Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 24 Oct 2013
Posts: 30
GMAT 1: 570 Q47 V23 GMAT 2: 620 Q49 V24 GMAT 3: 630 Q47 V29
WE: Operations (Energy and Utilities)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
08 Nov 2015, 11:01
X, Y, P & Q all are unique digit. Best and least time way is to try the options. Option III)  If X = 9, then Y must be '6', so that Y+X = 15. 1 carry over and so X+Y = 16, i.e, Sum = 165; i.e., P=1, Q=6, X=9, & Y=6. Since here Q=Y=6, whereas question state that all are different, this is not correct. Now option II): X=8, that means Y = 7 and hence sum will be 165; with P=1, Q=6, X=8 & Y=7. Since all are unique, this can be the answer. Similarly option I): X=7 will give Y=8, P=1, Q=6, which also is true with the given condition. Hence, correct answer is  D



Current Student
Joined: 03 May 2014
Posts: 68
Concentration: Operations, Marketing
GMAT 1: 680 Q48 V34 GMAT 2: 700 Q49 V35
GPA: 3.6
WE: Engineering (Energy and Utilities)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
08 Nov 2015, 12:12
The Sum is PQ5, and it is written that P, Q, X and Y are different. So what CAN be the value of X? Going by the option given X=7 so putting it in given condition, we get X=7 Y=8 and P=1 Q=6. so 1st is possible. Going by the option given X=8 so putting it in given condition, we get X=8 Y=7 and P=1 Q=6. so 2nd is possible. Going by the options given X=9 so putting it in given condition, we get X=9 Y=6 and P=1 Q=6. so 3rd is not possible as Y and Q are same and this condition is not allowed. So Answer is D
_________________
Beat verbal, Beat GMAT... Trying Hard to do that..... Kudos if my post helped you



Current Student
Joined: 31 May 2015
Posts: 9
Location: India
GMAT 1: 580 Q50 V19 GMAT 2: 650 Q50 V28
GPA: 3.38

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
08 Nov 2015, 18:17
The possible values XY can take are: 96, 69, 87, 78. (23 and 32 are eliminated as their sum gives two digit number.) Upon adding reverse of each of the above number with the corresponding original number, one will get a number in 'PQ5' form.
Thus, the different values X can take are: 6, 7, 8 and 9.
IMO : E.
Please correct me if wrong. Vicky.



Intern
Joined: 29 Aug 2015
Posts: 12

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
08 Nov 2015, 18:44
The only combinations for which the units digit (Y+X) equals to 5 are (6,9)(9,6) (7,8) (8,7) fora three digit number. Hence all the options given are possible values.
Option E.



Intern
Joined: 26 Aug 2014
Posts: 46
GMAT 1: 650 Q49 V30 GMAT 2: 650 Q49 V31
WE: Programming (Computer Software)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
11 Nov 2015, 03:22
Since XY + YX represents a three digit number, X+ Y must be greater than 10. Now, the last digit is 5 so there are only two possibilities left for X and Y : (7,8) or (9,6). Both of these possibilities add up to give 15. Given that X, Y , P and Q represent different integers, we cannot have (9,6) as our value for X or Y because 96 + 69 = 165 => X= Q => this is not possible. So the only alternative left is for X and Y to be either (7,8) So , X can take two values 7 or 8 Ans.: D



Manager
Joined: 25 Dec 2012
Posts: 121

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
11 Nov 2015, 06:51
Given:
XY +YX  PQ5  X,Y,P & Q Different non zero number.
 Hence X,Y,P,&Q cant be 5 and also X + Y or Y + X = gives the unit digit as 5.
When ever answering these sort of questions its always good to start from the numbers present in the answer choice. This will save lot of time. The given numbers are 7,8 & 9
Option 1 : If Y = 7, then X = 8 hence we will have 5 in the unit digit. So 78 + 87 = 165 and all the numbers are unique. Hence this is correct.
Option 2 : Since Option 1 and Option 2 are interchangeable we are not performing the same thing again and Option 2 is also correct.
Option 3: 9 + 6 = Gives 5 in the unit digit. Hence 96 + 69 = 165 which is not correct since X = Q. 6 repeats for both X and Q. But according to the question it should not since all are different numbers.
Hence the correct answer choise is (D). Which is Option 1 and Option 2 are the correct answers.



