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When 55 is divided by 3x the remainder is 2x. What is the value of x?

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When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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23 Jan 2015, 06:36
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When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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23 Jan 2015, 06:48
I am not sure but will go with B..

x = 11 is the integer value.....

Any quick way... I just plugged in the values

Last edited by Cadaver on 24 Jan 2015, 00:52, edited 1 time in total.

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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23 Jan 2015, 09:17
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3x * q + 2x = 55
x (3q+2) = 55 = 5 * 11

x should be 5 or 11 (normally, x, q should be integer. If not, their will not be definition of "remainder")

S1: x is odd => No clue
S2: x is 2-digit: x = 11 => Sufficient.

If the thing I say in Bold is correct => Answer is B

Is there any body help me for that quote?

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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24 Jan 2015, 00:25
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FROM statement no 1 we can obtain 2 odd numbers that satisfy the condition . BOTH 5 an 11 can satisfy condition

if X=5 then 3X= 15 and 55/15 gives reminder 10 which is equal to twice the number (5)
also , if X=11 then 3X= 33 and 55/33 gives reminder 22 which is equal to twice the number (11)

so stat ONE is not sufficient ...

Statement 2 is Sufficient because ONLY number 11 is a TWO-DIGIT number which satisfies the condition as we know 55 is an ODD integer so 3X CAN NOT bigger than 55 because 55 CAN NOT EVENLY DIVIDE TO 2 and GET a FULL INTEGER (IF 3X is greater than 55 the reminder would be 55 ) so 3X MUST be less than 55 and 2 digit numbers which satisfy this condition would be

10, 11, 12, 13, 14, 15, 16, 17 , 18 and among these numbers ONLY 11 can satisfy the condition therefore X is 11 and the statement is sufficient...

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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24 Jan 2015, 02:43
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Here we go------

55 = 5 * 11 and 55 * 1
we can write the given question as------

55 = 3x*q + 2*x

55 = x*(3q + 2) -----(1)

St1: x is an odd integer

Put x = 11, q = 1 in (1)------> True
Put x = 5, q = 3 in (1) ------> True

Two different values of x
Clearly not sufficient

St2: x is a 2-digit integer

Put x = 11, q = 3 in (1)------> only this one holds

Clearly B is sufficient to answer the question

Option B is correct

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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26 Jan 2015, 03:35
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Bunuel wrote:
When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

This problem is a good candidate for the "Pick Numbers / Play Devil's Advocate" strategy, as if you can come up with two different values of x, you can prove that a statement is not sufficient.

For statement 1, one combination is that 55/33 is 1 remainder 22, so x could be 11 and satisfy this statement. Another possibility is x = 5, as that would be 55/15 which would be 3 remainder 10. Since you've now found two possible values for x (11 and 5), you can prove that statement 1 is not sufficient.

Moving on from statement 1 to statement 2, you may also want to look at what you've learned from working with statement 1. x = 11 is a valid solution given statement 2 (x is 2 digits), so you have one solution in hand. And you should also recognize that x cannot be even, as 55 is odd and you couldn't have an even quotient plus an even remainder equal 55.

What you've also learned from trying x = 11 above is that that makes 3x + 2x = 55, meaning that x cannot be any bigger than 11. Accordingly, x = 11 is the only two-digit number that will work with statement 1, and the answer is B.
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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26 Jan 2015, 16:59
Bunuel wrote:
Bunuel wrote:
When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

This problem is a good candidate for the "Pick Numbers / Play Devil's Advocate" strategy, as if you can come up with two different values of x, you can prove that a statement is not sufficient.

For statement 1, one combination is that 55/33 is 1 remainder 22, so x could be 11 and satisfy this statement. Another possibility is x = 5, as that would be 55/15 which would be 3 remainder 10. Since you've now found two possible values for x (11 and 5), you can prove that statement 1 is not sufficient.

Moving on from statement 1 to statement 2, you may also want to look at what you've learned from working with statement 1. x = 11 is a valid solution given statement 2 (x is 2 digits), so you have one solution in hand. And you should also recognize that x cannot be even, as 55 is odd and you couldn't have an even quotient plus an even remainder equal 55.

