## Search found 338 matches

##### Re: Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q?\)

3^3 =27 and 5^2 = 25 Problem asks for approximate answer, so the above are approximately equal. So using the above 3^9 = 5^6, so 3^11 is about equal to 9*5^6 5^28 + 9*5^6 = 5^q Divide by 5^6 5^22 +9 = 5^(q-6) In the context of these large numbers, 9 is effectively 0, so 5^22 =5^(q-6) So q = 28, C

- by regor60

Sun Apr 25, 2021 9:43 am- Forum: Problem Solving
- Topic: Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q?\)
- Replies:
**1** - Views:
**27**

#### A magical leather pouch contains 2 alabaster marbles, 3 cerulean marbles, and 5 magenta marbles. First, four marbles are

###### Problem Solving

##### Re: A magical leather pouch contains 2 alabaster marbles, 3 cerulean marbles, and 5 magenta marbles. First, four marbles

Problem statement was transcribed incorrectly. There are 2 alabaster, otherwise solution doesn't work

- by regor60

Sun Mar 14, 2021 12:15 pm- Forum: Problem Solving
- Topic: A magical leather pouch contains 2 alabaster marbles, 3 cerulean marbles, and 5 magenta marbles. First, four marbles are
- Replies:
**2** - Views:
**151**

#### If \(P^2-QR=10,\) \(Q^2+PR=10,\) \(R^2+PQ=10,\) and \(R\ne Q,\) what is the value of \(P^2+Q^2+R^2?\)

###### Problem Solving

##### Re: If \(P^2-QR=10,\) \(Q^2+PR=10,\) \(R^2+PQ=10,\) and \(R\ne Q,\) what is the value of \(P^2+Q^2+R^2?\)

You're free to choose values for P,Q,and R that satisfy the equalities with the exception of R $$\ne$$ Q.

So, let P=Q

P^2 -PR = 10

P^2 + PR =10

from the first two equalities, therefore

P^2 = 10

this means that R must =0

Since P=Q, Q^2 also =10

So P^2+Q^2+R^2 =20,C

- by regor60

Sun Mar 14, 2021 6:36 am- Forum: Problem Solving
- Topic: If \(P^2-QR=10,\) \(Q^2+PR=10,\) \(R^2+PQ=10,\) and \(R\ne Q,\) what is the value of \(P^2+Q^2+R^2?\)
- Replies:
**1** - Views:
**64**

#### In the figure above, \(X\) and \(Y\) represent locations in a district of a certain city where the streets form a rectan

###### Problem Solving

##### Re: In the figure above, \(X\) and \(Y\) represent locations in a district of a certain city where the streets form a re

To get from X to Y 5 steps to the right and 3 steps up need to be taken and there are many paths. The problem is simplified in that no steps to the left or down are permitted. One can therefore see that the 5 steps to the right can be shown as RRRRR and the 3 up as UUU. As a group these 8 steps can ...

- by regor60

Wed Mar 10, 2021 12:59 pm- Forum: Problem Solving
- Topic: In the figure above, \(X\) and \(Y\) represent locations in a district of a certain city where the streets form a rectan
- Replies:
**1** - Views:
**72**

##### Algebra

Now in (1) we are given value of T so the equation becomes 0.15X+ 0.29Y = 4.40. We still have 1 equation and 2 variable 1 and 2. So we cannot solve for either of the variables X and Y. This is clearly NOT Sufficient. Just because the equation cannot be solved by the process of elimination of variab...

Source: Manhattan Prep If the number 200! is written in the form \(p \times 10^q\), where \(p\) and \(q\) are integers, what is the maximum possible value of \(q\)? A. 40 B. 48 C. 49 D. 55 E. 64 The OA is C We have to get the value of \(q\) where \(q\) is the exponent of \(10^q\). Thus, we have to ...

- by regor60

Thu Aug 01, 2019 6:22 am- Forum: Problem Solving
- Topic: If the number 200! is written in the form \(p \times 10^q\),
- Replies:
**4** - Views:
**439**

Source: Manhattan Prep If the number 200! is written in the form \(p \times 10^q\), where \(p\) and \(q\) are integers, what is the maximum possible value of \(q\)? A. 40 B. 48 C. 49 D. 55 E. 64 The OA is C We have to get the value of \(q\) where \(q\) is the exponent of \(10^q\). Thus, we have to ...

