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Need help on the following sets of problems


noob123

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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

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