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If quadrilateral ABCD, pictured above, has perimeter of 64, what is the length of the line segment AD?
Data Sufficiency
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 (...
- by Ian Stewart
Thu Jun 10, 2021 5:04 am- Forum: Data Sufficiency
- Topic: If quadrilateral ABCD, pictured above, has perimeter of 64, what is the length of the line segment AD?
- Replies: 1
- Views: 273
A certain customer at a health food store purchases organic bananas at a price of $0.7 each, and conventional bananas at
Data Sufficiency
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...
- by Ian Stewart
Thu Jun 10, 2021 5:00 am- Forum: Data Sufficiency
- Topic: A certain customer at a health food store purchases organic bananas at a price of $0.7 each, and conventional bananas at
- Replies: 1
- Views: 284
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
In the figure above, \(ABCD\) is a parallelogram, and \(E\) is the midpoint of side \(AD.\) The area of triangular regio
Problem Solving
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...
- by Ian Stewart
Tue Jun 08, 2021 5:20 am- Forum: Problem Solving
- Topic: In the figure above, \(ABCD\) is a parallelogram, and \(E\) is the midpoint of side \(AD.\) The area of triangular regio
- Replies: 1
- Views: 334
At a certain university, there are s students, \(w\) of whom are female and m of whom are male. The number of female phy
Problem Solving
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...
- by Ian Stewart
Tue Jun 08, 2021 5:13 am- Forum: Problem Solving
- Topic: At a certain university, there are s students, \(w\) of whom are female and m of whom are male. The number of female phy
- Replies: 1
- Views: 305
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: 308
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: 289
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: 237
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
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: 245
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: 10846
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: 244
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