## Search found 2544 matches

#### Alex deposited \(x\) dollars into a new account that earned \(8\) percent annual interest, compounded annually. One year

###### Problem Solving

##### Re: Alex deposited \(x\) dollars into a new account that earned \(8\) percent annual interest, compounded annually. One

In the first year, the initial deposit of $x earns 8% interest, so after one year, the account holds 1.08x dollars. Then an additional $x is deposited in the account, so the account now contains 1.08x + x = x(1.08 + 1) dollars. This amount now earns 8% interest over the second year, so at the end of...

- by Ian Stewart

Tue Jun 08, 2021 5:03 am- Forum: Problem Solving
- Topic: Alex deposited \(x\) dollars into a new account that earned \(8\) percent annual interest, compounded annually. One year
- Replies:
**1** - Views:
**152**

#### A rectangular solid brick of iron is melted and shaped into a cube. If the areas of different sides of the brick were 24

###### Problem Solving

##### Re: A rectangular solid brick of iron is melted and shaped into a cube. If the areas of different sides of the brick wer

We have a rectangular block measuring L by W by H, and we know: LW = 54 LH = 36 WH = 24 Notice if we multiply all three of LW, LH and WH together, we get (LW)(LH)(WH) = (54)(36)(24) (L^2 W^2 H^2) = (6)(9)(6^2)(6)(4) (LWH)^2 = (2^2)(6^4)(3^2) LWH = 2*6^2*3 = 6^3 So the volume of the rectangular block...

- by Ian Stewart

Tue Jun 08, 2021 4:57 am- Forum: Problem Solving
- Topic: A rectangular solid brick of iron is melted and shaped into a cube. If the areas of different sides of the brick were 24
- Replies:
**1** - Views:
**145**

#### In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of the

###### Data Sufficiency

##### Re: In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of

One way to find the area of a trapezoid is to average the lengths of the parallel sides, then multiply that average by the height. Applying that here, the area we want to find is [ (z +y)/2 ] * x and now in Statement 1, if we multiply both sides by x, and divide both sides by 2, the left side will l...

- by Ian Stewart

Tue Jun 08, 2021 4:27 am- Forum: Data Sufficiency
- Topic: In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of the
- Replies:
**1** - Views:
**121**

##### Re: Is the positive integer \(x\) prime?

I assume the question means to tell us y is some positive integer. If x and y are positive integers, then when we multiply their LCM and their GCD, we always get their product xy. So if their GCD is 1, that automatically means their LCM is xy, and if their LCM is xy, that automatically means their G...

- by Ian Stewart

Tue Jun 08, 2021 4:22 am- Forum: Data Sufficiency
- Topic: Is the positive integer \(x\) prime?
- Replies:
**1** - Views:
**110**

#### For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?

###### Problem Solving

##### Re: For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?

16a = 32^b

(2^4)a = (2^5)^b

(2^4)a = 2^(5b)

a = 2^(5b) / 2^4

a = 2^(5b - 4)

- by Ian Stewart

Sun Jun 06, 2021 6:22 pm- Forum: Problem Solving
- Topic: For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?
- Replies:
**1** - Views:
**120**

##### Re: Data sufficiency

Statement 1 says the ratio of his tax and insurance expense to his mortgage payments was 1 to 3. So 3/4 of Arturo's total costs went to mortgage payments, and the remaining 1/4 is divided, in some unknown way, between taxes and insurance, and Statement 1 is not sufficient. Statement 2 says the ratio...

- by Ian Stewart

Sat Jun 05, 2021 9:21 am- Forum: GMAT Math
- Topic: Data sufficiency
- Replies:
**5** - Views:
**5848**

##### Re: Number Properties, Remainders

When we divide y by y-1 in Statement 1, we'll get a quotient and remainder of 1 almost always, because y = (1)(y-1) + 1. There is only one exception: if y = 2, then when we divide by y - 1 = 1, we get a quotient of 2 and a remainder of 0, because that's the lone situation where y is divisible by y-1...

- by Ian Stewart

Sat Jun 05, 2021 9:16 am- Forum: Data Sufficiency
- Topic: Number Properties, Remainders
- Replies:
**1** - Views:
**121**

##### Re: What is the mode of the list above?

The GMAT almost never even mentions 'mode', and in the very rare questions where it does, all you need to know is its definition. As this question is designed, we need to be concerned about all kinds of potential technicalities -- how do we answer if the list might have no mode (which would be true ...

- by Ian Stewart

Sat Jun 05, 2021 9:13 am- Forum: Data Sufficiency
- Topic: What is the mode of the list above?
- Replies:
**1** - Views:
**119**

##### Re: Is \(7<\sqrt{n}<8?\)

Since every quantity here is positive, we can just square the inequality - the question is, "Is 49 < n < 64", from which the answer is instantly C.

- by Ian Stewart

Sat Jun 05, 2021 9:02 am- Forum: Data Sufficiency
- Topic: Is \(7<\sqrt{n}<8?\)
- Replies:
**1** - Views:
**111**

#### What is the difference between the fourth and third terms of the sequence defined by \(a_n=3^n-n^2?\)

###### Problem Solving

##### Re: What is the difference between the fourth and third terms of the sequence defined by \(a_n=3^n-n^2?\)

What is the first term of the sequence? The question needs to tell you - some sequences start at a_0, and some at a_1 (both in real math and on the GMAT), so if the question doesn't specify where the sequence starts, there's no way to know if the "third term" is a_2 or a_3. The GMAT would always be ...

- by Ian Stewart

Sat Jun 05, 2021 8:59 am- Forum: Problem Solving
- Topic: What is the difference between the fourth and third terms of the sequence defined by \(a_n=3^n-n^2?\)
- Replies:
**1** - Views:
**167**

#### In a box, there are 4 ballpoint pens and 3 fountain pens. How many possible selections can be formed which have at least

###### Problem Solving

##### Re: In a box, there are 4 ballpoint pens and 3 fountain pens. How many possible selections can be formed which have at l

I find it difficult sometimes to guess the intentions of questions written this way, because "two items of every type of pen" does not make sense, particularly with only two types of pen. But I gather we just want to count how many ways to pick two pens of each type, then two ballpoints and three fo...

- by Ian Stewart

Sat Jun 05, 2021 8:55 am- Forum: Problem Solving
- Topic: In a box, there are 4 ballpoint pens and 3 fountain pens. How many possible selections can be formed which have at least
- Replies:
**1** - Views:
**115**

#### If \(2^{98}=256L+N,\) where \(L\) and \(N\) are integers and \(0\le N\le 4,\) what is the value of \(N?\)

###### Problem Solving

##### Re: If \(2^{98}=256L+N,\) where \(L\) and \(N\) are integers and \(0\le N\le 4,\) what is the value of \(N?\)

There are several good ways to look at this. Algebraically, since 256 = 2^8, we can rewrite the equation: 2^98 - 256L = N 2^98 - (2^8)L = N 2^8 (2^90 - L) = N Notice now that on the left side, we're multiplying 256 by some other integer, 2^90 - L. Clearly we can't get 1, 2, 3 or 4 if we do that, bec...

- by Ian Stewart

Sat Jun 05, 2021 8:46 am- Forum: Problem Solving
- Topic: If \(2^{98}=256L+N,\) where \(L\) and \(N\) are integers and \(0\le N\le 4,\) what is the value of \(N?\)
- Replies:
**1** - Views:
**121**

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

###### Problem Solving

##### Re: Two dice are tossed once. The probability of getting an even number at the first die or a total of \(8\) is

This does not look like an official question to me, at least if it has been transcribed correctly. The probability the first die is even is 1/2, so since we want the probability either that happens or something else happens, the answer must be at least 1/2, and only D or E could possibly be right. W...

- by Ian Stewart

Sat Jun 05, 2021 8:38 am- Forum: Problem Solving
- Topic: Two dice are tossed once. The probability of getting an even number at the first die or a total of \(8\) is
- Replies:
**1** - Views:
**132**

##### Re: Probability

From 1000 through 2000 inclusive, there are 1001 integers, so the denominator must be 1001, and we already have only two candidate answers. There are a few ways to compute the numerator. For example, we might separate things into two cases: - numbers that end in three identical digits, like 1000, 12...

- by Ian Stewart

Sat Jun 05, 2021 8:34 am- Forum: Problem Solving
- Topic: Probability
- Replies:
**1** - Views:
**145**

##### Re: \(\sqrt{16+16}= \)

$$\sqrt{\left(16\ +\ 16\right)}=\ \sqrt{\left(2\right)\left(16\right)}\ =\ \sqrt{2\ }\sqrt{16}=\ 4\sqrt{2}$$

- by Ian Stewart

Sat Jun 05, 2021 8:25 am- Forum: Problem Solving
- Topic: \(\sqrt{16+16}= \)
- Replies:
**1** - Views:
**117**