GMAT Questions Chat Group

I think you’re still missing a number here. Did you take the possibility of 0 and 1 as remainder ?

I guess - you missed a number as well. Check for R = 0 & R = 1. IMO you should get 9

Did this in my head:
1) At k=0, its okay If k>0, (ex k=1) equation does not hold. For K 0?

(1) |k - 4| = |k| + 4

(2) k > k^3

Source: Jamboree | Difficulty: Hard [/quote]
Did this in my head:
1) At k=0, its okay If k>0, (ex k=1) equation does not hold. For K0 reduces the rhs while increasing the lhs

Smallest value of P needs only 2 twos and 1 three. Since p^3 is disivisble by 2^6*3^2. P must have 2^2*3^1. That way, when you raise p to the third you get 2^6*3^3 which is divisible by 2^6 and 3^2. You can have other values ofc, but we are looking at MUST BE so its the smallest.

7^x+1-7^x-1=2^y*3*7^12
7^x(7-1/7)=2^y*3*7^12
7^x(48/7)=2^y*3*7^12
7^x(2^4*3)=2^y*3*7^13
x=13, y=4
xy=(13*4)=40+12=52
C.

PS Question 2 - Nov 21

If 12 children purchased 34 candies and the range of the number of candies that they purchased is 2, which of the following can be the number of children who purchased 3 candies?

I. 2
II. 5
III. 11

A. I only
B. II only
C. I and II
D. I and III
E. I, II and III

Source: Math Revolution | Difficulty : Hard

If 11 bought 3 - 33 candies, 1 child buys 1 range=2. III. Okay

If 5 buy 3=15 candies, 34-15=19
7 children left. At least 1 child needs to buy more than 2, so not possible. II is out.

Answer must be D.

DS Question 1 - Nov 22

A drawer contains 6 socks. If two socks are randomly selected without replacement, what is the probability that both socks will be black?

(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.

Source: GMATPrepNow | Difficulty: Hard

PS Question 1 - Nov 22

How many positive integers less than 40 have six positive factors?

A. 2
B. 3
C. 4
D. 5
E. 6

Source: Other (PS Butler) | Difficulty: Medium

I got E for this.
The values I found: 12,18,20,28,30,32
For it to have 6 factors either perfect square*integer or x*y*z or x^5

PS Question 2 - Nov 22

When the integer n is divided by 33, the remainder is 24. Which of the following must be a divisor of n?

A. 11
B. 9
C. 7
D. 4
E. 3

Source: Other (PS Butler) | Difficulty: Medium

I don’t suppose 30 is correct. 30 = 5 * 2 * 3 , the number of factors will be 8

Should be D IMO

30 would be 5*2*3
(1+1)(1+1)(1+1)=6 no?

n=33k+24
n=3(11k+8)
n must be divisible by 3. Answer E

Nevermind I added the factors rather than multiply. Its D x)

DS Question 2 - Nov 22

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.

Source: Official Guide | Difficulty: Medium

Here is my take:

Question Stem Analysis:

We need to determine whether the median of the 3 numbers of a certain list is equal to the average of the 3 numbers, given that the 3 numbers are different. We can let the 3 numbers be a, b, and c such that a < b < c. Therefore, we need to determine whether b = (a + b + c)/3.

Statement One Alone:

We see that c - a = 2(c - b). Simplifying, we have:

c - a = 2c - 2b

2b - a = c

Now, let’s substitute this for c in b = (a + b + c)/3:

b = (a + b + (2b - a))/3 ?

b = 3b/3 ?

b = b ?

We can see that the answer is yes. Statement one alone is sufficient.

Statement Two Alone:

If the sum of the three numbers is equal to 3 times one of the numbers, then the average of the three numbers is equal to one of the three numbers. The average cannot equal the smallest or the largest integer; thus the average must equal the median.

To see why the average cannot equal the smallest integer, notice that a < b and a < c. Adding these two inequalities, we obtain:

2a < b + c

Adding a to each side, we have:

3a < a + b + c

Dividing each side by 3, we see that a < (a + b + c)/3, which shows that the average is strictly greater than the smallest integer. It can be shown using similar arguments that the average is strictly less than the largest integer. Since we know the average is equal to one of the three numbers and since the average cannot equal the smallest or the largest number, it is equal to the median. Statement two alone is sufficient.

Answer: D

Solution:

Let a side of the brass inlay in the center be x. Let’s analyze each statement:

I. 1

If the width of the uniform strip is 1, then a side of the entire wooden plaque is x + 2. Thus, the ratio of the area of the brass inlay to the wooden area is x^2 / [(x + 2)^2 - x^2]. Since we are told that this ratio is 25/39, let’s create the following equation:

x^2 / [(x + 2)^2 - x^2] = 25/39

39x^2 = 25[x^2 + 4x + 4 - x^2]

39x^2 = 100x + 100

39x^2 - 100x - 100 = 0

(3x - 10)(13x + 10) = 0

x = 10/3 or x = -10/13

Since there is no restriction on x (such as the side of the wooden plaque should be an integer etc.), it is possible that a side of the plaque is 10/3. We see that the width of the wooden strip can be 1.

II. 3

If the width of the uniform strip is 3, then a side of the wooden plaque is x + 6. Thus, the ratio of the area of the brass inlay to the wooden area is x^2 / [(x + 6)^2 - x^2]. Since we are told that this ratio is 25/39, let’s create the following equation:

x^2 / [(x + 6)^2 - x^2] = 25/39

39x^2 = 25[x^2 + 12x + 36 - x^2]

39x^2 = 300x + 900

39x^2 - 300x - 900 = 0

13x^2 - 100x - 300 = 0

(x - 10)(13x + 30) = 0

x = 10 or x = -30/13

We see that a side of the wooden plaque can be 10, and the width of the wooden strip can be 3.

III. 4

If the width of the uniform strip is 4, then a side of the wooden plaque is x + 8. Thus, the ratio of the area of the brass inlay to the wooden area is x^2 / [(x + 8)^2 - x^2]. Since we are told that this ratio is 25/39, let’s create the following equation:

x^2/[(x + 8)^2 - x^2] = 25/39

39x^2 = 25[x^2 + 16x + 64 - x^2]

39x^2 = 400x + 1,600

39x^2 - 400x - 1,600 = 0

(3x - 40)(13x + 40) = 0

x = 40/3 or x = -40/13

We see that a side of the wooden plaque can be 40/3 and the width of the wooden strip can be 4.

Answer: E

D should be correct

DS Question 1 - Nov 23

If f(x) is a linear function, what is the value of f(1)?

(1) f(x − 3) = f(x) + 1
(2) f(5) = 2f(3)

Source: Others | Difficulty : Hard

Hi I have a question I recently gave two gmat club tests. Scored a 42 and 43 on quant. Does anyone have any idea what this roughly translates to on the actual gmat quant?

One can use the linear equation form - mx + b.

Option B alone