What you've also learned from trying x = 11 above is that that makes 3x + 2x = 55, meaning that x cannot be any bigger than 11. Accordingly, x = 11 is the only two-digit number that will work with statement 1, and the answer is B.

Hi i think am wrong ...plz justify......Why every one tried the 2nd statment with 11......they have stated its a 2 digit integer ...then if we try with 10,...55/3(10) ---remainder is 15 and its not equal to 2(x) rite....then the answer must be "E".......am confused...

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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27 Jan 2015, 01:43
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karthikraja1 wrote:
Bunuel wrote:
Bunuel wrote:
When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

This problem is a good candidate for the "Pick Numbers / Play Devil's Advocate" strategy, as if you can come up with two different values of x, you can prove that a statement is not sufficient.

For statement 1, one combination is that 55/33 is 1 remainder 22, so x could be 11 and satisfy this statement. Another possibility is x = 5, as that would be 55/15 which would be 3 remainder 10. Since you've now found two possible values for x (11 and 5), you can prove that statement 1 is not sufficient.

Moving on from statement 1 to statement 2, you may also want to look at what you've learned from working with statement 1. x = 11 is a valid solution given statement 2 (x is 2 digits), so you have one solution in hand. And you should also recognize that x cannot be even, as 55 is odd and you couldn't have an even quotient plus an even remainder equal 55.

What you've also learned from trying x = 11 above is that that makes 3x + 2x = 55, meaning that x cannot be any bigger than 11. Accordingly, x = 11 is the only two-digit number that will work with statement 1, and the answer is B.

Hi i think am wrong ...plz justify......Why every one tried the 2nd statment with 11......they have stated its a 2 digit integer ...then if we try with 10,...55/3(10) ---remainder is 15 and its not equal to 2(x) rite....then the answer must be "E".......am confused...

How is the remainder when divided 55 by 30 15? It's 25.
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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27 Jan 2015, 02:10
Bunuel wrote:
Bunuel wrote:
When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

This problem is a good candidate for the "Pick Numbers / Play Devil's Advocate" strategy, as if you can come up with two different values of x, you can prove that a statement is not sufficient.

For statement 1, one combination is that 55/33 is 1 remainder 22, so x could be 11 and satisfy this statement. Another possibility is x = 5, as that would be 55/15 which would be 3 remainder 10. Since you've now found two possible values for x (11 and 5), you can prove that statement 1 is not sufficient.

Moving on from statement 1 to statement 2, you may also want to look at what you've learned from working with statement 1. x = 11 is a valid solution given statement 2 (x is 2 digits), so you have one solution in hand. And you should also recognize that x cannot be even, as 55 is odd and you couldn't have an even quotient plus an even remainder equal 55.

What you've also learned from trying x = 11 above is that that makes 3x + 2x = 55, meaning that x cannot be any bigger than 11. Accordingly, x = 11 is the only two-digit number that will work with statement 1, and the answer is B.

A new approach
Dividend = Divisor x quotient + Remainder

3x (k) + 2x = 55
x (3k+2) = 55
if
x = 11 k = 1
x=5 k=3
st - 1 can't say
st - 2 true.
therfore only B is sufficient

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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13 Jul 2015, 11:08
Can x=-55? Then st. 2 is insuf. too.

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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13 Jul 2015, 11:25
Vale1Spa wrote:
Can x=-55? Then st. 2 is insuf. too.

x can't be -55

Dividend = Divisor*Quotient + Remainder
e.g. when 17 is divided by 5(divisor) then the quotient is 3 and remainder is 2
i.e. 17 = 5*3 + 2

Here the statement 2 mentions that
" x is a 2-digit integer"
if you take x = -55 then it violates the condition "When 55 is divided by 3x the remainder is 2x"

I hope it helps!
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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13 Jul 2015, 11:26
Vale1Spa wrote:
Can x=-55? Then st. 2 is insuf. too.

NO, as per GMAT and OG, when you talk about divisbility and remainder, you are talking about positive divisors and not negative.

