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DS Question 1 - Nov 20

At a certain florist shop, roses can be purchased either individually or as a bouquet of 12 at a discount of p percent. What is the greatest number of roses that can be purchased with $45?

(1) The greatest number of roses that can be purchased with $30 is 24.
(2) p = 20

Source: Manhattan | Difficulty : Hard
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PS Question 1 - Nov 20

What is the range of the roots of ||x – 1| – 2| = 1?

A. 0
B. 2
C. 4
D. 6
E. 8

Source: GMAT Club Tests | Difficulty : Medium
x has 4 possible values, 0, 2, -2, 4. So the answer is D. 6

The greatest number of roses with $45 is 36.
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Suppose function f(x) is the integer part of number x. For example f(2.0)= 2, f(2.9999) = 2, f(2.1) = 2. The greatest number of roses with any amount of mony M is: f(M/15)*12 + f((M-f(M/15) * 15)/(15/12/(1-20%)))
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The greatest number of roses with $45 is 36.
Sorry ! I couldn’t catch this well. Do you mean that the answer is c ?

PS Question - 2

If p is a positive integer and p^3 is divisible by 576, the largest positive integer that must divide P is...

(A) 2
(B) 4
(C) 6
(D) 12
(E) 24

Source: Expert’s Global | Difficulty: Hard
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PS Question - 2

If p is a positive integer and p^3 is divisible by 576, the largest positive integer that must divide P is...

(A) 2
(B) 4
(C) 6
(D) 12
(E) 24

Source: Expert’s Global | Difficulty: Hard
Break 576 into factors: 6*96->6*3*32->2^6*3^2
As p^3 is divisible by 2^6*3^2, the smallest value of p is: 2^2*3= 12, which is D
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DS Question - 2 - Nov 20

Is x^3 + y^3 > x^2 + y^2?

(1) x + y > x^2 + y^2

(2) x^4 + y^4 > x^2 + y^2

Source: Manhattan | Difficulty: Hard
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DS Question - 2 - Nov 20

Is x^3 + y^3 > x^2 + y^2?

(1) x + y > x^2 + y^2

(2) x^4 + y^4 > x^2 + y^2

Source: Manhattan | Difficulty: Hard
Tricky Tricky. I am not sure if I got this one right, but A.

1) From plugging in values I can only think of cases where x and y are both proper fractions. e.g x=1/2 y=1/2, and all those cases lead to a "no" answer.
x and y cannot be negative integers here, else x+y will never be greater than, and if x or y is an integer and the other a fraction, statement 1 does not hold. However, X can be negative fraction Y can be positive, which leads to no answer as well.

2) very easy to disprove: x=y=-10 (no) but also x=y=10 (yes), two answers therefore insuff.
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DS Question - 2 - Nov 20

Is x^3 + y^3 > x^2 + y^2?

(1) x + y > x^2 + y^2

(2) x^4 + y^4 > x^2 + y^2

Source: Manhattan | Difficulty: Hard
Tricky Tricky. I am not sure if I got this one right, but A.

1) From plugging in values I can only think of cases where x and y are both proper fractions. e.g x=1/2 y=1/2, and all those cases lead to a "no" answer.
x and y cannot be negative integers here, else x+y will never be greater than, and if x or y is an integer and the other a fraction, statement 1 does not hold. However, X can be negative fraction Y can be positive, which leads to no answer as well.

2) very easy to disprove: x=y=-10 (no) but also x=y=10 (yes), two answers therefore insuff.
Well Tried buddy !! This is one of the hardest question on GC. The answer is E.

PS Question 3 - Nov 20 - This question was recently posted by Bunuel. A good one IMO :)

How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?

A. 6
B. 7
C. 8
D. 9
E. 10

Source: Others | Difficulty Level : Medium
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PS Question 3 - Nov 20 - This question was recently posted by Bunuel. A good one IMO :)

How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?

A. 6
B. 7
C. 8
D. 9
E. 10

Source: Others | Difficulty Level : Medium
Took me ages.. did it in my head
First case is R0 - lcm(2,3,5,7) is 210k has 4 digits in range
Now...
The only other case is R1. Units digit must be 1, since we are dividng by 5.
Now the pattern is 210k+1. k=0-4 inclusive, so 5 numbers

Should be D.
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PS Question 3 - Nov 20 - This question was recently posted by Bunuel. A good one IMO :)

How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?

