12 Easy Pieces (or not?)

The row begins with blue marble and ends with red marble. What cases can we have?

{blue, white, red} = 7*0 + 3
{blue, white, red, green, black, yellow, pink} {blue, white, red} = 7*1 + 3
{blue, white, red, green, black, yellow, pink} {blue, white, red, green, black, yellow, pink} {blue, white, red} = 7*2 + 3
{blue, white, red, green, black, yellow, pink} {blue, white, red, green, black, yellow, pink} {blue, white, red, green, black, yellow, pink} {blue, white, red} = 7*3 + 3
...

As you can see in any case the number of marbles must be a multiple of 7 plus 3.

Hope it's clear.

Is it not the other way around where -1/100 is the least number and -1/18 is the max negative number. I would have picked A as the answer.

No.

-1/18 = ~-0.06 and -1/100 = -0.01

-0.06 < -0.01



As you can see -1/100 is to the right of -1/18.

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.

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.
Would you please explain?

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.

How do you pick a smart number? Can you show how you strategize about this, since we need to make sure its divisible by18 but also the subsequent calculations wont result in fractional values that dont make sense.

We need a number 2/9 of which is an integer, so the number should be a multiple of 9. We also want (x*2/9)*3/4 = x*1/6 to be in integer, so the number also should be a multiple of 2 (and 3 but since we already established that the number should be a multiple of 9, then we can ignore that here). So, the number should be a multiple of 9*2 = 18.

Number plugging:

How to Do Math on the GMAT Without Actually Doing Math
The Power of Estimation for GMAT Quant
How to Plug in Numbers on GMAT Math Questions
Number Sense for the GMAT
Can You Use a Calculator on the GMAT?
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.

Are these really sub-600 questions...? If so, these must be the areas I am weakest in...

No, those are quite tricky 700+ questions. The name "12 Easy Pieces (or not?)" is meant to be ironic, juxtaposing the simplicity suggested by 'easy pieces' with the underlying complexity of the questions.

*Breathing a sigh of relief*

Lol. Thank you, Bunuel.

Doing Charles' study plan, on week 1, and got mixed up (and humbled) with the tags.

Bunuel , KarishmaB, Can you please suggest an easier way to figure out that n = 2 in this case ; Can I infer that n = 2 because there are two zero es in front of 737 ; hence n= 2 will satisfy the inequality ?  Hence , .001 < .00737 < .01 ; How do you arrive at this conclusion all on a sudden that n = 2 ? Please help.
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Use the Estimation concept. 

\(0.00737 = \frac{737}{10^5}\)

737 is less than 1000 but greater than 100. 

\(\frac{100}{10^5}<\frac{737}{10^5} < \frac{1000}{10^5}\)

\(\frac{1}{10^3}<\frac{737}{10^5} < \frac{1}{10^2}\)

So n = 2

Answer (B)

Check this video on Estimations: 
https://youtu.be/4Wy7BrQrjkM
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Thank you  KarishmaB for the wonderful explanation
­

If it were me, I'd get rid of the pesky decimal.

.00737*10^5 =737

So multiply all three by 10^5:

10^(4-n)<737<10^(5-n)

737 is less than 1000 and greater than 100, meaning n must be 2 by observation.

Posted from my mobile device

i'd like to share my solutions and my mistakes

1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1


this one was pretty simple, just consider that there are 3 colors, so the minimum number of picks to get 2 socks of the same color is 4. thus picking 4 socks gives you 100% probability that we pick 2 socks of the same color

2. If x is an integer and 9<x^2<99, then what is the value of maximum possible value of x minus minimum possible value of x?
A. 5
B. 6
C. 7
D. 18
E. 20

i fumbled this one badd! i did not consider negative numbers

min: x = +-4
max x = +-9
thus the difference is 9-(-9) = 18

3. Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before they meet?
A. 25 miles
B. 65 miles
C. 70 miles
D. 90 miles
E. 135 miles

this one was pretty straightforward. take the gap of 360, divide it by the relative speed of 90, they meet in 4 hours. so 1.5 h before they meet they travelled for 2.5 hours, 2.5h * relative speed of 90 = 225. 360-225 = 135

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

i got confused for a bit, but i did it right. to do that we have to consider the "opposite values" of x.
min --> y-x --> -7-5 = -12
max--> y-x --> 9-(-3) = 12


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

fumbled this one. but i love Bunuel explenation


7. After 2/9 of the numbers in a data set A were observed, it turned out that 3/4 of those numbers were non-negative. What fraction of the remaining numbers in set A must be negative so that the total ratio of negative numbers to non-negative numbers be 2 to 1?
A. 11/14
B. 13/18
C. 4/7
D. 3/7
E. 3/14

i got confused but it was pretty simple, we know that 2/9*3/4 = 1/6 is positive and 2/9*1/4 = 1/18 are negative. we want the negatives to be 2/3 (ratio is 2:1). so the remaining numbers --> 7/9*x plus 1/18 must be equal to 2/3 --> 7/9*x+1/18 = 2/3 --> x = 11/14


8. There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?
A. 3
B. 5
C. 6
D. 16
E. 19

pretty straightforward. we have 2 colors, so the worst case scenario is when we pick 2 and are of different colors, then the third pick will surely get you a color that you already have.


9. Julie is putting M marbles in a row in a repeating pattern: blue, white, red, green, black, yellow, pink. If the row begins with blue marble and ends with red marble, then which of the following could be the value of M?
A. 22
B. 30
C. 38
D. 46
E. 54

this is a sequence like problem. we have have a sequence of 7 colors, the last one is a red marble (the third in the sequence), meaning that the number of marble placed is something like 7k+3. the only number that, when subtracted 3 is divisible by 7 is 38.



10. If n is an integer and 1/10(n+1)<0.00737<1/(10^n), then what is the value of n?
A. 1
B. 2
C. 3
D. 4
E. 5

meaning that the minimum value will be 0.001, the maximum 0.01 --> or 10^-3 and 10^-2 --> n = 2
1/10(3)<0.00737<1/(10^2)

11. The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number p, what is the largest possible value of p?
A. 97
B. 151
C. 209
D. 211
E. 219

6 is a even number, so it cannot be in the unit digits, we have to form the biggest between 61 and 67 --> we get 67. we are left with 1,3,7,7 --> maximize the first digit --> 73 and 71. 211


If −1/3≤x≤−1/5 and −1/2≤y≤−1/4 what is the least value of x2∗y possible?
A. -1/100
B. -1/50
C. -1/36
D. -1/18
E. -1/6
x^2 is always positive, so we can pick for x the lower bound --> -1/3 --> x2 = 1/9, or the upper bound -1/5 --> 1/25. we want the greatest to be multiplied to y, that is negative, to achieve the lowest value possible of x2∗y, so we pick 1/9
y can only be negative, to maximize the x2∗y we get the lowest bound for sure --> -1/2
x2∗y = (1/9)(-1/2) = -1/18

Hi Bunuel

Can The Length of any side ever be equal to The Sum of Lengths of other 2 sides. For ex- If a=5 cm, b=3cm, and c=2 cm. I asked since you said any 1 side is always less than sum of other 2 sides and greater than their difference.

Thanks a ton!