Also, if x = -55, then 3x = -165 and remainder will be 2*-55 = -110

Thus your divisibility euiqation will become: 3x * p + 2x = -165-110 = -275 and this is NOT equal to 55. Thus you can not use -55 or for that matter any negative value.

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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14 Jul 2015, 06:59
Engr2012 wrote:
Vale1Spa wrote:
Can x=-55? Then st. 2 is insuf. too.

NO, as per GMAT and OG, when you talk about divisbility and remainder, you are talking about positive divisors and not negative.

Also, if x = -55, then 3x = -165 and remainder will be 2*-55 = -110

Thus your divisibility euiqation will become: 3x * p + 2x = -165-110 = -275 and this is NOT equal to 55. Thus you can not use -55 or for that matter any negative value.

Bunuel, Souvik

Can you confirm the statement above?

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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14 Jul 2015, 07:18
michaelyb wrote:
Engr2012 wrote:
Vale1Spa wrote:
Can x=-55? Then st. 2 is insuf. too.

NO, as per GMAT and OG, when you talk about divisbility and remainder, you are talking about positive divisors and not negative.

Also, if x = -55, then 3x = -165 and remainder will be 2*-55 = -110

Thus your divisibility euiqation will become: 3x * p + 2x = -165-110 = -275 and this is NOT equal to 55. Thus you can not use -55 or for that matter any negative value.

Bunuel, Souvik

Can you confirm the statement above?

Refer to the post by Bunuel: divisibility-multiples-factors-tips-and-hints-174998.html

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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14 Jul 2015, 07:49
Engr2012

Thanks for the reply, but I didn´t see your rule in the link - maybe you are referring to this one? http://gmatclub.com/forum/remainders-tips-and-hints-175000.html?fl=similar
If that´s the case, can I ALWAYS assume that when dealing with Remainder questions the quotient and remainer will never be negative?

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When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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14 Jul 2015, 08:05
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michaelyb wrote:
Engr2012

Thanks for the reply, but I didn´t see your rule in the link - maybe you are referring to this one? http://gmatclub.com/forum/remainders-tips-and-hints-175000.html?fl=similar
If that´s the case, can I ALWAYS assume that when dealing with Remainder questions the quotient and remainer will never be negative?

Point 1 from the link that I posted mentions:

DIVISIBILITY1. Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only).

"DEFINITION
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y=divisor∗quotient+remainder=xq+r and 0≤r<x."

Yes, for GMAT quant, whenever you talk about divisbility and remainders, the divisors, quotient and remainders will be positive integers.

There is a small thing to remember if you encounter a question with a 'negative remainder'. The negative remainder can actually be modified to become a 'true remainder' as shown below;

If you say : You are given a number of the form: Q = 12P - 3 ----> Q = 12P + (-6+3) ----> Q = 12P -6 + 3 ----> Q = 6 (2P-1) + 3. Thus this shows that although you were given a 'negative' remainder, you were still able to convert the negative form to an actual positive remainder. Above, I have shown that the remainder will be 3 when Q is divided by 6 and not -3 when divided by 12.

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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22 Apr 2016, 05:29
$$3xq + 2x = 55$$

$$x = \frac{55}{(3q + 2)}$$

Statement (1) x is an odd integer

means that (3q + 2) is a factor of 55, two solutions, 11 and 5 (insufficient)

(2) x is a 2-digit integer: sufficient X equals 11
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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08 Aug 2016, 13:13
what if we divide 55 by 51 (3*17) and get remainder of 4 (2*2)??

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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09 Aug 2016, 01:02
nrl.amin wrote:
what if we divide 55 by 51 (3*17) and get remainder of 4 (2*2)??

The stem says: when 55 is divided by 3x the remainder is 2x. Your example does not satisfy this condition.
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x? [#permalink]

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09 Aug 2016, 02:56
55=5*11
According to stem 55=3xq+2x. ==>55=x(3q+2)
So, x and 3q+2 will represent these two values i:e; 5 and 11. So, we have to find out which portion represent what.
statement 1 says x is odd. So, x can be 5 or 11 as both of these are odd.
Statement 2 says x is two digit number and hence it is 11. So it is sufficient.

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?   [#permalink] 09 Aug 2016, 02:56

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