Multiple Choice Questions

[sarasoleja]

I have a few multiple choice questions that have truly puzzled me:

Q1: If |x|<0.5 , (4-8x)^(-1/2)=

A. 1/2 (1+x+3x^2/2+....)
B. 1/2 (1-x+3x^2/2+....)
C. 1/2 (1+x-3x^2/2+....)
D. 2 (1+x+3x^2/2+....)
E. 1/2(1+x+3x^2/2)

The correct answer is A, how and why?

Q2: Consider the triangle of numbers below:

1
1 1 1
1 2 3 2 1
1 3 x 7 x 3 1
1 4 10 16 Y 16 10 4 1

X and Y equal
A. 10 and 32
B. 5 and 19
C. 6 and 13
D. 4 and 19
E. 6 and 19

The correct answer is E, how and why?

I would appreciate anything! I'm pretty desperate right now.

 

[soroban]

Hello, sarasoleja!

Q2: Consider the triangle of numbers below:


. . \(\displaystyle \begin{array}{ccccccccccc}R_1 & . & . & . & . & 1 & . & . & . & . \\ R_2 & . & . & . & 1 & 1 & 1 & . & . & . \\ R_3 & . & . & 1 & 2 & 3 & 2 & 1 & . & . \\ R_4 & . & 1 & 3 & x & 7 & x & 3 & 1 & . \\ R_5 & 1 & 4 & 10 & 16 & y & 16 & 10 & 4 & 1 \end{array}\)

\(\displaystyle \text{Find }x\text{ and }y.\)

. . \(\displaystyle (A)\;10,\:32 \qquad (B)\;5,\:19 \qquad (C)\;6,\:13 \qquad (D)\; 4,\:19 \qquad (E)\;6,\:19\)

The correct answer is (E) . . . How and why?

\(\displaystyle \text{Each number is the sum of three numbers above it in the preceding row.}\)


\(\displaystyle \text{In }R_2\text{ and }R_3,\text{ we have:}\)

. . \(\displaystyle \begin{array}{c}\underbrace{ .\;.\;1}1\;1\;.\;, \\ 1\;2\;3\;2\;1 \end{array} \qquad \begin{array}{c}.\;\underbrace{.\;1\;1}1\;,\;, \\ \;1 \; 2\; 3\; 2 \;1 \end{array} \qquad \begin{array}{c} . \; . \; \underbrace{1 \; 1 \; 1} . \; . \\ 1 \; 2 \; 3 \; 2 \; 1 \end{array}\)


\(\displaystyle \text{Hence, in }R_3\text{ and }R_4,\text{ we have:}\)

. . \(\displaystyle \begin{array}{ccccccc} . \; \underbrace{1 \; 2 \; 3} \; 2 \; 1 \; . \\ 1 \; 3 \; x \; 7 \; x \; 3 \; 1 \end{array}\)

\(\displaystyle \text{Therefore: }\:\boxed{x \:=\:6}\)


\(\displaystyle \text{Then in }R_4\text{ and }R_5,\text{ we have:}\)

. . \(\displaystyle \begin{array}{c} . \:\; 1 \;\; 3 \;\; \underbrace{6 \;\; 7 \;\; 6} \;\; 3 \;\; 1 \; . \\ 1 \; 4 \; 10 \; 16 \; y \; 16 \;10\; 4 \; 1 \end{array}\)

\(\displaystyle \text{Therefore: }\:\boxed{y \:=\:19}\)

 

[Deleted member 4993]

I have a few multiple choice questions that have truly puzzled me:

Q1: If |x|<0.5 , (4-8x)^(-1/2)=

A. 1/2 (1+x+3x^2/2+....)
B. 1/2 (1-x+3x^2/2+....)
C. 1/2 (1+x-3x^2/2+....)
D. 2 (1+x+3x^2/2+....)
E. 1/2(1+x+3x^2/2)

The correct answer is A, how and why?

Have done any calculus - like Taylor's series expansion of (a+x)[sup:1vt7ifvo]n[/sup:1vt7ifvo] ?

Q2: Consider the triangle of numbers below:

1
1 1 1
1 2 3 2 1
1 3 x 7 x 3 1
1 4 10 16 Y 16 10 4 1

X and Y equal
A. 10 and 32
B. 5 and 19
C. 6 and 13
D. 4 and 19
E. 6 and 19

The correct answer is E, how and why?

I would appreciate anything! I'm pretty desperate right now.