by: Darina16
19 mins
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (01:28) correct
52%
(01:30)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
Does x + y = 11 ?
(1) x^2 + y^2 = 101
(2) xy = 10
Are You Up For the Challenge: 700 Level Questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
RaghavKhanna
Joined: 03 May 2020
Last visit: 23 Aug 2025
Posts: 263
Location: India
Concentration: Marketing, Strategy
GMAT 1: 700 Q47 V39
GMAT 1: 700 Q47 V39
Posts: 263
Question Stem: Does x + y = 11 ?
Statement 1:
x^2 + y^2 = 101
(i) if x = 10, y = 1 ---- YES
(ii) if x = 9, y = \(\sqrt{20}\) ---- NO
=> Statement 1 is insufficient
Statement 2:
xy = 10
(i) if x = 10, y = 1 --- YES
(ii) if x =2, y = 5 --- NO
=> Statement 2 is insufficient
Statement 1 & Statement 2:
\((x+y)^{2}\) = \(x^{2} \) + \(y^{2}\) + 2xy
\((x+y)^{2}\) = 101 + 20
\((x+y)^{2}\) = 121
=> x+y = 11 (10,1) ---- YES
or x + y = -11 (-10,-1) ----- NO
=> Statement 1 & Statement 2 are together insufficient
Answer: E
Statement 1:
x^2 + y^2 = 101
(i) if x = 10, y = 1 ---- YES
(ii) if x = 9, y = \(\sqrt{20}\) ---- NO
=> Statement 1 is insufficient
Statement 2:
xy = 10
(i) if x = 10, y = 1 --- YES
(ii) if x =2, y = 5 --- NO
=> Statement 2 is insufficient
Statement 1 & Statement 2:
\((x+y)^{2}\) = \(x^{2} \) + \(y^{2}\) + 2xy
\((x+y)^{2}\) = 101 + 20
\((x+y)^{2}\) = 121
=> x+y = 11 (10,1) ---- YES
or x + y = -11 (-10,-1) ----- NO
=> Statement 1 & Statement 2 are together insufficient
Answer: E
Posts: 160
Is x+y=11
(1) x^2+y^2=101
(x+y)^2=101
x^2+y^2+2xy=101
Not Sufficient
(2) xy=10
Not Sufficient
(1) & (2)
x^2+2xy+y^2=101
x^2+20+y^2=101
(x+y)^2=81
x+y=9
Sufficient.
C
(1) x^2+y^2=101
(x+y)^2=101
x^2+y^2+2xy=101
Not Sufficient
(2) xy=10
Not Sufficient
(1) & (2)
x^2+2xy+y^2=101
x^2+20+y^2=101
(x+y)^2=81
x+y=9
Sufficient.
C
Posts: 229
Does x + y = 11 ?
(1) x^2 + y^2 = 101
There can be infinite solution for the above eqn.
x,y can take integer values,real, imaginary values
so this statement is insufficient
(2) xy = 10
There can be infinite solution for the above eqn.
x,y can take integer values,real, imaginary values
so this statement is insufficient
Combining 1 and 2
y=10/x
subsituting in 1st eqn
x^2 + (10/x)^2 = 101
We will get eqn as
x^4 - 101x^2 + 100=0
Solving this eqn
we will get
X=10 or -10 or 1 or -1
From above
Y=1 or -1 or 10 or -10
So we will get 4 different values for X+Y
Both are insufficient
(1) x^2 + y^2 = 101
There can be infinite solution for the above eqn.
x,y can take integer values,real, imaginary values
so this statement is insufficient
(2) xy = 10
There can be infinite solution for the above eqn.
x,y can take integer values,real, imaginary values
so this statement is insufficient
Combining 1 and 2
y=10/x
subsituting in 1st eqn
x^2 + (10/x)^2 = 101
We will get eqn as
x^4 - 101x^2 + 100=0
Solving this eqn
we will get
X=10 or -10 or 1 or -1
From above
Y=1 or -1 or 10 or -10
So we will get 4 different values for X+Y
Both are insufficient
Quote:
(x+y)^2=11^2
x^2+y^2+2xy=121
(1) insufic
(2) insufic
(1/2) sufic
|(x+y)^2|=101+2(10)=121
|x+y|=11 or -11
ans (E)
Does x + y = 11 ?
(1) x^2 + y^2 = 101
--Considering statement 1 alone:
Case 1: x =10 and y=1; we get x + y = 11; Answer YES.
Case 2: x =-10 and y=-1; we get x + y = -11; Answer NO.
As YES and NO both possible; this statement is not sufficient.
(2) xy = 10
--Considering statement 2 alone:
Case 1: x =10 and y=1; we get x + y = 11; Answer YES.
Case 2: x =-10 and y=-1; we get x + y = -11; Answer NO.
As YES and NO both possible; this statement is not sufficient.
