Divisibility and Primes

[gmattesttaker2]

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

A) 13
B) 14
C) 15
D) 16
E) 17

[spoiler]Ans: B)[/spoiler]


My approach is as follows:

A/B = 4.35

A/B = 4 + 0.35
= 4 + (35/100)
= 4 + (7/20)

However, I am lost after this point. Can you please assist? Thanks a lot.

Best Regards,
Sri

[niketdoshi123]

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

A) 13
B) 14
C) 15
D) 16
E) 17

[spoiler]Ans: B)[/spoiler]


My approach is as follows:

A/B = 4.35

A/B = 4 + 0.35
= 4 + (35/100)
= 4 + (7/20)

However, I am lost after this point. Can you please assist? Thanks a lot.

Best Regards,
Sri

Since 7/20 is the decimal part.
7n, a multiple of 7, has to be the remainder.
only option B satisfies the condition.

[rijul007]

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

A) 13
B) 14
C) 15
D) 16
E) 17

[spoiler]Ans: B)[/spoiler]


My approach is as follows:

A/B = 4.35

A/B = 4 + 0.35
= 4 + (35/100)
= 4 + (7/20)

However, I am lost after this point. Can you please assist? Thanks a lot.

Best Regards,
Sri

A/B = 4 + (7/20)
A = 4B + (7/20)*B
A - 4B = (7/20)*B

Hence, (7/20)*B is the remainder

A/B = 4.35 = 435/100 = 87/20
From this we know that,
A = 87k
B = 20k

Substitute this value of B in the remainder value, (7/20)*B
(7/20)*20k = 7k

Hence, the remainder will always be a multiple of 7

Option B is correct

[GMATGuruNY]

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

A) 13
B) 14
C) 15
D) 16
E) 17

When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.

We should write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = R.
Divisor = B.
Decimal = .35= 35/100 = 7/20.
Plugging these values into remainder/divisor = decimal, we get:
R/B = 7/20.

Since R/B is in its most reduced form, we know that B must be a multiple of 20 and that R must be a multiple of 7.
Only answer choice B is a multiple of 7.

The correct answer is B.

[gmattesttaker2]

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

A) 13
B) 14
C) 15
D) 16
E) 17

When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.

We should write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = R.
Divisor = B.
Decimal = .35= 35/100 = 7/20.
Plugging these values into remainder/divisor = decimal, we get:
R/B = 7/20.

Since R/B is in its most reduced form, we know that B must be a multiple of 20 and that R must be a multiple of 7.
Only answer choice B is a multiple of 7.

The correct answer is B.

Hello Mitch,

Thank you very much for the detailed explanation.

Best Regards,
Sri

[Scott@TargetTestPrep]

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

A) 13
B) 14
C) 15
D) 16
E) 17

We can create the following equation:

A/B = 4.35

A/B = Q + 35/100

A/B = Q + 7/20

We see that the remainder is a multiple of 7; thus, the remainder could be 14.

Answer: B