Here’s and example of a SMART MATH problem for GEOMETRY.
Problem
The figure ABCD is a parallelogram. Find the perimeter of ABCD.
AB =
BC =
DC =
AD =
- 22
- 48
- 53
- 59
- 32
The Usual Method
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Since ABCD is a parallelogram, AB = DC and AD = BC.
=
and
=
and
Solving these two equations simultaneously, we get:
x = 3.5 and y = 2
Hence, AB = DC = 2(3.5) + 2(2) + 7 = 18 and,
AD = BC = 3.5 + 4(2) = 11.5
Hence, total perimeter = 2 (18 + 11.5) = 59
(Ans: 4)
Estimated Time to arrive at the answer = 75 seconds.
Using Technique
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The perimeter of parallelogram ABCD = sum of length of all sides
= +
+
+
=
Now, from the options, just subtract 14. This will give us the value of , which is a multiple of 5
.
Hence, that option which is a multiple of 5 after subtracting 14 from it should be the answer.
22 – 14 = 8 (Not a multiple of 5 and so it is not the correct answer)
48 – 14 = 34 (Not a multiple of 5 and so it is not the correct answer)
53 – 14 = 39 (Not a multiple of 5 and so it is not the correct answer)
59 – 14 = 45 (Is a multiple of 5 and so it is the correct answer)
32 – 14 = 18 (Not a multiple of 5 and so it is not the correct answer)
(Ans: 4)
Estimated Time to arrive at the answer = 15 seconds.
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