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- For which of the following expressions is it true that the value of the expression is the same for x = 37 as for x = -37? Select all that apply.

- |1 – x|
^{2} - 1 – x
^{2} - (1 – x)
^{2 } -
x
^{2}/ ∣x∣^{2}

Answer: B, D

Let’s consider each option.

A: don’t be fooled by the modulus(absolute value) sign. In this case, 1- x will be very different depending on x = -37 or 37.

B: x^{2} will be the same irrespective of x = -37 or 37 so 1- x^{2} will also be the same. SELECT

C: 1- x will be very different depending on x = -37 or 37, and so will (1 – x)^{2}

D: x^{2} = |x|^{2} substitute any small values to check. SELECT

- The operation ⊕ is defined by the equation x⊕y = (x−y) / (3x−y) . What is the value of (-2⊕2) – (2⊕-2)?

Answer: 0

-2⊕2 = (-2-2)/(-6 -2) = -4/-8 = 0.5

2⊕-2 = (2+2)/(6+2) = 4/8 = 0.5

Difference is 0

- If a sequence of 10 consecutive odd integers with increasing values has 9 as its 9th term, what is the sum of the terms of the sequence?

- 20
- 22
- 28
- 32
- 40

Answer: A

Solution: Don’t jump to arithmetic progression formulae

If the first number in the series was 1, then the series would have progressed as 1, 3, 5, 7, 9

9 would be the 5^{th} term. But 9 is the 9^{th} term so the series must have started with the previous 4 odd numbers

-7, -5, -3, -1, 1, 3, 5, 7, 9, 11

Upon addition the positive and negative terms cancel out and we are left with 9+ 11 = 20

- If p = r/2, q = 3r/4, s = pq/r
^{2}, and t = (p+q) / (1+s) what is t in terms of r

- 9r/10
- 10r/11
- 5r/2
- 10r/3
- 55r/32

Answer: B

s = (r/2 x 3r/4)/r^{2} = (3r^{2}/8)/r^{2} = 3r^{2}/8r^{2} = 3/8

p+q = r/2 + 3r/4 = 5r/4

t = (5r/4)/(1+3/8) = (5r/4)/(11/8) = 40r/44 = 10r/11

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- 3a + 5
- 3a – 9
- 3a + 10
- 3a – 4
- 3a + 4

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