GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Aug 2019, 04:42 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # When 55 is divided by 3x the remainder is 2x. What is the value of x?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 57237
When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

2
15 00:00

Difficulty:   95% (hard)

Question Stats: 48% (02:28) correct 52% (02:24) wrong based on 362 sessions

### HideShow timer Statistics

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.

_________________
##### Most Helpful Community Reply
Intern  Joined: 27 Mar 2014
Posts: 22
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

6
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
Otherwise: Answer is C.

Is there any body help me for that quote?
##### General Discussion
Manager  Joined: 03 Oct 2014
Posts: 126
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40 WE: Engineering (Aerospace and Defense)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

I am not sure but will go with B..

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

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

Originally posted by Cadaver on 23 Jan 2015, 07:48.
Last edited by Cadaver on 24 Jan 2015, 01:52, edited 1 time in total.
Manager  Joined: 13 Dec 2013
Posts: 59
Location: Iran (Islamic Republic of)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

1
ANSWER is B

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...

SO answer is B.....   Manager  Joined: 27 Oct 2013
Posts: 202
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

2
1
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
Math Expert V
Joined: 02 Sep 2009
Posts: 57237
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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.
_________________
Intern  Joined: 21 Aug 2013
Posts: 3
Concentration: International Business, Leadership
GPA: 2.9
WE: Programming (Computer Software)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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...
Math Expert V
Joined: 02 Sep 2009
Posts: 57237
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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.
_________________
Manager  Joined: 14 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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
Intern  Joined: 13 Jul 2015
Posts: 6
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

Can x=-55? Then st. 2 is insuf. too.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

Vale1Spa wrote:
Can x=-55? Then st. 2 is insuf. too.

x can't be -55

Please note:

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!
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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.
Intern  Joined: 11 Nov 2014
Posts: 30
Concentration: Technology, Strategy
GMAT 1: 660 Q48 V31 GMAT 2: 720 Q50 V37 GPA: 3.6
WE: Consulting (Consulting)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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?
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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
Intern  Joined: 11 Nov 2014
Posts: 30
Concentration: Technology, Strategy
GMAT 1: 660 Q48 V31 GMAT 2: 720 Q50 V37 GPA: 3.6
WE: Consulting (Consulting)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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?
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

1
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).

Your link as well talks about the same thing:

"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.
Senior Manager  B
Joined: 23 Sep 2015
Posts: 371
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38 WE: Real Estate (Mutual Funds and Brokerage)
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

$$3xq + 2x = 55$$

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

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
_________________
Intern  Joined: 05 Jun 2015
Posts: 2
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

what if we divide 55 by 51 (3*17) and get remainder of 4 (2*2)??
Math Expert V
Joined: 02 Sep 2009
Posts: 57237
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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.
_________________
Manager  S
Joined: 06 Oct 2015
Posts: 87
Location: Bangladesh
Concentration: Accounting, Leadership
Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

### Show Tags

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.

Answer B Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?   [#permalink] 09 Aug 2016, 03:56

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  