Inequalities
Today we’ve got an inequalities data sufficiency question on tap from GMATPrep. Set your timer for 2 minutes and go!
Is m + z > 0?
(1) m “ 3z > 0
(2) 4z “ m > 0
This is a yes/no data sufficiency question. I’m just going to remind myself of the rules: an always yes answer to a statement is sufficient, an always no answer is also sufficient, and a maybe or sometimes yes / sometimes no answer is not sufficient.
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Challenge Problem Showdown – February 6th, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
Challenge Problem Showdown – January 30th, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
For all positive integers n and m, the function A(n) equals the following product:(1 + 1/2 + 1/22)(1 + 1/3 + 1/32)(1 + 1/5 + 1/52)…(1 + 1/pn + 1/pn2), where pn is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
Challenge Problem Showdown – January 23rd, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means twenty-one. A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?
Statistical “Combo” Problems
Today we’re going to talk about statistics problems in which we have to combine knowledge of more than oneconcept.Try this GMATPrep problem first; set your timer for 2 minutes and go!
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than 130,000 and less than 150,000.
III. At least one of the homes was sold for less than $130,000.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Sigh. I hate roman numeral questions. I have to do more work to solve the problem, and I never like that. : )
Challenge Problem Showdown – January 16th, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
If x is positive and not equal to 1, then the product of x1/n for all positive integers n such that 21 ≤ n ≤ 30 is between
Challenge Problem Showdown – January 9th, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
If k is a positive integer, which of the following must be divisible by 24?
Challenge Problem Showdown – January 2nd, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
If x and y are both integers chosen at random between 1 and 100, inclusive, what is the approximate probability that x/y is an integer?
Challenge Problem Showdown – December 5th, 2011
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
A circle is inscribed within a regular hexagon in such a way that the circle touches all sides of the hexagon at exactly one point per side. Another circle is drawn to connect all the vertices of the hexagon. Expressed as a fraction, what is the ratio of the area of the smaller circle to the area of the larger circle?
Challenge Problem Showdown – November 28th, 2011
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
If x < y < z but x2 > y2 > z2 > 0, which of the following must be positive?