标题: GMAT 数学题（16） [打印本页] 作者: sdcar2010 时间: 2011-2-13 03:45 标题: GMAT 数学题（16） 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作者: kazemi 时间: 2011-2-13 04:30
推算过程太长，我应该不会算，直接从五个答案中按从大到小顺序代入验证作者: sdcar2010 时间: 2011-2-14 06:59
推算过程太长，我应该不会算，直接从五个答案中按从大到小顺序代入验证
-- by 会员 kazemi (2011/2/13 4:30:45)
All right. Here are the five choices:
A) 45 B) 55 C) 66 D) 78 E) 91作者: zoechancruz 时间: 2011-2-14 07:40
答案选B么作者: kazemi 时间: 2011-2-14 08:39
提示，看从E到A这些数*2都有哪些因子作者: sdcar2010 时间: 2011-2-14 11:17
答案选B么
-- by 会员 zoechancruz (2011/2/14 7:40:01)
Hmmmm.
45+55 = 100 does look convenient as an answer choice. But that would be too easy.作者: kazemi 时间: 2011-2-14 11:50
Don't know what you're saying here...
I can tell 91*2=13*14作者: sdcar2010 时间: 2011-2-14 11:56
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.作者: kazemi 时间: 2011-2-14 12:08
I thought u were on the wrong direction...作者: sdcar2010 时间: 2011-2-14 12:15
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作者: lpchen0613 时间: 2011-2-14 15:40
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，仅供参考参考作者: sdcar2010 时间: 2011-2-14 21:30
LS is right. The answer is E, 91.作者: sdcar2010 时间: 2011-2-14 21:37
The key is to realize that the sum of any consecutive A(n) and A(n+1) is a square 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.