Question

几道GMAT的数学题，求高人的解答！（要有详细的思路和题目的翻译即可）

1、If （10的50次方减去74）is written as an integer in base 10 notation,what is the sum of the digits in that integer?
A、424 B、433 C、440 D、449 E、467

2、What is the median number of employees assigned per project for the projects at Company Z?
(1)25 percent of the projects at Company Z have 4 or more employees assigned to each project
(2)35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
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、Statement (1) and (2) TOGETHER are NOT sufficient

Answer 1

1. 10⁵⁰ as an integer in base 10 notation is 1 followed by 50 zeros. Substracting 74 from it, you get a number starting with 48 nines followed by 26, so the sum of all the digits is 48*9 + 2 + 6 = 440, The answer is D.

2. So 25% projects have 4 or more employees assigned to each, and 35% with 2 or fewer assigned to each. The rest of (1 - 35% - 25%) = 40%, including the 50% point, must have exactly 3 employees assigned to it, The median number of employees assigned per project is 3.

Statement (1) is not enough, since it's possible that the rest 75% of projects all have 2 or fewer employees assigned per project.

Statement (2) is not enough, since it's possible that the rest 65% of projects all have 4 or more employees assigned per project.

So the answer is C.

Answer 2

10的50次方就是1后面50个0 ，减去74，最后两位是26，前面有48个9,所以和就是48*9+6+2=440