- by regor60

Thu Aug 01, 2019 6:19 am- Forum: Problem Solving
- Topic: If the number 200! is written in the form \(p \times 10^q\),
- Replies:
**4** - Views:
**439**

Source: Manhattan Prep A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is \(\frac{5}{12}\), what is the probability of selecting two rubies from the bag, without replacement?...

- by regor60

Mon Jul 22, 2019 7:46 am- Forum: Problem Solving
- Topic: A certain bag of gemstones is composed of two-thirds
- Replies:
**5** - Views:
**578**

5 boys and 5 girls randomly select seats around a circular table that seats 10. What is the probability that two girls will sit next to one another? A.11/24 B.23/24 C.23/48 D.47/48 E.125/126 OA: E The answer works only if the question is interpreted to mean "two or more". Therefore, to not have any...

- by regor60

Tue Jun 25, 2019 5:57 am- Forum: Problem Solving
- Topic: 5 boys and 5 girls randomly select
- Replies:
**2** - Views:
**406**

Call the numbers X and Y. So X+Y=1 and XY=-1 given the problem statement. Let's square X+Y = X^2+2XY+Y^2 = 1. Since XY=-1, we can substitute: X^2+Y^2-2 = 1. So, X^2+Y^2 = 3. Multiplying X^2+Y^2 by X+Y = (X+Y)(X^2+Y^2) = X^3 + Y^3 +XY^2 + YX^2 = (3)(1) Factor an XY from the last two terms: X^3+Y^3 + ...

- by regor60

Wed May 08, 2019 7:31 am- Forum: Problem Solving
- Topic: The sum of two numbers is 1 and their product is -1. What is
- Replies:
**4** - Views:
**456**

In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women? (A) 50% (B) 40% (C) 25% (D) 20% (E) 10% [spoiler]OA=C[/spoi...

- by regor60

Mon Apr 22, 2019 10:00 am- Forum: Problem Solving
- Topic: In Smithtown, the ratio of right-handed people to
- Replies:
**2** - Views:
**363**

A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children: Nicole, Ronit, Kim, Deborah, Mark, and Terrance. If Deborah will only eat the kind of cookie that Kim eats, in how many different ways can the cookies be distributed? (A) 5040 (B) 50...

- by regor60

Mon Apr 22, 2019 9:49 am- Forum: Problem Solving
- Topic: A woman has seven cookies - four chocolate chip and three
- Replies:
**2** - Views:
**453**

=> The maximum number of draws we can make without drawing 5 balls of a single color is 3 + 4 + 4 + 4 + 4 = 14. This occurs when we draw 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls and 4 white balls. If we draw one more ball, then we will have drawn 5 balls of a single color. Thus, to ...

- by regor60

Wed Mar 20, 2019 6:34 am- Forum: Problem Solving
- Topic: A box contains 3 red balls, 4 green balls, 5 yellow balls, 6
- Replies:
**4** - Views:
**1579**

GMATH practice exercise (Quant Class 16) The product of the positive 4-digit integer 118A and 25847 is 4758 units less than a number that leaves remainder 1 when divided by 5. How many values are possible for the digit A? (A) None (B) Only 1 (C) Only 2 (D) Only 3 (E) More than 3 Answer: [spoiler]__...

- by regor60

Thu Feb 07, 2019 12:00 pm- Forum: Problem Solving
- Topic: The product of the positive 4-digit integer 118A and 25847
- Replies:
**2** - Views:
**334**

Hi regor60, I agree that this prompt is poorly-worded. The "intent" is to ask for every 4-letter arrangement that fits the given restrictions, INCLUDING "words" that do not appear in the dictionary (re: arrangements that are not actually words). GMAT question-writers are far more specific with how ...

- by regor60

Tue Feb 05, 2019 10:57 am- Forum: Problem Solving
- Topic: In how many ways can a 4-letter word be formed from the
- Replies:
**6** - Views:
**618**