On combing also, we are not able to eliminate any of the case discussed above.
IMO answer is E.
(1) x^2 + y^2 = 101
--Considering statement 1 alone:
Case 1: x =10 and y=1; we get x + y = 11; Answer YES.
Case 2: x =-10 and y=-1; we get x + y = -11; Answer NO.
As YES and NO both possible; this statement is not sufficient.
(2) xy = 10
--Considering statement 2 alone:
Case 1: x =10 and y=1; we get x + y = 11; Answer YES.
Case 2: x =-10 and y=-1; we get x + y = -11; Answer NO.
As YES and NO both possible; this statement is not sufficient.
On combing also, we are not able to eliminate any of the case discussed above.
IMO answer is E.
NiftyNiffler
McCombs School Moderator
Joined: 26 May 2019
Last visit: 15 Aug 2021
Posts: 324
Location: India
Schools: INSEAD Jan '20 LSE MFin "21 McCombs '23 Tepper '23
GMAT 1: 690 Q50 V33
Products:
Does x + y = 11 ?
(1) x^2 + y^2 = 101
(2) xy = 10
st1 in itself can take any values for x and y. so INSUFFICIENT
st2 can also make any values for x and y feasible. INSUFFICIENT
When taken together,
(x+y)^2 = x^2 + y^2 + 2xy = 101 + 20 = 121
So, x + y = 11 or -11, hence INSUFFICIENT.
The answer should be E
(1) x^2 + y^2 = 101
(2) xy = 10
st1 in itself can take any values for x and y. so INSUFFICIENT
st2 can also make any values for x and y feasible. INSUFFICIENT
When taken together,
(x+y)^2 = x^2 + y^2 + 2xy = 101 + 20 = 121
So, x + y = 11 or -11, hence INSUFFICIENT.
The answer should be E
ostrick5465
Joined: 30 Jul 2019
Last visit: 24 Jul 2026
Posts: 196
Location: Viet Nam
WE:Education (Education)
Products:
Posts: 196
Does x + y = 11 ?
(1) x^2 + y^2 = 101
(2) xy = 10
(1) Can't solve x, y exactly. Insufficiency.
(2) Can't solve x, y exactly. Insufficiency
(1) & (2) => x=10, y=1 or x=-10, y=-1 => Insufficiency
Choice E
_________________
(1) x^2 + y^2 = 101
(2) xy = 10
(1) Can't solve x, y exactly. Insufficiency.
(2) Can't solve x, y exactly. Insufficiency
(1) & (2) => x=10, y=1 or x=-10, y=-1 => Insufficiency
Choice E
_________________
My Goal: GMAT 740+
minustark
Joined: 14 Jul 2019
Last visit: 01 Apr 2021
Posts: 465
Status:Student
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Products:
Does x + y = 11 ?
(1) x^2 + y^2 = 101
(2) xy = 10
1) when x = 10, y = 1, Yes. But when x =\( \sqrt{101}\), y = 0, definitely No as 11^2 = 121. Not sufficient.
2) If x and y are 2 and 5, then not. If they are 10 and 1, then yes. Not sufficient.
Together, x^2 + 2xy + y^2 = 121, so, (x+y)^2 == (11)^2. (x+y) can either be 11 or -11. Not sufficient.
E is the answer.
(1) x^2 + y^2 = 101
(2) xy = 10
1) when x = 10, y = 1, Yes. But when x =\( \sqrt{101}\), y = 0, definitely No as 11^2 = 121. Not sufficient.
2) If x and y are 2 and 5, then not. If they are 10 and 1, then yes. Not sufficient.
Together, x^2 + 2xy + y^2 = 121, so, (x+y)^2 == (11)^2. (x+y) can either be 11 or -11. Not sufficient.
E is the answer.
bidskamikaze
Joined: 07 Jan 2018
Last visit: 29 Oct 2022
Posts: 251
Location: India
Schools: ESMT NUS '22 IIMA PGPX'23 NTU
GMAT 1: 710 Q49 V38
Does x + y = 11 ?
(1) x^2 + y^2 = 101
(2) xy = 10
1) x^2 + y^2 = 101
x and y can take values: 10, 1; -10, -1
- insufficient
2) xy = 10
x and y can take values: 10, 1; -10, -1; 5, 2; -5, -2; \sqrt{10}, \sqrt{10}.
- insufficient
Combine:
Still, we are left with two cases of 10, 1; -10, -1
- Insufficient.
Answer E.
(1) x^2 + y^2 = 101
(2) xy = 10
1) x^2 + y^2 = 101
x and y can take values: 10, 1; -10, -1
- insufficient
2) xy = 10
x and y can take values: 10, 1; -10, -1; 5, 2; -5, -2; \sqrt{10}, \sqrt{10}.
- insufficient
Combine:
Still, we are left with two cases of 10, 1; -10, -1
- Insufficient.
Answer E.
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.