GMAT 数学题（16）

sdcar2010

There are a group of triangular numbers.  If A(n) is the nth number of this group, then A(n) = (n*(n+1))/2. n is an integer bigger than 0.

There are a group of square numbers.  If Bn is the nth number of this group, then B(n) = n^2. n is an integer bigger than 0.

If A(n) + A(m) = B(p) while both A(n) and A(m) are smaller than 100, what is the the largest possible value for A(n)? Why?

A) 45
B) 55
C) 66
D) 78
E) 91

sdcar2010

弱弱问一句，什么叫triangular numbers ？

-- by 会员 neverlandlin (2011/2/14 21:50:00)

http://en.wikipedia.org/wiki/Triangular_number

A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The nth triangle number is the number of dots in a triangle with n dots on a side.
A triangle number is, equivalently, the sum of the nnatural numbers from 1 to n.

neverlandlin

弱弱问一句，什么叫triangular numbers ？

sdcar2010

The key is to realize that the sum of any consecutive A(n) and A(n+1) is a square number!!!

55+66 = 121
66+78 = 144
78+91 = 169
...

sdcar2010

LS is right.  The answer is E, 91.

lpchen0613

答案选E，2A(n)=13*（13+1）， 所以A(n)=91，
        2 A(m)=12*（12+1）所以 A(m)=78
               B(p)=13^2=169
               A(n)+A(m)=91+78=169= B(p)
   这样对吧，自己做的，大家看看，仅供参考参考

sdcar2010

Another way to describe this problem is:

The sum of two triangular numbers is a square number.  What is the biggest possible value for the triangular number smaller than 100?

A) 45
B) 55
C) 66
D) 78
E) 91

kazemi

I thought u were on the wrong direction...

sdcar2010

A(n) and A(m) is from:
A) 45
B) 55
C) 66
D) 78
E) 91

B(p) is from 100, 121, 144, etc.

A(n) + A(m) = B(p)

What is the biggest possible A(n)?

45 +55 =100 fulfills the requirement of the equation.  But 55 is not the biggest possible answer.

kazemi

Don't know what you're saying here...

I can tell 91*2=13*14