Share
Question of the Day
If x is an integer, is x between 27 and 54?
(1) The remainder when x is divided by 7 is 2.
(2) The remainder when x is divided by 3 is 2.
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Write Down the Information Given
x is an integer.
Find the Real Information
x is not a decimal or fraction.
Question Asked
Is x between 27 and 54?
Find the Real Question
Is 27 < x < 54?
Translate the Statements
(1) This tells us that x is 2 more than a multiple of 7. Some of these numbers are in the range and others are not. Numbers in the range: 30, 37, 44, 51. Some numbers not in the range: 16, 23, 58.
Insufficient.
Eliminate A and D.
(2) This tells us x is 2 more than a multiple of 3. Thus, x could be any number that is 2 more than a multiple of 3 (some of which are in the range and some are not. Numbers in the range: 29, 32, 35, 38, 41, 44, 47, 50, 53. Some numbers not in the range: 23, 26, 56.
Insufficient.
Eliminate B.
(1) + (2) Since 23 and 44 (as well as other numbers) meet both the rules in (1) and in (2) the value of x cannot be determined to be in the given range.
Insufficient.
Eliminate C.
Choose E.
x is an integer.
Find the Real Information
x is not a decimal or fraction.
Question Asked
Is x between 27 and 54?
Find the Real Question
Is 27 < x < 54?
Translate the Statements
(1) This tells us that x is 2 more than a multiple of 7. Some of these numbers are in the range and others are not. Numbers in the range: 30, 37, 44, 51. Some numbers not in the range: 16, 23, 58.
Insufficient.
Eliminate A and D.
(2) This tells us x is 2 more than a multiple of 3. Thus, x could be any number that is 2 more than a multiple of 3 (some of which are in the range and some are not. Numbers in the range: 29, 32, 35, 38, 41, 44, 47, 50, 53. Some numbers not in the range: 23, 26, 56.
Insufficient.
Eliminate B.
(1) + (2) Since 23 and 44 (as well as other numbers) meet both the rules in (1) and in (2) the value of x cannot be determined to be in the given range.
Insufficient.
Eliminate C.
Choose E.