Search found 2550 matches
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 ...
- 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: 289
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 an...
- 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: 246
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: 215
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: 238
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: 259
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: 213
Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores \(10\) in
Problem Solving
Re: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores \(10\) i
Presumably this question means to talk about 6-sided dice labeled from 1 through 6. When you roll one die, your average roll is 3.5, so when you roll three dice, your average sum will be (3)(3.5) = 10.5. With ordinary dice, you're as likely to roll something above average as you are to roll somethin...
- by Ian Stewart
Sat Jun 05, 2021 8:23 am- Forum: Problem Solving
- Topic: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores \(10\) in
- Replies: 1
- Views: 231
Re: how to use fractional exponents
you can perform these three operations in any order you want; This is not true in general. If you start with the number -2, you can square that, then take the square root, but you cannot square root it first, then square the result, because the square root of a negative number is undefined. Because...
- by Ian Stewart
Sat Jun 05, 2021 8:11 am- Forum: GMAT Math
- Topic: how to use fractional exponents
- Replies: 2
- Views: 8702
After the yearly performance appraisal, Boogle, fired 25% of its senior software engineers. What percentage of employees
Data Sufficiency
Re: After the yearly performance appraisal, Boogle, fired 25% of its senior software engineers. What percentage of emplo
The wording could be better, but if we start with T employees, 35% of whom are senior engineers, then we start with 0.35T = (7/20)T senior engineers. We know a quarter of these engineers are fired, so the number of engineers and the total number of employees both drop by (1/4)(0.35T) = (7/80)T. So n...
- by Ian Stewart
Wed Feb 12, 2020 5:46 am- Forum: Data Sufficiency
- Topic: After the yearly performance appraisal, Boogle, fired 25% of its senior software engineers. What percentage of employees
- Replies: 1
- Views: 482
At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their
Problem Solving
Re: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their
80% of all interns receive less than 6 hours of sleep. 75% of all interns receive less than 6 hours of sleep and report feeling tired. So, subtracting, 5% of all interns receive less than 6 hours of sleep and do not report feeling tired. We then also have the remaining 20% of interns who get more th...
- by Ian Stewart
Wed Feb 12, 2020 5:32 am- Forum: Problem Solving
- Topic: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their
- Replies: 3
- Views: 1314
A certain company has budgeted $1,440 for entertaiment expenses for the year, divided into 12...
Problem Solving
Re: A certain company has budgeted $1,440 for entertaiment expenses for the year, divided into 12...
Dividing $1440 by 12, they budgeted $120 per month, so $360 for three months. If they spent $300, they were $60 under budget.
- by Ian Stewart
Wed Feb 12, 2020 5:27 am- Forum: Problem Solving
- Topic: A certain company has budgeted $1,440 for entertaiment expenses for the year, divided into 12...
- Replies: 2
- Views: 620
Re: In the figure to the right, is b > a?
I assume the picture is meant to display straight lines. The angles in a circle add to 360 degrees, so here 3a + 3b = 360, and a + b = 120. So if we know a, we can find b and certainly answer the question, so Statement 1 is sufficient. If a+b = 120 and a < 60, then b > 60 must be true, so from State...
- by Ian Stewart
Wed Feb 12, 2020 5:24 am- Forum: Data Sufficiency
- Topic: In the figure to the right, is b > a?
- Replies: 1
- Views: 470
On the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square. What are the coordinates of the
Problem Solving
Re: On the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square. What are the coordinates of
If you understand slopes well, you can answer the question without much algebra. Recall that perpendicular slopes are negative reciprocals. So if you travel, say, 5 units to the right and 2 units up along one line, then to travel the same distance along a perpendicular line, you would need to travel...
- by Ian Stewart
Tue Feb 11, 2020 1:43 pm- Forum: Problem Solving
- Topic: On the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square. What are the coordinates of the
- Replies: 2
- Views: 591
Re: Percent and Interest Problems
Samantha invests i1 dollars in bond X, which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y, which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y? 1) \((r1)^2 > (r2)^2\) 2) The ra...
- by Ian Stewart
Tue Feb 11, 2020 1:39 pm- Forum: Data Sufficiency
- Topic: Percent and Interest Problems
- Replies: 1
- Views: 544
Re: Is the standard deviation of set Q equal to 0?
Economist GMAT Is the standard deviation of set Q equal to 0? 1) The average (arithmetic mean) of set Q is equal to the greatest number in Q. 2) The mean of the set Q is equal to the greatest number in Q. OA A I don't understand the question. First, in math, a "set" cannot contain repeate...
- by Ian Stewart
Tue Feb 11, 2020 1:33 pm- Forum: Data Sufficiency
- Topic: Is the standard deviation of set Q equal to 0?
- Replies: 1
- Views: 595