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

 It is currently 18 Sep 2019, 00:28

### 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

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

# 12 Easy Pieces (or not?)

Author Message
TAGS:

### Hide Tags

Manager
Joined: 13 Apr 2019
Posts: 107
Location: India
Concentration: Marketing, Operations
GPA: 3.5
WE: General Management (Retail)
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

04 Aug 2019, 03:49
6. Anna has 10 marbles: 5 red, 2 blue, 2 green and 1 yellow. She wants to arrange all of them in a row so that no two adjacent marbles are of the same color and the first and the last marbles are of different colors. How many different arrangements are possible?
A. 30
B. 60
C. 120
D. 240
E. 480

_ _ _ _ _ _ _ _ _ _

Since no adjacent colors can be same, reds can only be positioned in 2 ways (either position numbers 1,3,5,7,9 or numbers 2,4,6,8,10)

given this, whatever order we now place remaining 5, they will always meet the Anna's condition. So, number of ways will 2*5!/(2!*2!*1!) =60
Manager
Joined: 01 Jan 2019
Posts: 59
Concentration: Finance, Economics
GPA: 3.24
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

04 Aug 2019, 13:27
Bunuel wrote:
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12

To get max value of y-x take max value of y and min value of x: 9-(-3)=12;
To get min value of y-x take min value of y and max value of x: -7-(5)=-12;

Hence, the range of all possible values of y-x is -12<y-x<12.

Why is it not A? Can’t we simply subtract x from y? Then the answer will be A?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 58060
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

04 Aug 2019, 13:58
Shef08 wrote:
Bunuel wrote:
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12

To get max value of y-x take max value of y and min value of x: 9-(-3)=12;
To get min value of y-x take min value of y and max value of x: -7-(5)=-12;

Hence, the range of all possible values of y-x is -12<y-x<12.

Why is it not A? Can’t we simply subtract x from y? Then the answer will be A?

Posted from my mobile device

You can only apply subtraction when the signs of inequalities are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

For more check Manipulating Inequalities.
_________________
Manager
Joined: 01 Jan 2019
Posts: 59
Concentration: Finance, Economics
GPA: 3.24
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

04 Aug 2019, 20:30
Bunuel wrote:
Shef08 wrote:
Bunuel wrote:
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12

To get max value of y-x take max value of y and min value of x: 9-(-3)=12;
To get min value of y-x take min value of y and max value of x: -7-(5)=-12;

Hence, the range of all possible values of y-x is -12<y-x<12.

Why is it not A? Can’t we simply subtract x from y? Then the answer will be A?

Posted from my mobile device

You can only apply subtraction when the signs of inequalities are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

For more check Manipulating Inequalities.

Thank you, Bunuel!
Manager
Joined: 01 Jan 2019
Posts: 59
Concentration: Finance, Economics
GPA: 3.24
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

04 Aug 2019, 20:57
azhrhasan wrote:
Shef08 wrote:
Bunuel wrote:
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12

To get max value of y-x take max value of y and min value of x: 9-(-3)=12;
To get min value of y-x take min value of y and max value of x: -7-(5)=-12;

Hence, the range of all possible values of y-x is -12<y-x<12.

Why is it not A? Can’t we simply subtract x from y? Then the answer will be A?

Posted from my mobile device

Here's how to solve using your approach:

A: -7<y<9
B: -3<x<5 this means B': -5<-x<3

A+B':: -12< y-x < 12

Never subtract or multiply or divide inequalities until you are sure of the sign. On the other hand, Addition can be done always irrespective of the sign.
Always use the addition approach on inequalities and never try to shortcut it by multiplying or dividing or subtracting

That’s a great insight! I’ll have this fitted in my brains! Thanks a ton
Intern
Joined: 22 Dec 2018
Posts: 17
WE: Medicine and Health (Health Care)
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

28 Aug 2019, 06:37
Bunuel wrote:
10. If $$n$$ is an integer and $$\frac{1}{10^{n+1}}<0.00737<\frac{1}{10^n}$$, then what is the value of n?
A. 1
B. 2
C. 3
D. 4
E. 5

Also no need for algebraic manipulation. 1/10^(n+1) is 10 times less than 1/10^n, and both when expressed as decimals are of a type 0.001 (some number of zeros before 1) --> so the given expression to hold true we should have: 0.001<0.00737<0.01, which means that n=2 (1/10^n=0.01 --> n=2).

Hi Bunuel,

I am unable to understand how did we get 0.001 for 1/10^(n+1).
From what i understand 1/10^(n+1) is of form 1/10^n x 10^1.

Thanks
Intern
Joined: 22 Dec 2018
Posts: 17
WE: Medicine and Health (Health Care)
Re: 12 Easy Pieces (or not?)  [#permalink]

### Show Tags

28 Aug 2019, 07:06
Bunuel wrote:
swatjazz wrote:
Bunuel wrote:
10. If $$n$$ is an integer and $$\frac{1}{10^{n+1}}<0.00737<\frac{1}{10^n}$$, then what is the value of n?
A. 1
B. 2
C. 3
D. 4
E. 5

Also no need for algebraic manipulation. 1/10^(n+1) is 10 times less than 1/10^n, and both when expressed as decimals are of a type 0.001 (some number of zeros before 1) --> so the given expression to hold true we should have: 0.001<0.00737<0.01, which means that n=2 (1/10^n=0.01 --> n=2).

Hi Bunuel,

I am unable to understand how did we get 0.001 for 1/10^(n+1).
From what i understand 1/10^(n+1) is of form 1/10^n x 10^1.

Thanks

1/10^1 = 0.1
1/10^2 = 0.01
1/10^3 = 0.001
...

Thus, both 1/10^(n+1) and 1/10^n when expressed as decimals are of a type 0.001 (some number of zeros before 1). So, not that both are equal to 0.001 but both will be 0. followed by some number of zeros before 1.

Thanks so much! It's crystal clear now. Much appreciated for quick response.
Re: 12 Easy Pieces (or not?)   [#permalink] 28 Aug 2019, 07:06

Go to page   Previous    1   2   3   4   5   [ 87 posts ]

Display posts from previous: Sort by