GRE Prep 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.
The sum of x and y is at least 2 but no more than 5. If the
[#permalink]
18 Mar 2018, 06:15
18 Mar 2018, 06:15
Expert Reply
00:00
Question Stats:
59% (01:18) correct
40% (02:43) wrong based on 22 sessions
Hide Show timer Statistics
The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
Drill 2
Question: 8
Page: 498
Question: 8
Page: 498
Re: The sum of x and y is at least 2 but no more than 5. If the
[#permalink]
18 Mar 2018, 07:30
18 Mar 2018, 07:30
1
Expert Reply
Explanation
Translate what you are told into algebra: 2 ≤ x + y ≤ 5 and 0 ≤ 2x + 3y ≤ 40.
By manipulating the inequalities, you find that 2 − y ≤ x ≤ 5 – y and –2x ≤ 3y ≤ 40 − 2x.
Substitute the endpoints of the values of x into the second inequality: –2(2 – y) ≤ 3y ≤ 40 − 2(2 − y) and –2(5 − y) ≤ 3y ≤ 40 − 2(5 − y).
By solving for y, the first range yields –4 ≤ y ≤ 36, and the second yields –10 ≤ y ≤ 30, meaning –10 ≤ y ≤ 36 overall.
Translate what you are told into algebra: 2 ≤ x + y ≤ 5 and 0 ≤ 2x + 3y ≤ 40.
By manipulating the inequalities, you find that 2 − y ≤ x ≤ 5 – y and –2x ≤ 3y ≤ 40 − 2x.
Substitute the endpoints of the values of x into the second inequality: –2(2 – y) ≤ 3y ≤ 40 − 2(2 − y) and –2(5 − y) ≤ 3y ≤ 40 − 2(5 − y).
By solving for y, the first range yields –4 ≤ y ≤ 36, and the second yields –10 ≤ y ≤ 30, meaning –10 ≤ y ≤ 36 overall.
Target Test Prep Representative
Joined: 09 May 2016
Status:Head GRE Instructor
Affiliations: Target Test Prep
Posts: 183
Given Kudos: 114
Location: United States
Re: The sum of x and y is at least 2 but no more than 5. If the
[#permalink]
01 Jun 2018, 09:27
01 Jun 2018, 09:27
1
Expert Reply
sandy wrote:
The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
We can create the following inequalities:
2 ≤ x + y ≤ 5
0 ≤ 2x + 3y ≤ 40
Multiplying the first inequality by -2, we have:
-4 ≥ -2x - 2y ≥ -10
-10 ≤ -2x - 2y ≤ -4
Adding this to 0 ≤ 2x + 3y ≤ 40, we have:
-10 ≤ y ≤ 36
Answer: C