Intern
Joined: 26 Jan 2014
Posts: 8

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
11 Nov 2015, 07:50
go by options If x=7, y must be 8 7 8 +8 7 ________ 1 6 5 ......... P,Q,X,Y,all are different numbers If x=8, y must be 7 8 7 +7 8 ________ 1 6 5 ......... P,Q,X,Y are different
If x=9, y must be 6 9 6 +6 9 ________ 1 6 5 ......... here Y=Q condition fails.
so answer is option "D"



Retired Moderator
Joined: 18 Sep 2014
Posts: 1148
Location: India

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
11 Nov 2015, 11:03
X Y +Y X ________ P Q 5 Inorder to give rise to 3 digit no when added we need to select set of integers will result in 2 digit when added and 5 in units place. X/Y can be {7,8} or {6,9} out if all these data, value of X can be any one of the four values above. {7/8/6/9} So answer is (E) I , II and III
_________________
The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated
http://gmatclub.com/forum/rulesforpostinginverbalgmatforum134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources.
My posts http://gmatclub.com/forum/beautyofcoordinategeometry213760.html#p1649924 http://gmatclub.com/forum/callingallmarchaprilgmattakerswhowanttocross213154.html http://gmatclub.com/forum/possessivepronouns200496.html http://gmatclub.com/forum/doublenegatives206717.html http://gmatclub.com/forum/thegreatestintegerfunction223595.html#p1721773 https://gmatclub.com/forum/improvereadinghabit233410.html#p1802265



Manager
Joined: 31 Aug 2011
Posts: 199

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
12 Nov 2015, 11:18
I just plugged in 69+96 , 87+78 and 78+87 (all three work)
_________________
If you found my contribution helpful, please click the +1 Kudos button on the left, I kinda need some =)



Intern
Status: SINGLE
Affiliations: NONE
Joined: 23 Sep 2015
Posts: 6
Location: India
Concentration: Technology, International Business
GPA: 4
WE: Information Technology (Computer Software)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
12 Nov 2015, 11:25
Answer is D because when we add XY=87 and YX=78 (or vice versa) we get PQ5=165 where X=8 OR X=7. Also we can see here X,Y,P,Q all are different.



Intern
Joined: 02 Oct 2012
Posts: 15
Location: India
Concentration: Operations, General Management
GPA: 3.6
WE: Operations (Energy and Utilities)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
12 Nov 2015, 13:32
XY +YX  PQ5
Now, we know that P,Q,X,Y are distinct nonzero digits. Again, (XY + YX) will always be divisible by 11.....(a) { Since, XY = 10X + Y and YX = 10Y + X Therefore, XY + YX = 11(X+Y) } Now from (a) and by the question PQ5 is a there digit number, the only possible value of PQ5 which is divisible by 11 and having unit digit 5 is 165. Therefore, P=1, Q=6.....(b) Again, PQ5 = XY + YX = 11(X+Y)......from (a) or, 11(X+Y) = 165 or, X+Y = 15.........(c)
Now since X,and Y are single digit numbers, therefore either {X,Y} = {7,8} or {8,7} Or {X,Y} ={9,6} or {6,9}
78(XY) +87(YX)  165(PQ5)
Or
69(XY) +96(YX)  165(PQ5)
But from the question stem, P,Q,X,Y are distinct nonzero digits. Therefore {X,Y} = {6,9} or {9,6} is not possible., since in this case P = X = 6.
Therefore the possible values of X is 7, or 8.
The the option id "D", I & II Only.



Intern
Joined: 25 Apr 2009
Posts: 1

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
12 Nov 2015, 16:28
Answer d number 7&8



Current Student
Joined: 14 Jun 2015
Posts: 90
Location: India
GMAT 1: 680 Q46 V37 GMAT 2: 750 Q50 V40
GPA: 3.5
WE: Information Technology (Telecommunications)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
12 Nov 2015, 21:30
X Y +Y X ________
The sum of the two digit numbers above is a three digit number PQ5, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I) 7 II) 8 III) 9
Method used Plugging in.
If x=7, Y should be 8(to get unit digit of sum as 5) so, 78 87  165
x=7, y=8, p=1, q=6. Satisfies the condition that all digits are different. So x can be 7
If x=8, Y should be 7(to get unit digit of sum as 5) so, 87 78  165
x=8, y=7, p=1, q=6. Satisfies the condition that all digits are different. So x can be 8
If x=9, Y should be 6(to get unit digit of sum as 5) so, 96 69  165
x=9, y=6, p=1, q=6. Does not satisfies the condition that all digits are different. y=q=6. So x cannot be 9
Ans: (D) I and II only



Intern
Status: You think you cannot?? Rethink & repeat until its done  Abdul Rauf Liaqat
Joined: 09 Nov 2015
Posts: 20
Location: Pakistan
Concentration: Entrepreneurship, Strategy
GPA: 3.03
WE: Operations (Telecommunications)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
Updated on: 13 Nov 2015, 04:03
Using Backsolving method to answer the question. We have to choose X which when add with Y comes upto be "15" because we have unit digit available as 5 (in the Question QP5). So, choosing X=8, then Y must be 7, if you put these values above, you will get the answer 165. Now, choose X= 7, then Y must be 8, so putting these will have same answer too as 165 Now if we choose X=9, then Y must be 6 to make unit digit 5, but this way Y & P will have same value as 6 but question states that X,Y,Q,P are all different non zero numbers, So X can be I, II only. Option D
_________________
+1 Kudos will be appreciated if you find this post helpful Take up one idea. Make that one idea your life  think of it, dream of it, live on that idea. Let the brain, muscles, nerves, every part of your body, be full of that idea, and just leave every other idea alone. This is the way to success  Swami Vivekananda



