[GMAT math practice question]
If x and y are different positive integers, what is the value of x+y?
1) x^2+y^2=25
2) xy = 12
If x and y are different positive integers, what is the valu
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Hello.
I know how to solve this Question because I already saw it.
We want to know what is the value of x+y.
x=3 and y=4, then x^2+y^2=25 and x+y=7.
Since we've got a unique value for x+y, this statement is SUFFICIENT.
- If x=2 and y=6 then xy=12 and x+y=8.
Again, since we've got two different values for x+y, this statement is NOT SUFFICIENT.
This implies that the correct answer is the option A.
I'd like to see another explanation for this DS question.
I know how to solve this Question because I already saw it.
We want to know what is the value of x+y.
Since x and y are positive integers, then the unique option that satisfies the given condition is:1) x^2+y^2=25
x=3 and y=4, then x^2+y^2=25 and x+y=7.
Since we've got a unique value for x+y, this statement is SUFFICIENT.
- If x=12 and y=1 then xy=12 and x+y=13.2) xy = 12
- If x=2 and y=6 then xy=12 and x+y=8.
Again, since we've got two different values for x+y, this statement is NOT SUFFICIENT.
This implies that the correct answer is the option A.
I'd like to see another explanation for this DS question.
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Condition 1) & 2)
( x + y )^2 = x^2 + y^2 + 2xy = 25 + 2*12 = 25 + 24 = 49
x + y = ±7
Since x and y are positive, x + y = 7.
Both conditions, taken together, are sufficient.
Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1)
Since x is a positive integer, there are 5 possible values for x.
Case 1: x = 1
We have x^2 + y^2 = 1 + y^2 = 25 or y^2 = 24. There is no integer solution.
Case 2: x = 2
We have x^2 + y^2 = 4 + y^2 = 25 or y^2 = 21. There is no integer solution.
Case 3: x = 3
We have x^2 + y^2 = 9 + y^2 = 25 or y^2 = 16. Since y is positive, y= 4, and x + y = 3 + 4 = 7.
Case 4: x = 4
We have x^2 + y^2 = 16 + y^2 = 25 or y^2 = 9. Since y is positive, y= 3, and x + y = 4 + 3 = 7.
Case 5: x = 5
We have x^2 + y^2 = 25 + y^2 = 25 or y^2 = 0. There is no positive integer solution.
Thus, we have a unique solution: x + y = 7.
Condition 1) is sufficient.
Condition 2)
If x = 1 and y = 12, then x + y = 13.
If x = 2 and y = 6, then x + y = 8.
Since we don't have a unique solution, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Condition 1) & 2)
( x + y )^2 = x^2 + y^2 + 2xy = 25 + 2*12 = 25 + 24 = 49
x + y = ±7
Since x and y are positive, x + y = 7.
Both conditions, taken together, are sufficient.
Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1)
Since x is a positive integer, there are 5 possible values for x.
Case 1: x = 1
We have x^2 + y^2 = 1 + y^2 = 25 or y^2 = 24. There is no integer solution.
Case 2: x = 2
We have x^2 + y^2 = 4 + y^2 = 25 or y^2 = 21. There is no integer solution.
Case 3: x = 3
We have x^2 + y^2 = 9 + y^2 = 25 or y^2 = 16. Since y is positive, y= 4, and x + y = 3 + 4 = 7.
Case 4: x = 4
We have x^2 + y^2 = 16 + y^2 = 25 or y^2 = 9. Since y is positive, y= 3, and x + y = 4 + 3 = 7.
Case 5: x = 5
We have x^2 + y^2 = 25 + y^2 = 25 or y^2 = 0. There is no positive integer solution.
Thus, we have a unique solution: x + y = 7.
Condition 1) is sufficient.
Condition 2)
If x = 1 and y = 12, then x + y = 13.
If x = 2 and y = 6, then x + y = 8.
Since we don't have a unique solution, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
The key to this problem is that x and y are DIFFERENT positive integers. We need to determine x + y.Max@Math Revolution wrote:[GMAT math practice question]
If x and y are different positive integers, what is the value of x+y?
1) x^2+y^2=25
2) xy = 12
Statement One Alone:
x^2+y^2=25
We see that in order for statement one to be true, either x = 3 and y = 4 OR x = 4 and y = 3. In either case x + y = 7. Statement one alone is sufficient to answer the question.
Statement Two Alone:
xy = 12
There are several possible pairs of positive integers such that the equation is true. For example, x = 3 and y = 4 OR x = 6 and y = 2. In the former case, x + y = 7; however, in the latter case, x + y = 8. Statement two alone is not sufficient to answer the question.
Answer: A
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews