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

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...

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

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...

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

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...

Is the positive integer $$x$$ prime?

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

16a = 32^b
(2^4)a = (2^5)^b
(2^4)a = 2^(5b)
a = 2^(5b) / 2^4
a = 2^(5b - 4)

Data sufficiency

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

Number Properties, Remainders

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

What is the mode of the list above?

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

Is $$7<\sqrt{n}<8?$$

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 $$a_n=3^n-n^2?$$

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 ...

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

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...

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

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...

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

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...

Probability

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

$$\sqrt{16+16}=$$

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