Intern
Joined: 01 Nov 2015
Posts: 10
Concentration: General Management

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
12 Nov 2015, 23:18
D ie 1&2 only X &Y can't be less than 5 else ans would have been 55 not PQ5 So options are 7,8 or 6,9 Manually add 69+96 = 165 thus Q=x or y So not possible Next 78+87=165 which provides all unique nos Thus X=7 or 8



Intern
Joined: 14 May 2015
Posts: 4

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
13 Nov 2015, 00:13
XY +YX  PQ5
Logically, there are 2 types of addition resulting in 5 in the unit digit: 5 and 15. If X+Y=5 then X and Y must each be less than 5 (since 0<X, Y<9). This means the result can only be a 2digit number => eliminate this possibility. If X+Y= 15 we have 4 sets: {X,Y}={(7,8); (8,7); (6,9); (9,6)}. All these sets have result of 165, satisfy conditions that X, Y, P, Q are different nonzero digits. So X can be 6, 7, 8, 9.
Answer is E.



Intern
Joined: 05 Jun 2013
Posts: 35

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
13 Nov 2015, 04:00
X Y Y X  P Q 5  Going by answer choices , X can be either 7,8 or 9 1)First lets substitute X =7 if X =7 , Y should be equal to 8 to get the last digit as 8. So the number will be 78 +87  165 
2)Now lets substitute, X=8 and therefore Y becomes 7 to get last digit as 5.
87 78  165 
3)Now lets substitute, X=9 and now Y becomes 6 to get last digit as 5. 96 +69  165  But since both Y=Q=6, therefore X cannot be equal to 9. So X can be equal to only 7 or 8 which is choice D.



Intern
Joined: 10 Sep 2012
Posts: 25

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
13 Nov 2015, 07:04
Explanation to Qn#1: XY can be written as 10X+Y YX can be written as 10Y+X Adding both gives 11X + 11Y or 11(X + Y) Given, 11(X + Y) = PQ5, implies that X + Y has to end with a 5, so that its product with 11 yields a number ending in a 5
Now, out of the given choices, both 7 & 8 satisfy the above condition for X. As far as 9 is concerned, if it were true, then since X is 9, then Y must be 6 to yield a sum ending with 5. But in that case, 9 + 6 shall yield a carry forward of 1, which, when added to the overall sum, will result in a digit repeated (thus contradicting the given condition of having different digits for X, Y, P and Q.
Hence only possible solutions are 7 and 8. Thus answer is D i.e. I and II only.
We can verify by plugging our answer choices > 78 + 87 = 165 (satisfied) and 69 + 96 = 165 (not satisfied bcoz Q and X/Y a not distinct).



Intern
Joined: 06 Jul 2014
Posts: 20
WE: Supply Chain Management (Manufacturing)

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
13 Nov 2015, 08:42
X Y +Y X ________
The sum of the two digit numbers above is a three digit number PQ5, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I) 7 II) 8 III) 9
(A) I only (B) II only (C) III only (D) I and II only (E) I , II and III Explanation: X Y +Y X ________ PQ5 Above summation implies X+Y=15 (5 is not possible as P is not zero,Given).This implies XY could be69, 96,87 or 78.Here PQ5 =165 Hence Q=6.Therefore X could be 7,8 or 9( not 6 as P,Q,X,Y are all different non zero digit and Q=6). Therefore Correct answer is "E". Kudos pl



Intern
Joined: 06 Aug 2015
Posts: 1
Concentration: Technology, Statistics
GPA: 2.86

Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers
[#permalink]
Show Tags
13 Nov 2015, 08:55
The answer is D.
According to the question, the last digit of the result from addition is 5. Thus, X + Y = 15, since X + Y can't be 5 because both the digits would then yield 55(two digits) as a result. but the question states that the result must be 3 digits i.e. PQ5.
So it also means that the sum must be 165, regardless of the value of X and Y. Here, X and Y must be 7 and 8, or 6 and 9 (not respectively) since X + Y = 15. Now, the question says that P,Q,X and Y are different integers. So, X and Y can't be 6 and 9 since Q=6. Thus XY must be either 78 or 87. Therefore, X can be either 8 or 7. So the correct answer is D.




Re: Jamboree and GMAT Club Contest: The sum of the two digit numbers &nbs
[#permalink]
13 Nov 2015, 08:55



Go to page
Previous
1 2 3
Next
[ 49 posts ]



