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In the figure above, points A, B, C, and D are collinear and are semicircles with diameters d1 cm, d2 cm, and d3 cm, respective
In the figure above, points A, B, C, and D are collinear and are semicircles with diameters d1 cm, d2 cm, and d3 cm, respective
admin
2022-10-18
91
问题
In the figure above, points A, B, C, and D are collinear and
are semicircles with diameters d
1
cm, d
2
cm, and d
3
cm, respectively. What is the sum of the lengths of
, in centimeters?
(1) d
1
:d
2
:d
3
is 3:2:1.
(2) The length of AD is 48 cm.
选项
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.
答案
B
解析
Since the circumference of a semicircle is π(diameter/2), it follows that
has length π(d
1
/2)cm,
has length π(d
2
/2)cm, and
has length π(d
3
/2) cm. Therefore, the sum of the lengths, in centimeters, of
. is π(d
1
/2)+π(d
2
/2)+π(d
3
/2)=(π/2)(d
1
/2+d
2
/2+d
3
/2)
Determine the value of(π/2)(d
1
/2+d
2
/2+d
3
/2)
(1) Given that d
1
:d
2
:d
3
is 3:2:1, it is not possible to determine the value of (π/2)(d
1
/2+d
2
/2+d
3
/2) because d
1
, d
2
, and d
3
could be 3,2, and 1 (d
1
+ d
1
+ d
1
= 6) or d
1
, d
1
, and d
1
could be 6, 4, and 2 (d
1
+ d
2
+ d
3
= 12); NOT sufficient.
(2) Given that AD = 48 and AD = d
1
+ d
1
+ d
1
, it follows that = (π/2)(d
1
/2+d
2
/2+d
3
/2)=(π/2)(48); SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
转载请注明原文地址:https://kaotiyun.com/show/yttO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
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