<p>Grid In: </p>
<p>What is the greatest of 5 consecutive integers if the sum of these integers equals 185? </p>
<p>MC: </p>
<p>How many positive three-digit integers have the hundreds digit equal to 3 and the units digit (ones digit) equal to 4? </p>
<p>A) 10
B) 19
C) 20
D) 190
E) 200 </p>
<p>Can someone explain these to me? I always have trouble with problems like these!</p>
<p>Grid In:
Let’s say x is the first of the 5 consecutive integers. Notice that they add up to 185. The expression would be:
x + x+1 + x+2 + x+3 + x+4 = 185
5x+10 = 185
5x = 175
x = 35
Now, reread what the question is looking for. The greatest of these integers is x+4.
35+ 4 = 39</p>
<p>MC:
A)
The 10 are:
304, 314, 324, 334, 354, 364, 374, 384, and 394</p>
<p>Someone please correct me if I’m wrong.</p>
<p>u r correct there are 10. only 10 digits that can go into the tens place.</p>
<p>newaccount, you’re right but you forgot to write 344 in your list.</p>
<p>Oops haha.</p>
<p>
</p>
<p>The average of these 5 integers is just 185/5 = 37. There will be two integers greater than 37 in the set, and two integers less than 37. Hence the set is {35, 36, 37, 38, 39} and your answer is 39.</p>
<p>
</p>
<p>Any three digit integer can be represented by</p>
<hr>
<p>each blank representing a place</p>
<p>There is only one possibility for the hundreds digit (3), and only one possibility for the ones digit (4). There are 10 possibilities for the tens digit (0-9). Hence there are a total of</p>
<p>1 x 10 x 1 = 10 positive three digit integers fulfilling the previous conditions.</p>