GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 09 Dec 2019, 18:41

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

100 liters of 20% alcohol is mixed with x liters of x% alcohol to give

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
VP
VP
User avatar
V
Joined: 23 Feb 2015
Posts: 1343
GMAT ToolKit User Premium Member
100 liters of 20% alcohol is mixed with x liters of x% alcohol to give  [#permalink]

Show Tags

New post 22 Oct 2019, 10:04
3
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (02:56) correct 35% (02:35) wrong based on 54 sessions

HideShow timer Statistics

100 liters of 20% alcohol is mixed with x liters of x% alcohol to give a mixture that contains at least 35% alcohol. What is the minimum value x can take?
A. 100 liters
B. 80 liters
C. 60 liters
D. 50 liters
E. 40 liters

_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
Henry Wadsworth Longfellow

SEARCH FOR ALL TAGS
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1143
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: 100 liters of 20% alcohol is mixed with x liters of x% alcohol to give  [#permalink]

Show Tags

New post 22 Oct 2019, 10:22
1
Asad wrote:
100 liters of 20% alcohol is mixed with x liters of x% alcohol to give a mixture that contains at least 35% alcohol. What is the minimum value x can take?
A. 100 liters
B. 80 liters
C. 60 liters
D. 50 liters
E. 40 liters


100*20/100 + x*x/100 ≥ (100+x)*35/100
—> 20 + x^2/100 ≥ 35 + 35x/100
—> x^2 - 35x - 1500 ≥ 0
—> (x - 60)(x + 25) ≥ 0
Solution is x ≤ -25 or x ≥ 60
Minimum value of x is 60 (since c cannot be negative)

IMO Option C

Posted from my mobile device
Intern
Intern
avatar
Joined: 13 Sep 2019
Posts: 1
Re: 100 liters of 20% alcohol is mixed with x liters of x% alcohol to give  [#permalink]

Show Tags

New post 22 Oct 2019, 10:28
1
Currently we have 20% of 100 liters alcohol = 20 liters alcohol in 100 liter solution.

Now we need atleast 35% in total and % alcohol= number of liters of alcohol added.

First take D. 50 liters:
50% of 50 liters = 25 liters

Total liters of solution = 100+50 = 150.
Total liters of alcohol = 20+25 = 45.

45/150<35% - so eliminate D and E also (since E will definitely be lesser than 35% if even lesser % of solution is alcohol)

Now we need to check C:

60% of 60 = 36

total liters of alcohol =20+36=56

total liters of solution = 100+60 = 160

56/160= 7/20 = 35% exactly.

So now we can eliminate D & E since all we need is the minimum value of X

X=60

Hence C is the answer
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8647
Location: United States (CA)
Re: 100 liters of 20% alcohol is mixed with x liters of x% alcohol to give  [#permalink]

Show Tags

New post 26 Oct 2019, 08:49
1
Asad wrote:
100 liters of 20% alcohol is mixed with x liters of x% alcohol to give a mixture that contains at least 35% alcohol. What is the minimum value x can take?
A. 100 liters
B. 80 liters
C. 60 liters
D. 50 liters
E. 40 liters



We can create the inequality:

100 * 0.2 + x * x/100 ≥ 0.35(100 + x)

20 + x^2/100 ≥ 35 + 0.35x

x^2/100 ≥ 15 + 0.35x

x^2 ≥ 1500 + 35x

x^2 - 35x - 1500 ≥ 0

(x + 25)(x - 60) ≥ 0

If this were an equation, we would have -25 or 60 as the solutions. Of course, x can’t be negative, so x = 60 is the only value that would make the expression (x + 25)(x - 60) equal to 0. If x > 60, the expression would be greater than 0. Therefore, x is at least 60, so its minimum value is 60 liters.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
User avatar
B
Joined: 24 Jul 2019
Posts: 152
Location: Austria
GPA: 3.9
CAT Tests
Re: 100 liters of 20% alcohol is mixed with x liters of x% alcohol to give  [#permalink]

Show Tags

New post 24 Nov 2019, 07:00
Asad wrote:
100 liters of 20% alcohol is mixed with x liters of x% alcohol to give a mixture that contains at least 35% alcohol. What is the minimum value x can take?
A. 100 liters
B. 80 liters
C. 60 liters
D. 50 liters
E. 40 liters


I dont get this problem, these values could all be the right answers.
100 liters of 20% alcohol are mixed with x liters of x% alcohol

So we neither know the added liters nor the % of the added liters. What is the MINIMUM value x can take to give a solution that contains at least 35% alcohol.

Say 40 liters is a 100% solution

100 + 40 = 140 liters
20 + 40 alcohol

60/140 > 0.35 ; possible
_________________
Let's get some
VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1491
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
CAT Tests
Re: 100 liters of 20% alcohol is mixed with x liters of x% alcohol to give  [#permalink]

Show Tags

New post 25 Nov 2019, 01:55
Asad wrote:
100 liters of 20% alcohol is mixed with x liters of x% alcohol to give a mixture that contains at least 35% alcohol. What is the minimum value x can take?
A. 100 liters
B. 80 liters
C. 60 liters
D. 50 liters
E. 40 liters


we can alligation method here

20.................x%


35


35 - x 15

we got the ratio here .

15 reflects the x liters portion

only 60 is basically the multiple of 15.......

Best answer is C
GMAT Club Bot
Re: 100 liters of 20% alcohol is mixed with x liters of x% alcohol to give   [#permalink] 25 Nov 2019, 01:55
Display posts from previous: Sort by

100 liters of 20% alcohol is mixed with x liters of x% alcohol to give

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne