Question 15 :
Two sides of a right triangle are 3 and 4. The third side is
(A) 1 (B) 3 (C) 5 (D) 7 (E) not uniquely determined
Solution :
In a right triangle, the square of hypotenuse side is equal to the sum of the squares of other two sides.
Third side = √3^{2} + 4^{2}
= √(9 + 16)
= √25
= 5
Hence the answer is 5.
Question 16 :
A cube 3 by 3 by 3 is painted red on all six faces and then cut into 27 smaller 1 by 1 by 1 cubes. How many of these new smaller cubes have exactly two faces that are painted red?
(A) 6 (B) 8 (C) 12 (D) 21 (E) 27
Solution :
Like this we may find 12 cubes under the given condition.
Question 17 :
If 2 blobs = 3 glops and 3 blobs = 2 chunks, then 1 chunk =
(A) 1 glop (B) 2/3 glop (C) 3/2 glops
(D) 4/9 glop (E) 9/4 glops
Solution :
Given that :
2 blobs = 3 glops ----(1)
3 blobs = 2 chunks ----(2)
1 glap = (2/3) blobs
1 blob = 2/3 chunks
2/3 chunks = (2/3) blobs
1 chunk = 1 blob
Hence 1 blob is the answer.
(18) and (19) The two pie charts show the ice cream flavor preferences of the students at two high schools.
Question 18 :
The ratio of Montague students who prefer vanilla to Montague students who prefer chocolate is
(A) 10:9 (B) 4:3 (C) 3:10 (D) 3:4 (E) 2:5
Solution :
Percentage of students who prefer Vanilla flavor
= 40%
Percentage of students who prefer chocolate flavor
= 30%
= 40 : 30
= 4 : 3
The the answer is 4 : 3.
Question 19 :
If the number of Montague students who prefer vanilla is M and the number of Capulet students who prefer vanilla is C, then
(A) M > 2C (B) M = 2C (C) M = C (D) M < C
(E) The relationship cannot be determined from the given information
Solution :
In Montague high, percentage of students who prefer Vanilla flavor (M) = 40%
In Capulet high, percentage of students who prefer Vanilla flavor (C) = 20%
Hence the required relationship is M = 2C.
Question 20 :
If x is an integer, which one of the following must be odd?
(A) 3x + 1 (B) 3x + 2 (C) 4x - 1
(D) 4x - 2 (E) 5x – 2x
Solution :
Since x is an integer, it may be odd or even.By multiplying odd or even number by 4, we get even number and by subtracting even number by 1, we get odd integer.
Hence 4x - 1 is the correct answer.
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