Manhattan GMAT Challenge Problem of the Week-27 Aug 2010

srinivasskc

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O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x.
Likewise , E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x.

According to these definitions, the value of O(3.2)+E(-1.7)+o(-1.3)+e(2.7) is:

A) 2
B) 3
C) 4
D) 5
E) 6
 
If n is a positive integer greater than 1, what is the smallest positive difference between two different factors of n?

(1) sqrt{n+1}/10 is a positive integer.

(2) n is a multiple of both 11 and 9.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone 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 to answer the question asked, and additional data are needed.


Give your answer with explanation.
 
Let a %u201C2-placer%u201D be a terminating decimal, between 0 and 1, for which the shortest possible representation has exactly 2 decimal places. For example, 0.09 and 0.87 are 2-placers, but 0.70 is not a 2-placer (because it can be written as 0.7, with only one decimal place). If m, n, and the product of m and n are each 2-placers, how many different values are possible for the sum m + n?

A) 40
B) 48
C) 60
D) 72
E) 197

Post answer with explanation.
 
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