## Search found 2276 matches

#### Find the number of integer solutions to $$|a| + |b| + |c| = 10,$$ where none of $$a, b$$ or $$c$$ is $$0.$$

##### Find the number of integer solutions to $$|a| + |b| + |c| = 10,$$ where none of $$a, b$$ or $$c$$ is $$0.$$

Find the number of integer solutions to $$|a| + |b| + |c| = 10,$$ where none of $$a, b$$ or $$c$$ is $$0.$$

A. 36

B. 72

C. 144

D. 288

E. 576

Source: e-GMAT

#### A certain list, $$L,$$ contains a total of $$n$$ numbers, not necessarily distinct, that are arranged in increasing orde

##### A certain list, $$L,$$ contains a total of $$n$$ numbers, not necessarily distinct, that are arranged in increasing orde

A certain list, $$L,$$ contains a total of $$n$$ numbers, not necessarily distinct, that are arranged in increasing order. If $$L_1$$ is the list consisting of the first $$n_1$$ numbers in $$L$$ and $$L_2$$ is the list consisting of the last $$n_2$$ numbers in $$L,$$ is $$17$$ a mode for $$L?$$ (1) ...

#### Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 per ###### Problem Solving ##### Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 per

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350 (B...

#### If $$x, y,$$ and $$n$$ are positive integers, is $$\left(\dfrac{x}{y}\right)^n$$ greater than $$1,000 ?$$

##### If $$x, y,$$ and $$n$$ are positive integers, is $$\left(\dfrac{x}{y}\right)^n$$ greater than $$1,000 ?$$

If $$x, y,$$ and $$n$$ are positive integers, is $$\left(\dfrac{x}{y}\right)^n$$ greater than $$1,000 ?$$

(1) $$x=y^3$$ and $$n>y.$$

(2) $$x>5y$$ and $$n>x.$$

Source: GMAT Paper Tests

#### Mixture $$A$$ is $$20$$ percent alcohol, and mixture $$B$$ is $$50$$ percent alcohol. If the two are poured together to

##### Mixture $$A$$ is $$20$$ percent alcohol, and mixture $$B$$ is $$50$$ percent alcohol. If the two are poured together to

Mixture $$A$$ is $$20$$ percent alcohol, and mixture $$B$$ is $$50$$ percent alcohol. If the two are poured together to create a $$15$$-gallon mixture that contains $$30$$ percent alcohol, approximately how many gallons of mixture $$A$$ are in the mixture? (A) 3 gallons (B) 4 gallons (C) 5 gallons (...

#### The research funds of a certain company were divided among three departments, $$X, Y,$$ and $$Z.$$ Which one of the

##### The research funds of a certain company were divided among three departments, $$X, Y,$$ and $$Z.$$ Which one of the

The research funds of a certain company were divided among three departments, $$X, Y,$$ and $$Z.$$ Which one of the three departments received the greatest proportion of the research funds? (1) The research funds received by departments $$X$$ and $$Y$$ were in the ratio $$3$$ to $$5,$$ respectively....

#### When positive integer $$n$$ is divided by $$3,$$ the remainder is $$2.$$ When $$n$$ is divided by $$7,$$ the remainder

##### When positive integer $$n$$ is divided by $$3,$$ the remainder is $$2.$$ When $$n$$ is divided by $$7,$$ the remainder

When positive integer $$n$$ is divided by $$3,$$ the remainder is $$2.$$ When $$n$$ is divided by $$7,$$ the remainder is $$5.$$ How many values less than $$100$$ can $$n$$ take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5

Source: Veritas Prep

#### If $$ab \ne 0$$ and $$a + b \ne 0,$$ is $$\dfrac1{a+b}< \dfrac1{a} + \dfrac1{b} ?$$

##### If $$ab \ne 0$$ and $$a + b \ne 0,$$ is $$\dfrac1{a+b}< \dfrac1{a} + \dfrac1{b} ?$$

If $$ab \ne 0$$ and $$a + b \ne 0,$$ is $$\dfrac1{a+b}< \dfrac1{a} + \dfrac1{b} ?$$

(1) $$|a| + |b| = a + b$$

(2) $$a > b$$

Source: Manhattan GMAT

#### In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was

##### In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was

In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was $$\dfrac35.$$ After $$600$$ additional Republicans and $$500$$ additional Democrats registered, the ratio was $$\dfrac45.$$ After these registrations, there were how many more voters in...

#### The function $$f$$ is defined for all positive integers $$n > 4$$ as $$f(n) = 3n - 9$$ if $$n$$ is odd and

##### The function $$f$$ is defined for all positive integers $$n > 4$$ as $$f(n) = 3n - 9$$ if $$n$$ is odd and

The function $$f$$ is defined for all positive integers $$n > 4$$ as $$f(n) = 3n - 9$$ if $$n$$ is odd and $$f(n) = 2n - 7$$ if $$n$$ is even. What is the value of the positive integer $$a?$$

(1) $$f(f(a)) = a$$

(2) $$f(f(f(a)))$$ is odd.

Source: Manhattan GMAT

A $$5$$-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than $$1$$ if the original wire was cut at an arbitrary point? A) $$\dfrac16$$ B) $$\dfrac15$$ C) $$\dfrac3{10}$$ D) $$\d... #### If \(x,$$ $$y,$$ and $$z$$ are integers, with $$x<y<z,$$ what is the average (arithmetic mean) of $$x, y,$$ and $$z?$$

##### If $$x,$$ $$y,$$ and $$z$$ are integers, with $$x<y<z,$$ what is the average (arithmetic mean) of $$x, y,$$ and $$z?$$

If $$x,$$ $$y,$$ and $$z$$ are integers, with $$x<y<z,$$ what is the average (arithmetic mean) of $$x, y,$$ and $$z?$$

(1) $$(x+y)z=5$$

(2) $$x+z<3$$

Source: Manhattan GMAT

#### How many roots does the equation $$\sqrt{x^2+1}+\sqrt{x^2+2}=2$$ have?

##### How many roots does the equation $$\sqrt{x^2+1}+\sqrt{x^2+2}=2$$ have?

How many roots does the equation $$\sqrt{x^2+1}+\sqrt{x^2+2}=2$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4

Source: GMAT Club Tests

by VJesus12

Wed Feb 23, 2022 4:09 am
Forum: Problem Solving
Topic: How many roots does the equation $$\sqrt{x^2+1}+\sqrt{x^2+2}=2$$ have?
Replies: 1
Views: 214

#### In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic

##### In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic

In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence $$a, b, c, d, e,$$ each term after the first is the sum of the preceding term and the constant $$k.$$ Which of the following is NOT an arithmetic sequence? A. \(a, b - 1,...

#### At the beginning of last month, a stationery store had in stock 250 writing pads, which had cost the store $0.75 each. ###### Data Sufficiency ##### At the beginning of last month, a stationery store had in stock 250 writing pads, which had cost the store$0.75 each.

At the beginning of last month, a stationery store had in stock 250 writing pads, which had cost the store \$0.75 each. During the same month, the store made only one purchase of writing pads. What was the total amount spent by the store on the writing pads it had in stock at the end of the month? (1...