calispec wrote:
kwhitejr wrote:
Can you elaborate on the explanation for question #4?
This.
I don't really follow the brief explanations so far.
4. Is \(x^4+y^4>z^4\)? The best way to deal with this problem is plugging numbers. Remember on DS questions when plugging numbers,
goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.
(1) \(x^2+y^2>z^2\)
It's clear that we get YES answer very easily with big x and y (say 10 and 10), and small z (say 0).
For NO answer let's try numbers from Pythagorean triples:
\(x^2=3\), \(y^2=4\) and \(z^2=5\) (\(x^2+y^2=7>5=z^2\)) --> \(x^4+y^4=9+16=25=z^4\), so we have answer NO (\(x^4+y^4\) is NOT more than \(z^4\), it's equal to it).
Not sufficient.
(2) \(x+y>z\). This one is even easier: again we can get YES answer with big x and y, and small z.
As for NO try to make z some big enough negative number: so if \(x=y=1\) and \(z=-5\), then \(x^4+y^4=1+1=2<25=z^4\).
Not sufficient.
(1)+(2) As we concluded YES answer is easily achievable. For NO try the case of \(x^2=3\), \(y^2=4\) and \(z^2=5\) again: \(x+y=\sqrt{3}+\sqrt{4}>\sqrt{5}\) (\(\sqrt{3}+2\) is more than 3 and \(\sqrt{5}\) is less than 3), so statement (2) is satisfied, we know that statement (1) is also satisfied (\(x^2+y^2=7>5=z^2\)) and \(x^4+y^4=9+16=25=z^4\). Not sufficient.
Answer: E.
pankajattri wrote:
2. Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.
Answer should be C.
(1) Any two angles can be 90 degrees so Insuff.
(2) No Information about angles DAB and CDA are gien so Insff.
Two adjecent angles can not be 90 otherwise the other two will also be 90 in which case either of ABC or BCD = 180 (not a corner but a straight line). This implies that either ABC or BCD has to be 90. Again ABC can not be 90 otherwise BCD = 2(ABC) = 180 (a straight line). S0 there is only one possible situation where BAD = BCD = 90, which implies ABC = 1/2 (BCD) = 45 and ADC = 360 - (90+90+45) = 135.
OA for this question is E, not C. Also: The degree measure of angle
ABC is twice the degree measure of angle BCD, not vise-versa as you've used in your calculations.
Consider following cases:
90(DAB)+90(ABC)+45(BCD)+135(ADC) - answer NO;
90(DAB)+120(ABC)+60(BCD)+90(ADC) - answer YES.
Two different answers, hence not sufficient.
Answer: E.
Hope it's clear.