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Practice Questions Chat 19 Nov 2022, 14:09
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Is there a VERBAL group?
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Practice Questions Chat Updated on: 19 Nov 2022, 18:47
Originally posted by Dip050701 on 19 Nov 2022, 18:46.
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gmatophobia
DS Question-2 Nov 19

If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

Source: Manhattan | Difficulty: Hard
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C

gmatophobia
DS Question-2 Nov 19

If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

Source: Manhattan | Difficulty: Hard
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C
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Practice Questions Chat Updated on: 19 Nov 2022, 22:52
Originally posted by gmatophobia on 19 Nov 2022, 22:48.
Last edited by gmatophobia on 19 Nov 2022, 22:52, edited 3 times in total.
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gmatophobia
PS Question 1 - Nov 19

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

A) 0 and 13
B) 0 and 14
C) 1 and 10
D) 1 and 9
E) 2 and 8

Source: Official Guide | Difficulty : Hard
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A

gmatophobia
DS Question 1 - Nov 19

Is the average of n consecutive integers equal to 1 ?

(1) n is even
(2) if S is the sum of the n consecutive integers, then 0 < S < n

Source: Manhattan | Difficulty: Hard
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D

gmatophobia
PS Question - 2

If 2f(x) + f(x^2 - 1) = 1, for all x, then what is the value of f(-root(2)) ?

A. -1/3
B. 0
C. 1/3
D. 2/3
E. 1

Source: GMAT Club Tests | Difficulty: Hard
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C

gmatophobia
DS Question-2 Nov 19

If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

Source: Manhattan | Difficulty: Hard
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C

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
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Practice Questions Chat 19 Nov 2022, 23:12
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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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Practice Questions Chat Updated on: 20 Nov 2022, 03:23
Originally posted by jscmm on 20 Nov 2022, 03:14.
Last edited by jscmm on 20 Nov 2022, 03:23, edited 1 time in total.
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gmatophobia
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
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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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Practice Questions Chat 20 Nov 2022, 06:22
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The greatest number of roses with $45 is 36.
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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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Practice Questions Chat 20 Nov 2022, 07:14
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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
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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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Practice Questions Chat 20 Nov 2022, 08:17
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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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Practice Questions Chat 20 Nov 2022, 09:42
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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
Show more
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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Practice Questions Chat Updated on: 20 Nov 2022, 10:40
Originally posted by gmatophobia on 20 Nov 2022, 10:36.
Last edited by gmatophobia on 20 Nov 2022, 10:40, edited 1 time in total.
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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.
Show more
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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Practice Questions Chat 20 Nov 2022, 11:19
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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
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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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Practice Questions Chat 20 Nov 2022, 11:31
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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
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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Awesome !! Kudos to you ..
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Practice Questions Chat 20 Nov 2022, 16:22
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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.
Show more
I too am getting the same choice.. A, what’s the answer? gmatophobia
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Practice Questions Chat Updated on: 20 Nov 2022, 19:05
Originally posted by gmatophobia on 20 Nov 2022, 19:01.
Last edited by gmatophobia on 20 Nov 2022, 19:05, edited 4 times in total.
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gmatophobia
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
Show more
Show SpoilerOA
D

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
Show more
Show SpoilerOA
E

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
Show more
Show SpoilerOA
D

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
Show more
Show SpoilerOA
E

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
Show more
Show SpoilerOA
D

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
Show more
Just added the OA to all the questions, the answer to this question is E.
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Practice Questions Chat 20 Nov 2022, 22:56
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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 ?
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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
Show more

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

Hope it helps.
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Practice Questions Chat Updated on: 21 Nov 2022, 01:45
Originally posted by Rabab36 on 21 Nov 2022, 01:41.
Last edited by Rabab36 on 21 Nov 2022, 01:45, edited 1 time in total.
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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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