A. 6
B. 7
C. 8
D. 9
E. 10

Source: Others | Difficulty Level : Medium
Took me ages.. did it in my head
First case is R0 - lcm(2,3,5,7) is 210k has 4 digits in range
Now...
The only other case is R1. Units digit must be 1, since we are dividng by 5.
Now the pattern is 210k+1. k=0-4 inclusive, so 5 numbers

Should be D.
Awesome !! Kudos to you ..
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DS Question - 2 - Nov 20

Is x^3 + y^3 > x^2 + y^2?

(1) x + y > x^2 + y^2

(2) x^4 + y^4 > x^2 + y^2

Source: Manhattan | Difficulty: Hard
Tricky Tricky. I am not sure if I got this one right, but A.

1) From plugging in values I can only think of cases where x and y are both proper fractions. e.g x=1/2 y=1/2, and all those cases lead to a "no" answer.
x and y cannot be negative integers here, else x+y will never be greater than, and if x or y is an integer and the other a fraction, statement 1 does not hold. However, X can be negative fraction Y can be positive, which leads to no answer as well.

2) very easy to disprove: x=y=-10 (no) but also x=y=10 (yes), two answers therefore insuff.
I too am getting the same choice.. A, what’s the answer? gmatophobia
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PS Question 1 - Nov 20

What is the range of the roots of ||x – 1| – 2| = 1?

A. 0
B. 2
C. 4
D. 6
E. 8

Source: GMAT Club Tests | Difficulty : Medium

gmatophobia
DS Question 1 - Nov 20

At a certain florist shop, roses can be purchased either individually or as a bouquet of 12 at a discount of p percent. What is the greatest number of roses that can be purchased with $45?

(1) The greatest number of roses that can be purchased with $30 is 24.
(2) p = 20

Source: Manhattan | Difficulty : Hard

gmatophobia
PS Question - 2

If p is a positive integer and p^3 is divisible by 576, the largest positive integer that must divide P is...

(A) 2
(B) 4
(C) 6
(D) 12
(E) 24

Source: Expert’s Global | Difficulty: Hard

gmatophobia
DS Question - 2 - Nov 20

Is x^3 + y^3 > x^2 + y^2?

(1) x + y > x^2 + y^2

(2) x^4 + y^4 > x^2 + y^2

Source: Manhattan | Difficulty: Hard

gmatophobia
PS Question 3 - Nov 20 - This question was recently posted by Bunuel. A good one IMO :)

How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?

A. 6
B. 7
C. 8
D. 9
E. 10

Source: Others | Difficulty Level : Medium

saisandeep1997
mysterymanrog
gmatophobia
DS Question - 2 - Nov 20

Is x^3 + y^3 > x^2 + y^2?

(1) x + y > x^2 + y^2

(2) x^4 + y^4 > x^2 + y^2

Source: Manhattan | Difficulty: Hard
Tricky Tricky. I am not sure if I got this one right, but A.

1) From plugging in values I can only think of cases where x and y are both proper fractions. e.g x=1/2 y=1/2, and all those cases lead to a "no" answer.
x and y cannot be negative integers here, else x+y will never be greater than, and if x or y is an integer and the other a fraction, statement 1 does not hold. However, X can be negative fraction Y can be positive, which leads to no answer as well.

2) very easy to disprove: x=y=-10 (no) but also x=y=10 (yes), two answers therefore insuff.
I too am getting the same choice.. A, what’s the answer? @gmatophobia
Just added the OA to all the questions, the answer to this question is E.
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PS Question 1 - Nov 21

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?

I. 1
II. 3
III. 4

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II , and III

Source: Official Guide | Difficulty: Hard
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Sorry ! I couldn’t catch this well. Do you mean that the answer is c ?
gmatophobia, Sorry for the confusion. Since Bouquet is in discount. The idea is to have as many bouquets as possible. The greatest number of roses with $30 is 24. Luckily 24 is exactly 2 times of 12, and therefore, the 24 roses should be bought in 2 bouquets. Then 1 bouquet (12 roses) is $15. Luckily, $45 is exactly 3 times of $15, and therefore, we can purchase 3 bouquets with $45. So the answer is 3*12 = 36.
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Please help Q: If x and y are integers and 7^x+1 - 7^x-1 / 3 = 2^y . (49^6) what is the value of xy?

(A) 104
(B) 96
(C) 52
(D) 48
(E) 44
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Please help Q: If x and y are integers and 7^x+1 - 7^x-1 / 3 = 2^y . (49^6) what is the value of xy?

(A) 104
(B) 96
(C) 52
(D) 48
(E) 44

Discussed in detail here: https://gmatclub.com/forum/if-x-and-y-a ... 87422.html

Hope it helps.
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7^x(49-1)/3=2^y(7^12)

dividing 48/3 will give 16 i.e 7^x *2^4=2^y*7^12

x=12 y=4

ans D
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