Search found 2550 matches


Re: If quadrilateral ABCD, pictured above, has perimeter of 64, what is the length of the line segment AD?

I've never needed to know, in more than ten years of answering official GMAT Quant questions, that when a rectangle's diagonals are perpendicular, that rectangle is a square. But that's what this question is testing. If you know that, Statement 2 is clearly sufficient alone, and Statement 1 is not (...


Re: A certain customer at a health food store purchases organic bananas at a price of $0.7 each, and conventional banana

If the person bought x organic and y conventional bananas, he spent 70x + 60y cents. From Statement 1, we know 70x + 60y = 560, so 7x + 6y = 56. Here 7x and 56 are both divisible by 7, so 6y must be too (if it's not clear why, we can rewrite the equation 6y = 56 - 7x, and now since the right side is...


Re: Word Problems

Ralph is giving out Valentine's Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one? 1) Ralph has 40 Valentine's Day cards to give out 2) If the number of...

by Ian Stewart

Thu Jun 10, 2021 4:56 am
Forum: Data Sufficiency
Topic: Word Problems
Replies: 1
Views: 339

Re: Word Problems

Using Statement 1 alone, we know if we double Brandon's age and double Carla's age, we get two numbers that are 4 apart. When you double two positive numbers, you double their difference, so Brandon's age and Carla's age must be 2 apart, and Statement 1 is sufficient alone. Or you could see that alg...

by Ian Stewart

Thu Jun 10, 2021 4:44 am
Forum: Data Sufficiency
Topic: Word Problems
Replies: 1
Views: 262

Re: In the figure above, \(ABCD\) is a parallelogram, and \(E\) is the midpoint of side \(AD.\) The area of triangular r

If we take the horizontal side AD to be the base b of the parallelogram, then its area is bh, where h is its corresponding height. Using the horizontal side as the base of the triangle, the triangle then has the same height h as the parallelogram. The triangle's base is b/2, because E is the midpoin...


Re: At a certain university, there are s students, \(w\) of whom are female and m of whom are male. The number of female

It's just a weighted average or mixtures situation. We know 12% of one group (women) and 25% of another group (men) are in physics. So overall, when we look at men and women together, somewhere between 12% and 25% are in physics. So the number of physics students p is somewhere between 12% of all st...


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...


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...


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...


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: 221

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: 10845

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: 245

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: 243

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: 228