Hi,
I have doubt in the following problems, help would be appreciated :)
1) In the following problem (Princeton 1014 - Integer Properties),
If | x^2 * y | = | (-w) * z |, then which of the following could be true ?
Indicate all possible values
A) x^2 = wz
B) | x^2 * y| = | (-w) * z |
C) - (wz) = wz
D) | - x^2 | = | (-w) * z |
E) - w = z
F) x^2 = - | y |
Ans) A,C,D,E
My doubt is,
Answer choice "B" is an valid answer right ? (The book says A,C,D,E)
Suppose I consider X=1, Y=1, Z=1, W=1
which satisfies the main condition | x^2 * y | = | (-w) * z | => 1 = 1
Plugging those values into answer choice "B" we get,
| 1 * 1 | = | (-1) * 1 |
1 =1
2) If (x-y)^3 > (x-y)^2, then which one of the following must be true ?
A) x^3
B) x^5
C) x^3 > y^2
D) x^5 > y^4
E) x^3 > y^3
Soln: Since the value (x-y) is a square, we can divide by (x-y)^2 throughout
=> x-y > 1
x>1+y
x is greater than y - so the answer must be either option C or D, the book says E (can someone please explain how?)
3) a,b,c are multiples of 15 and a
Quantity A: Remainder when b is divided by c
Quantity B: Remainder when (b+c) is divided by a
Case 1 : 15
Quantity A : 45 R
Quantity B : 0 R
Case 2 : 15
Quantity A : 60 R
Quantity B : 0 R
Clearly A is greater (which is the answer given in the book)
But what if we consider,
a
a = - 45
b = - 30
c = - 15
Quantity A : 0 R
Quantity B : 0 R
hence ©
and the final answer (D). Is it the right way of going about ?
Thanks
-noob
