GMAT Club Legend

Joined: 08 Jul 2010

Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator

Posts: 5911

Location: India

GMAT: QUANT EXPERT

Schools: IIM (A), ISB

WE:Education (Education)

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

Bunuel wrote:

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?A. 1B. 2C. 4D. 6

E. 8

GMATinsight
Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!!
One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions ConsultingCall/mail: +91-9999687183 l (for FREE Demo class/consultation)

SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l GMAT730+ESCP

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

Bunuel wrote:

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?A. 1B. 2C. 4D. 6

E. 8

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

If x is divided by 7, the remainder is 5

The easiest number to work with is the smallest, 5.

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

What is the remainder if 4x is divided by 7?

Brent Hanneson – Creator of gmatprepnow.comI’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…

Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more

Non-Human User

Joined: 09 Sep 2013

Posts: 24628

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]

Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]