Quant Question of the Day Chat : Quantitative Questions

bb · 2022-10-20T20:57:38-07:00

Hello everyone and welcome to the GMAT Club's Quant Question of the Day If you would like to join the Quant Question of the Day Chat Group, Join the chat group here Group moderator is gmatophobia Welcome aboard! -BB And I have some news for the group - I would like to welcome gmatophobia as the new Moderator of this chat group. Please give him a day or two to get situation and get this group going with posting questions as well as sharing any interesting posts and links. Welcome gmatophobia - you are the first Quant Chat group moderator we have had

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gmatophobia

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

03 Dec 2022, 03:03

DS Question 2 - Dec 3

Is quadrilateral ABCD a rhombus?

(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]

03 Dec 2022, 07:19

gmatophobia wrote:

DS Question 2 - Dec 3

Is quadrilateral ABCD a rhombus?

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

Source: GMAT Club Tests | Difficulty: Medium

E ?

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

03 Dec 2022, 07:42

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]

Updated on: 03 Dec 2022, 09:50

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]

03 Dec 2022, 09:55

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]

Updated on: 03 Dec 2022, 09:56

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]

Updated on: 03 Dec 2022, 10:00

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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gmatophobia

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

03 Dec 2022, 10:01

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]

03 Dec 2022, 10:01

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]

Updated on: 03 Dec 2022, 23:38

gmatophobia wrote:

DS Question 2 - Dec 3

Is quadrilateral ABCD a rhombus?

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

Source: GMAT Club Tests | Difficulty: Medium

Show SpoilerOA

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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

Show SpoilerOA

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

Show SpoilerOA

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

Show SpoilerOA

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]

04 Dec 2022, 04:54

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]

04 Dec 2022, 06:59

Starting in half an hour from now

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

Youtube link

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

04 Dec 2022, 07:54

gmatophobia wrote:

Starting in half an hour from now

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

Youtube link

Thanks

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

Updated on: 04 Dec 2022, 21:22

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

Show SpoilerOA

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

Show SpoilerOA

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]

05 Dec 2022, 07:34

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

Show SpoilerOA

A

Explanation please.

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

05 Dec 2022, 09:03

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]

05 Dec 2022, 09:12

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

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gmatclubot

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

05 Dec 2022, 09:12

Quant Question of the Day Chat

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