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# Quant Question of the Day Chat

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Re: Quant Question of the Day Chat [#permalink]
DS Question 2 - Dec 3

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

Source: GMAT Club Tests | Difficulty: Medium
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 2 - Dec 3

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

Source: GMAT Club Tests | Difficulty: Medium

E ?
Quant Chat Moderator
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Re: Quant Question of the Day Chat [#permalink]
PS Question 2 - Dec 03

If n = 9! – 6^4, which of the following is the greatest integer k such that 3^k is a factor of n ?

A. 1
B. 3
C. 4
D. 6
E. 8

Source: Official Guide | Difficulty: Hard
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 2 - Dec 03

If n = 9! – 6^4, which of the following is the greatest integer k such that 3^k is a factor of n ?

A. 1
B. 3
C. 4
D. 6
E. 8

Source: Official Guide | Difficulty: Hard

Annoying factors here! This is what I did:

n=9!-6^4
n=9!-81*16
n=(9*8)(7!-9*2)
n=(9*8)(18)(7*5*4*2-1)
n=(9*8)(18)(279)
n=(3^2*2^3)(3^2*2)(3^2*31)
n=2^4*3^6*31
there are 6 threes in n, therefore D.

Originally posted by mysterymanrog on 03 Dec 2022, 09:48.
Last edited by mysterymanrog on 03 Dec 2022, 09:50, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
mysterymanrog wrote:
n=9!-6^4
n=9!-81*16
n=(9*8)(7!-9*2)
n=(9*8)(18)(7*5*4*2-1)
n=(9*8)(18)(279)
n=(3^2*2^3)(3^2*2)(3^2*31)
n=2^4*3^6*31
there are 6 threes in n, therefore D.

I don’t understand the passage from 3 to 4 about 18

n=(9*8)(7!-9*2)
n=(9*8)(18)(7*5*4*2-1)
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Re: Quant Question of the Day Chat [#permalink]
luca1999 wrote:
mysterymanrog wrote:
n=9!-6^4
n=9!-81*16
n=(9*8)(7!-9*2)
n=(9*8)(18)(7*5*4*2-1)
n=(9*8)(18)(279)
n=(3^2*2^3)(3^2*2)(3^2*31)
n=2^4*3^6*31
there are 6 threes in n, therefore D.

I don’t understand the passage from 3 to 4 about 18

so 9*2 is equal to 18 right? 7! is 7*6*5*4*3*2*1

6*3 is equal to 18

thats common to both, so you can pull it out because calculating 7! is too much

Originally posted by mysterymanrog on 03 Dec 2022, 09:55.
Last edited by mysterymanrog on 03 Dec 2022, 09:56, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
no prroblem

It might be easier to rewrite 9! in prime factors, but that might be very time consuming

Originally posted by mysterymanrog on 03 Dec 2022, 09:56.
Last edited by mysterymanrog on 03 Dec 2022, 10:00, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
mysterymanrog wrote:
n=9!-6^4
n=9!-81*16
n=(9*8)(7!-9*2)
n=(9*8)(18)(7*5*4*2-1)
n=(9*8)(18)(279)
n=(3^2*2^3)(3^2*2)(3^2*31)
n=2^4*3^6*31
there are 6 threes in n, therefore D.

Nice approach -

You could have also taken 3^4 common upfront.

3^4[(8*7*2*5*4*2)-2^4]

3^4(4480 - 16)

3^4(4464)

4464 is divisible by 9

hence 3^6
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
mysterymanrog wrote:
n=9!-6^4
n=9!-81*16
n=(9*8)(7!-9*2)
n=(9*8)(18)(7*5*4*2-1)
n=(9*8)(18)(279)
n=(3^2*2^3)(3^2*2)(3^2*31)
n=2^4*3^6*31
there are 6 threes in n, therefore D.

Nice approach -

You could have also taken 3^4 common upfront.

3^4[(8*7*2*5*4*2)-2^4]

3^4(4480 - 16)

3^4(4464)

4464 is divisible by 9

hence 3^6

Yes this is probably fastest
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 2 - Dec 3

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

Source: GMAT Club Tests | Difficulty: Medium

E

gmatophobia wrote:
PS Question 1 - Dec 3

Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

A. 1/36
B. 3/36
C. 11/36
D. 20/36
E. 23/36

Source: GMAT Paper Tests | Difficulty: Hard

D

gmatophobia wrote:
PS Question 2 - Dec 03

If n = 9! – 6^4, which of the following is the greatest integer k such that 3^k is a factor of n ?

A. 1
B. 3
C. 4
D. 6
E. 8

Source: Official Guide | Difficulty: Hard

D

gmatophobia wrote:
DS Question 1 - Dec 03

What is the value of xy ?

(1) x + y = 7
(2) (x + 1)(y – 1) = 6

Source: GMATPrepNow | Difficulty: Medium

E

PS Question 1 - Dec 4

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take Machine X alone to produce 2w widgets?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Source: Official Guide | Difficulty : Hard

Originally posted by gmatophobia on 03 Dec 2022, 23:36.
Last edited by gmatophobia on 03 Dec 2022, 23:38, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
DS Question 1 - Dec 04

Set T is a finite set of positive consecutive multiples of 14. How many of these integers are also multiples of 21?

(1) Set T consists of 30 integers.
(2) The smallest integer in set T is a multiple of 21.

Source: Veritas Prep | Difficulty: Hard
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Re: Quant Question of the Day Chat [#permalink]
Starting in half an hour from now

9:30am NY | 2:30pm London | 8pm Mumbai

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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
Starting in half an hour from now

9:30am NY | 2:30pm London | 8pm Mumbai

Thanks
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Dec 4

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take Machine X alone to produce 2w widgets?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Source: Official Guide | Difficulty : Hard

E

gmatophobia wrote:
DS Question 1 - Dec 04

Set T is a finite set of positive consecutive multiples of 14. How many of these integers are also multiples of 21?

(1) Set T consists of 30 integers.
(2) The smallest integer in set T is a multiple of 21.

Source: Veritas Prep | Difficulty: Hard

A

PS Question 1 - Dec 5

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

A. 4
B. 5
C. 6
D. 7
E. 8

Source: Official Guide | Difficulty: Medium

Originally posted by gmatophobia on 04 Dec 2022, 21:20.
Last edited by gmatophobia on 04 Dec 2022, 21:22, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
gmatophobia wrote:
DS Question 1 - Dec 04

Set T is a finite set of positive consecutive multiples of 14. How many of these integers are also multiples of 21?

(1) Set T consists of 30 integers.
(2) The smallest integer in set T is a multiple of 21.

Source: Veritas Prep | Difficulty: Hard

A

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Re: Quant Question of the Day Chat [#permalink]
DS Question 1 - Dec 5

Are the numbers k/4, z/3, and r/2 in increasing order?

(1) 3 < z < 4
(2) r < z < k

Source: Others | Difficulty: Medium

DS Question 2 - Dec 5

The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.

Source: Official Guide | Difficulty: Hard
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 2 - Dec 5

The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.

Source: Official Guide | Difficulty: Hard

D
Re: Quant Question of the Day Chat [#permalink]
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