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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, 07:36
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48% (01:39) correct 52% (01:43) wrong based on 351 sessions
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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, 10:17
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 2digit: 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?




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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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Updated on: 24 Jan 2015, 01:52
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.



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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, 01:25
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 TWODIGIT 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.....



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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, 03:43
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 2digit 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, 04:35
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 2digit 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 twodigit 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, 17:59
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 2digit 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 twodigit 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, 02:43
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 2digit 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 twodigit 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, 03:10
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 2digit 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 twodigit 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, 12:08
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, 12:25
Vale1Spa wrote: Can x=55? Then st. 2 is insuf. too. x can't be 55Please note: Dividend = Divisor*Quotient + Remaindere.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 2digit 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, 12:26
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 = 165110 = 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, 07:59
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 = 165110 = 275 and this is NOT equal to 55. Thus you can not use 55 or for that matter any negative value. Bunuel, SouvikCan 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, 08:18
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 = 165110 = 275 and this is NOT equal to 55. Thus you can not use 55 or for that matter any negative value. Bunuel, SouvikCan you confirm the statement above? Refer to the post by Bunuel: divisibilitymultiplesfactorstipsandhints174998.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, 08:49
Engr2012Thanks for the reply, but I didn´t see your rule in the link  maybe you are referring to this one? http://gmatclub.com/forum/remainderstipsandhints175000.html?fl=similarIf 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, 09:05
michaelyb wrote: Engr2012Thanks for the reply, but I didn´t see your rule in the link  maybe you are referring to this one? http://gmatclub.com/forum/remainderstipsandhints175000.html?fl=similarIf 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 (2P1) + 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, 06:29
\(3xq + 2x = 55\) \(x = \frac{55}{(3q + 2)}\) 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 2digit 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, 14:13
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, 02:02



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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, 03:56
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.
Answer B




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