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\(M\) is a positive two-digit number. When the digits are reversed, the number is \(N.\) If \(K = M + N,\) which of the

\(M\) is a positive two-digit number. When the digits are reversed, the number is \(N.\) If \(K = M + N,\) which of the following is true? A. \(K\) must be even. B. \(K\) cannot be square. C. \(K\) cannot be divisible by \(13.\) D. \(K\) must be divisible by \(11.\) E. If \(M\) is even then \(K\) mu...


In triangle \(ABC\) above, what is the length of side \(BC?\)

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In triangle \(ABC\) above, what is the length of side \(BC?\)

(1) Line segment \(AD\) has length \(6.\)
(2) \(x = 36\)

Answer: A

Source: Official Guide

by Vincen

Sat Nov 27, 2021 4:48 am
Forum: Data Sufficiency
Topic: In triangle \(ABC\) above, what is the length of side \(BC?\)
Replies: 1
Views: 36

Let \(S\) be the set of permutations of the sequence \(2, 3, 4, 5, 6\) for which the first term is not \(2.\) A permutat

Let \(S\) be the set of permutations of the sequence \(2, 3, 4, 5, 6\) for which the first term is not \(2.\) A permutation is chosen randomly from \(S.\) The probability that the second term is \(5\) is given by \(\dfrac{a}{b}\) (in lowest terms). What is \(a+b?\) (A) 5 (B) 6 (C) 11 (D) 16 (E) 19 A...


If \(a\) and \(b\) are positive numbers, what are the coordinates of the midpoint of line segment \(CD\) in the \(xy\)-p

If \(a\) and \(b\) are positive numbers, what are the coordinates of the midpoint of line segment \(CD\) in the \(xy\)-plane?

(1) The coordinates of \(C\) are \((a, 1-b)\)
(2) The coordinates of \(D\) are \((1-a, b)\)

Answer: C

Source: GMAT Prep


How many factors of the number \(2^4 \cdot 3\cdot 5^2\) are even?

How many factors of the number \(2^4 \cdot 3\cdot 5^2\) are even?

A) 10
B) 12
C) 16
D) 18
E) 24

Answer: E

Source: e-GMAT


A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners

A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid \(\$12\) more than he or she would have if all diners had contributed eq...


The hypotenuse of an isosceles right triangle has a length of \(h,\) and the triangle has an area of \(a.\) Which of the

The hypotenuse of an isosceles right triangle has a length of \(h,\) and the triangle has an area of \(a.\) Which of the following must be true?

A) \(a=4h^2\)

B) \(a=2h^2\)

C) \(a=h^2\)

D) \(4a=h^2\)

E) \(2a=h^2\)

Answer: D

Source: Princeton Review


At a certain bakery, each roll costs \(r\) cents, and each doughnut costs \(d\) cents. If Alfredo bought rolls and dough

At a certain bakery, each roll costs \(r\) cents, and each doughnut costs \(d\) cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll? (1) Alfredo paid \(\$5.00\) for \(8\) rolls and \(6\) doughnuts. (2) Alfredo would have paid \(\$ 10.00\) if he had bou...


If \(a\) and \(b\) are integers such that \(a > b > 1,\) which of the following cannot be a multiple of either \(a\) or

If \(a\) and \(b\) are integers such that \(a > b > 1,\) which of the following cannot be a multiple of either \(a\) or \(b?\)

(A) \(a - 1\)
(B) \(b + 1\)
(C) \(b - 1\)
(D) \(a + b\)
(E) \(ab\)

Answer: C

Source: Manhattan GMAT


The value of a rare baseball card \(A\) appreciated by \(20\) percent over a five-year period; over the next five years,

The value of a rare baseball card \(A\) appreciated by \(20\) percent over a five-year period; over the next five years, the value plummeted by \(50\) percent. Over the same total time period, the value of another card \(B\) increased by \(100\%.\) At the end of ten years, the reduced value of \(A\)...


\(s(n)\) is a \(n\)-digit number formed by attaching the first \(n\) perfect squares, in order, into one integer.

\(s(n)\) is a \(n\)-digit number formed by attaching the first \(n\) perfect squares, in order, into one integer. For example, \(s(1) = 1, \, s(2) = 14, \, s(3) = 149, \, s(4) = 14916, \, s(5) = 1491625,\) etc. How many digits are in \(s(99)?\) A. 350 B. 353 C. 354 D. 356 E. 357 Answer: B Source: Ve...


Susan and Iman are each typing a term paper. Who finishes first?

Susan and Iman are each typing a term paper. Who finishes first?

(1) Susan begins typing at 9 a.m. and finishes at 5 p.m.
(2) Iman finishes typing 6 hours after she starts.

Answer: E

Source: Princeton Review


In a certain boys camp, \(20\%\) of the total boys are from school \(A\) and \(30\%\) of those study science. If there

In a certain boys camp, \(20\%\) of the total boys are from school \(A\) and \(30\%\) of those study science. If there are \(49\) boys in the camp that are from school \(A\) but do not study science then what is the total number of boys in the camp? A. 70 B. 245 C. 150 D. 35 E. 350 Answer: E Source:...


In the first hour of a bake sale, students sold either chocolate chip cookies, which sold for \(\$1.30,\) or brownies,

In the first hour of a bake sale, students sold either chocolate chip cookies, which sold for \(\$1.30,\) or brownies, which sold for \(\$1.50.\) What was the ratio of chocolate chip cookies sold to brownies sold during the first hour of the bake sale? (1) The average price for the items sold during...


A \(2\)-year certificate of deposit is purchased for \(k\) dollars. If the certificate earns interest at an annual rate

A \(2\)-year certificate of deposit is purchased for \(k\) dollars. If the certificate earns interest at an annual rate of \(6\) percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of \(2\) years? A. \(k(1.06)^2\) B. \(k(1.06)^8\) C. \(k...