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Thread: Exponent Question Cannot Answer for my life

  1. #1
    Eager! gmat78854p just joined TestMagic.
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    Exponent Question Cannot Answer for my life

    I have seen other people post this same question and I also came across it. I cannot understand it for the life of me the way that people have explained it. My eyes are going blurry looking at it. I figure I should ask one of the gurus to break it down verbally and numerically. Heres the question.

    2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
    a.9

    b.11
    c.13
    d.15
    e.17


    Thank you so much

  2. #2
    Trying to make mom and pop proud azhiker just joined TestMagic.
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    Q If 2^x – 2 ^(x-2) = 3*2^13, what is x?
    a.9
    b.11

    c.13
    d.15
    e.17

    Answer:
    1. 2^x – 2 ^(x-2) = 3*2^13
    2. 2^x – 2 ^x/2^2 = 3*2^13
    3. 2^2*2^x/2^2 - 2^x/2^2 =3*2^13
    4. 2^2*2^x - 2^x =3*2^13*2^2
    5. 4*2^x - 2^x=3*2^15
    6. 3*2^x=3*2^15
    Comparing the LHS and RHS it is obvious that x=15.
    Answer is D.

  3. #3
    Eager! gmat78854p just joined TestMagic.
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    Thank you

    but can you please verbalise it. I cannot understand why or how you are doing what you are doing starting with step 3. Why aye tou able to multiply 2^2*2^x/2^2?

  4. #4
    Trying to make mom and pop proud dmact just joined TestMagic.
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    2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
    a.9
    b.11

    c.13
    d.15
    e.17
    You can solve it like this

    1. 2^x – 2 ^(x-2) = 3*2^13
    2. 2^x – 2 ^x/2^2 = 3*2^13


    now taking 2^ common from LHS u get
    3. 2^x (1– 1/2^2) = 3*2^13
    Since 2^2 =4 so now
    4. 2^x (1– 1/4) = 3*2^13
    1-1/4 =3/4 = 3 /2^2
    5. 2^x (3/4) = 2^x (3/2^2)=2^x (3)2^(-2)=3*2^13
    now regroping all exponents of 2s u get
    2^(x-2)3 =3*2^13
    since LHS =RHS therefore
    x-2 =13
    hence x=15
    hope this is helpful.

  5. #5
    TestMagic Guru manish8109 is on the way! manish8109's Avatar
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    2^X - 2 ^(X-2) = 3 * 2 ^ 13.
    first consider the LHS
    LHS= 2^x - 2^(x-2)
    = 2^x - 2^x/2^2
    since 2^x is common so we can write the above eqn as
    = 2^x(1-1/4)
    = 2^x *3/4
    = 2^x * 3/2^2
    = 2^x/2^2 * 3
    = 2^(x-2) *3 since a^x/a^y = a^(x-y)
    quating it with RHS
    2^(x-2)*3 = 3*2^13
    for LHS=RHS
    2^(x-2)=2^13
    x-2=13
    x=15(ANS)
    hope it helps.

  6. #6
    Eager! GmatJunky just joined TestMagic. GmatJunky's Avatar
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    If 2^x – 2 ^(x-2) = 3*2^13, what is x?
    a.9

    b.11
    c.13
    d.15
    e.17

    Please view attachment:
    I hope you can follow it...
    Attached Images

  7. #7
    Eager! gmat78854p just joined TestMagic.
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    Thank you

    Thank you so much guys this was extremely helpful. Really appreciate it.

  8. #8
    Trying to make mom and pop proud rampage just joined TestMagic.
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    Quote Originally Posted by gmat78854p
    2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
    a.9

    b.11
    c.13
    d.15
    e.17
    I'm ignoring 9, 11 and 13; they are invalid choices as all of them are less than 3*2^13. That leaves us with 15 and 17.

    Starting with: 2^17 - 2^15 = 3*2^13

    2^17 - 2^15
    ------------ = 3
    2^13

    2^17 2^15
    ----- - ----- = 3
    2^13 2^13


    2^(17-13) - 2^(15-13) = 3
    2^4 - 2^2 = 3

    16 - 4 = 3 ? nope

    Has to be 15 then. Sounds simpler to me.

  9. #9
    TestMagic Guru-in-Training Da_Gr8_Mperor just joined TestMagic. Da_Gr8_Mperor's Avatar
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    Wonderful explanations mentioned above.

  10. #10
    Eager! menonan just joined TestMagic. menonan's Avatar
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    actually the easiest way wud be
    put values say 4 for x
    that wud give 2^4 - 2^2
    u realize that u can take 2^2 outside...
    which wud give 2^2(2^2 - 1)
    which is 2^2(3)
    ao u realize that 3 comes in any case.
    here take 2^x-2 outside
    ie 2^(x-2) [2^2-1]
    2^(x-2)* 3
    x-2 = 13
    x = 15

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