Wednesday, August 5, 2009

Question of the day - 4th August, 2009

Question 1

If xyz ≠ 0, is x (y + z) ≥ 0?

(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|

Question 2

How many different prime factors does N have?

(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

Answers will be posted in 24 hrs. Check back for detailed explanation

Thanks,
Quant-Master
Posted by GMAT at 2:03 AM

8 comments:

  1. GMATAugust 5, 2009 at 10:56 PM

    Solution to Question 1:

    For x(y+z) to be greater than or equal to zero x should be +ve and y+Z should also be +ve or x should be -ve and y+z should also be -ve

    from statement 1 we can infer that y and z both are of same sign. Try different numbers if you are not sure

    from statement 2 we can infer that x and y both are of same sign. Try different numbers if you are not sure

    Hence x and y+z are of same sign. When you multiply to numbers of same sign you get an +ve number Hence C

    Thanks
    Quant-Master

    ReplyDelete
  2. GMATAugust 5, 2009 at 11:02 PM

    Solution to Question 2:

    This is best explained by example

    Statement 1:2N has 4 different prime factors.

    case i)Lets say the number N is 2*3*5*7 it has 4 different prime factors now 2N will be 2^2*3*5*7 still 4 different prime factors
    case ii) Lets say the Number N is 3*5*7, it has 3 different prime factors now 2N will be 2*3*5*7 which means now the prime factors have changed from 3 to 4.

    Hence from statement 1 it can be either 3 or 4 factors (insufficient)

    Statement 2: N ^2 has 4 different prime factors.

    After squaring a number N which has n prime factors will still have n prime factors only.
    Example N= 2*3*5*7
    N^2 = 2^2*3^2*5^2*7^2

    which still has 4 prime factors hence statement B alone is sufficient

    Hence B

    Thanks,
    Quant-Master

    ReplyDelete
  3. AnonymousAugust 6, 2009 at 5:22 AM

    It would be nice if you explain bit elaborately.

    Thanks

    ReplyDelete
  4. GMATAugust 6, 2009 at 12:02 PM

    Let me know to which question you need elaborate explanation.

    Thanks,
    Quant-Master

    ReplyDelete
  5. AnonymousAugust 8, 2009 at 12:31 AM

    Hi GMAT,

    I have been struggling with the concept of
    |x| - |y| gt or lt |x-y|
    I remember u mentioning some funda that for the above eqn to hold true |y| > |x| and x and y should be of the same sign.

    Can you take it up a little bit.

    ReplyDelete
  6. GMATAugust 8, 2009 at 11:07 PM

    @ anonymous

    Let's start from scratch

    |x| means no matter what the symbol of x be, by placing modulus(||)it becomes positive.

    (1) |y + z| = |y| + |z|

    Now in the RHS of the above eqn, by placing modulus to both y and z we have made them +ve (same sign).

    Now take LHS, either y and z should be +ve to equal with RHS or both should be -ve. If both are negative we can write LHS as |-(y+z)| and finally this will be nothing but |y+z| coz of modulus symbol.

    Let me know if you need further explanation.

    Thanks,
    Quant-Master

    ReplyDelete
  7. John PanellaAugust 15, 2009 at 5:08 PM

    Hi GMAT,

    So from your explanation can I assume that, y and z should have the same sign because otherwise, the values on LHS and RHS will not be the same?

    ReplyDelete
  8. GMATAugust 17, 2009 at 11:11 PM

    yes John. That's the only way to satisfy the equation

    Thanks,
    Quant-Master

    ReplyDelete

Subscribe to: Post Comments (Atom)