When 28 is divided by the positive integer x, the remainder is 1. What

Question

When 28 is divided by the positive integer x, the remainder is 1. What is the sum of all the possible values of x for which this is true?

A. 2
B. 3
C. 9
D. 30
E. 39

GMATinsight · Accepted Answer

The number that divide 28 completely will be the factors of 28

The Numbers which leave remainder 1 when divide 28 will be Dividing 27 perfectly i.e. Factors of 27

Factors of 27 = {1, 3, 9, 27}

But 1 is not acceptable as it divides each integer completely

So Sum of all numbers satisfying the required condition = 3+9+27 = 39

Answer: Option E

ENGRTOMBA2018 · Answer

The only possible values of the form 28=xp+1 are 3,9 or 27

The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.

TimeTraveller · Answer

The values x can hold such that the given conditions are met would be 3, 9 and 27. Sum (3+9+27) = 39. Ans (E).

cutegirlsimran · Answer

First we have to check what number will give a reminder of 1 when 28 is divided by that number
we know that

Dividend/Divisor = Quotient + Reminder/Divisor

28/x = Q + 1/x or 28 = xQ + 1

First, we must find which numbers leave a remainder of 1. 
These numbers must be divisors of 27 (which is 1 less than 28) greater than 1. 
Such divisors of 27 are 3, 9, 27.

so add all 3+9+27 = 39

So E is the correct Answer Choice

abhinav008 · Answer

The biggest integer x which will give remainder 1 when 28 is divided by it is 27
so 28= 27*Q + 1
Now 27 can be divided by 3 and 9 only ( excluding 1 )
Thus 3 and 9 will also give remainder 1

So sum = 27+9+3 = 39
So E

ashokk138 · Answer

28 - 27 = 1;

Hence x can be factors of 27 => 1, 3, 9, 27
1 cannot be used here, since 1 divides all integers evenly.

Hence the sum of the no.s = 3+9+27 = 39

Option E

aimtoteach · Answer

A quick scan will give us 3 and 9 as the desired numbers that leave 1 as remainder.

But before jumping to options - there is also 27 that will give 1 as a remainder.

So the answer is 3+9+27 = 39.

Option E

Bunuel · Answer

800score Official Solution:

First, we must find which numbers leave a remainder of 1. These numbers must be divisors of 27 (which is 1 less than 28) greater than 1. Such divisors of 27 are 3, 9, 27.

The first number is 3: 28/3 = 9, remainder 1.
The next number after that is 9: 28/9 = 3, remainder 1.
27 also gives a remainder of 1, giving 3 possible values
for x.

Adding these three values, we get 3 + 9 + 27 = 39.

The correct answer is choice (E).

Psk13 · Answer

can anybody please explain why are we leaving 1 from the factors of 27?

Bunuel · Answer

We are told that when 28 is divided by the positive integer x, the remainder is 1. Though 1 is in fact a factor of 27, it does not satisfy the given condition: 28 divided by 1 gives the remainder of 0, not 1.

TheNightKing · Answer

The first value of x can be 27. Because 28/27 gives a remainder 1. So we boil down to D and E.
The same works with 9 and 3. 
So 3+9+27=39..
Hence E

Kritisood · Answer

hi

28=xK+1
27=xK
27/x=K where K is an integer
now x can take values 1,3,9.27 hence total = 40
why are we not considering 1 here?

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When 28 is divided by the positive integer x, the remainder is 1. What

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When 28 is divided by the positive integer x, the remainder is 1. What

Prep Toolkit

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