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If \(x = 2t\) and \(y = \dfrac{t}3,\) what is the value of \(x^2 - y^2?\)

If \(x = 2t\) and \(y = \dfrac{t}3,\) what is the value of \(x^2 - y^2?\)

(1) \(t^2 - 3 = 6\)
(2) \(t^3 = -27\)

Answer: D

Source: Official Guide


\(S\) is the infinite sequence \(S_1 = 2, S_2 = 22, S_3 = 222,\ldots, S_k = S_{k-1} + 2(10k-1).\) If \(p\) is the sum of

\(S\) is the infinite sequence \(S_1 = 2, S_2 = 22, S_3 = 222,\ldots, S_k = S_{k-1} + 2(10k-1).\) If \(p\) is the sum of the first \(30\) terms of \(S,\) what is the eleventh digit of \(p,\) counting right to left from the units digit?

A) 1
B) 2
C) 4
D) 6
E) 9

Answer: C

Source: Manhattan GMAT


Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1,

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased? (1) Guy's gross income increased by 4 percent on January 1, 1989. (2) Guy's deductions increased by 15 percent on Ja...


If \(a, b,\) and \(c\) are nonzero numbers and \(a + b = c,\) which of the following is equal to \(1?\)

If \(a, b,\) and \(c\) are nonzero numbers and \(a + b = c,\) which of the following is equal to \(1?\)

(A) \(\dfrac{a - b}{c}\)

(B) \(\dfrac{a - c}{b}\)

(C) \(\dfrac{b - c}{a}\)

(D) \(\dfrac{b - a}{c}\)

(E) \(\dfrac{c - b}{a}\)

Answer: E

Source: Official Guide


If Jack’s and Kate’s annual salaries in 1985 were each 10 percent higher than their respective annual salaries in 1984,

If Jack’s and Kate’s annual salaries in 1985 were each 10 percent higher than their respective annual salaries in 1984, what was Jack’s annual salary in 1984? (1) The sum of Jack’s and Kate’s annual salaries in 1984 was $50,000. (2) The sum of Jack’s and Kate’s annual salaries in 1985 was $55,000. A...


The ratio of textbooks to novels to atlases in a certain classroom is 2 to 4 to 3. If there are no other books in the

The ratio of textbooks to novels to atlases in a certain classroom is 2 to 4 to 3. If there are no other books in the classroom, and if the teacher adds textbooks until novels make up 32% of the books present, which of the following could be the number of atlases in the room? A. 9 B. 16 C. 34 D. 51 ...


The table above shows the number of students in a certain high school class who are boys and the number of students in

2015-10-26_2106.png The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class? (1) Of the boys in the class, 15 are studying biology. (2) The number of ...


The sequence \(a_1, a_2, \ldots, a_n,\ldots\) is such that \(a_n=2a_{n-1}-x\) for all positive integers \(n \ge 2\) and

The sequence \(a_1, a_2, \ldots, a_n,\ldots\) is such that \(a_n=2a_{n-1}-x\) for all positive integers \(n \ge 2\) and for certain number \(x.\) If \(a_5=99\) and \(a_3=27,\) what is the value of \(x?\)

A. 3
B. 9
C. 18
D. 36
E. 45

Answer: A

Source: Official Guide


A parabola in the coordinate geometry plane is represented by the equation \(y = x^2 + k,\) where \(k\) is a constant

A parabola in the coordinate geometry plane is represented by the equation \(y = x^2 + k,\) where \(k\) is a constant greater than \(0.\) Line \(L\) intersects this parabola at exactly one point. Is this point of intersection in Quadrant \(I?\) (1) The slope of line \(L\) is positive. (2) \(x\) is g...


In a certain game, a large bag is filled with blue, green, purple, and red chips worth \(1, 5, x\) and \(11\) points eac

In a certain game, a large bag is filled with blue, green, purple, and red chips worth \(1, 5, x\) and \(11\) points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the ...


The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one

The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window seat. The view from the window seats in 5 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is a...


If \(m\) and \(n\) are positive integers and \(mn = k,\) is \(m + n = k + 1?\)

If \(m\) and \(n\) are positive integers and \(mn = k,\) is \(m + n = k + 1?\)

(1) \(m = 1\)

(2) \(k\) is a prime number.

Answer: D

Source: GMAT Prep


The temperature of a certain cup of coffee \(10\) minutes after it was poured was \(120\) degrees Fahrenheit. If the

The temperature of a certain cup of coffee \(10\) minutes after it was poured was \(120\) degrees Fahrenheit. If the temperature \(F\) of the coffee \(t\) minutes after it was poured can be determined by the formula \(F=120\cdot 2^{-at}+60,\) where \(F\) is in degrees Fahrenheit and a is a constant....


If \(x\) is positive, is \(x > 3 ?\)

If \(x\) is positive, is \(x > 3 ?\)

(1) \((x - 1)^2 > 4\)
(2) \((x - 2)^2 > 9\)

Answer: D

Source: GMAT Prep

by M7MBA

Tue Mar 23, 2021 7:56 am
Forum: Data Sufficiency
Topic: If \(x\) is positive, is \(x > 3 ?\)
Replies: 0
Views: 28

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter complete

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days. How many days would it have taken the second carpenter to do the complete job working alone? A) 4 2/3 B) 7 C) 9 D) 14 E) 24 Answer: D Source: GMAT Paper T...