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mysterymanrog
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GMAT Questions Chat Group 03 Dec 2022, 02:40
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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
P(Even, Any)=1/2
Ways to get 8
(2,6)(3,5)(4,4)(5,4)(6,2) - 5/36
Ways to get 8 with even in first die: 3/36
1/2+5/36-3/36=20/36
D.
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GMAT Questions Chat Group 03 Dec 2022, 02:52
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Awesome mysterymanrog ... Way to go !!
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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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GMAT Questions Chat Group 03 Dec 2022, 07:19
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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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GMAT Questions Chat Group 03 Dec 2022, 07:42
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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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GMAT Questions Chat Group Updated on: 03 Dec 2022, 09:50
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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gmatophobia
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.
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GMAT Questions Chat Group 03 Dec 2022, 09:55
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mysterymanrog
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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GMAT Questions Chat Group Updated on: 03 Dec 2022, 09:56
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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mysterymanrog
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
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GMAT Questions Chat Group Updated on: 03 Dec 2022, 10:00
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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no prroblem

It might be easier to rewrite 9! in prime factors, but that might be very time consuming
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GMAT Questions Chat Group 03 Dec 2022, 10:01
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mysterymanrog
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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mysterymanrog
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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GMAT Questions Chat Group Updated on: 03 Dec 2022, 23:38
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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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
E

gmatophobia
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
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
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
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GMAT Questions Chat Group 04 Dec 2022, 04:54
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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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GMAT Questions Chat Group Updated on: 04 Dec 2022, 21:22
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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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
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
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GMAT Questions Chat Group 05 Dec 2022, 07:34
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gmatophobia
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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GMAT Questions Chat Group 05 Dec 2022, 09:03
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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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GMAT Questions Chat Group 05 Dec 2022, 09:12
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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
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GMAT Questions Chat Group Updated on: 05 Dec 2022, 10:41
Originally posted by mysterymanrog on 05 Dec 2022, 10:28.
Last edited by mysterymanrog on 05 Dec 2022, 10:41, edited 2 times in total.
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gmatophobia
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
You can create equation:
(x-1)(x+2)=area2 and x^2=area2
1) we have (x-1)(x+2)=70
x^2+2x-x-2=70
x^2+x-72=0
(x+9)(x-8)=0
x is -9 or 8. Remeber, lengths cannot be neg so x=8. Suff
2) Only 1 dimension had increase and that was by 2 inches. Therefore 2=x(1+1/4)
Can clearly solve for x, sufficient.

D.

gmatophobia
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
1 is clearly insuff
2) If k is pos and the rest are negative, no
If k is negative and the rest are negative, no
if all are pos maybe
3) z is between 3 and 4 and rIf we take extreme value of k, k/4 is much larger than z/3
But if K is a smaller value, say 6, then it is increasing order since z/3 will be larger.

E.

Rohstar750
gmatophobia
gmatophobia
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.
LCM of 14 and 21=
7*3*2=42 Therefore any m42 in the set will be a m of 21.
14,28,42 - every third multiple of 14 will be a m42 which is also a m21.
The problem tells us that they are consectuive multiples - so all integers will be increasing and will be unique in the set.
1) tells us that there are 30 integers in the set.
We can test a bit:
If the set starts with m14, then:
m14,m14,m42,m14,m14,m42 - every second value of the set is m42 so 9 integers in the set will be m42.
If rhe set starts with m42 the pattern is the same:
m42, m14,m14,m42,m14,m14
if the second number is m42 the same:
m14,m42,m14,m14,m42
So we will always have 9 m42s in the set, so 9 m21s.
B) is not sufficient for us to determine
The smallest integer can be m21, if there is only 1 member of the set, there is only 1 m21 but if there are 9 members, it will be more than 1. NS.

A
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