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OG 16 Question 67

This topic has 6 expert replies and 2 member replies
Azizakaria Senior | Next Rank: 100 Posts
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OG 16 Question 67

Post Tue Oct 27, 2015 1:54 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    67. If k is an integer and (0.0025)(0.025)(0.00025) X 10k is an integer, what is the
    least possible value of k?
    (A) -12
    (B) -6
    (C) 0
    (D) 6
    (E) 12

    I don't understand why the right answer is E

    I solved for A as (25 X 10^-4)(25 X 10^-3)(25 X 10^-5) X 10^k

    thanks in advance

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    Post Tue Oct 27, 2015 4:22 am
    The OE for this problem has a typo.
    The prompt should read as follows:

    Azizakaria wrote:
    67. If k is an integer and (0.0025)(0.025)(0.00025) X 10^k is an integer, what is the least possible value of k?
    (A) -12
    (B) -6
    (C) 0
    (D) 6
    (E) 12
    (0.0025)(0.025)(0.00025) X 10^k

    = (25)(10ˉ⁴)(25)(10ˉ³)(25)(10ˉ⁵)(10^k)

    = 25³(10ˉ¹²)(10^k).

    We can PLUG IN THE ANSWERS, which represent the least possible value of k.

    A: 25³(10ˉ¹²)(10ˉ¹²) = 25³(10ˉ²⁴).
    B: 25³(10ˉ¹²)(10ˉ⁶) = 25³(10ˉ¹⁸).
    C: 25³(10ˉ¹²)(10⁰) = 25³(10ˉ¹²).
    D: 25³(10ˉ¹²)(10⁶) = 25³(10ˉ⁶).
    E: 25³(10ˉ¹²)(10¹²) = 25³(10⁰) = 25³.

    Only E yields an integer value

    The correct answer is E.

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    Post Tue Oct 27, 2015 7:23 am
    Azizakaria wrote:
    67. If k is an integer and (0.0025)(0.025)(0.00025) X 10^k is an integer, what is the
    least possible value of k?
    (A) -12
    (B) -6
    (C) 0
    (D) 6
    (E) 12

    Another approach is to convert everything to fractions.

    (0.0025)(0.025)(0.00025) X 10^k is an integer
    So, (25/10,000)(25/1,000)(25/100,000) X 10^k is an integer
    Simplify to get: (25³/1,000,000,000,000) X 10^k is an integer
    To create an integer, we need 1,000,000,000,000 to EQUAL 10^k
    So, k = 12

    Answer: E

    Cheers,
    Brent

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    GMAT/MBA Expert

    Max@Math Revolution Legendary Member
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    Post Thu Oct 29, 2015 1:16 am
    Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


    If k is an integer and (0.0025)(0.025)(0.00025) X 10^k is an integer, what is the
    least possible value of k?
    (A) -12
    (B) -6
    (C) 0
    (D) 6
    (E) 12



    (0.0025)(0.025)(0.00025) X 10^k =(25/10^4)*(25/10^3)*(25/10^5)*10^k.
    (25/10^4)*(25/10^3)*(25/10^5) = (25^3)/(10^12).
    That (25^3)/(10^12)*10^k is an integer implies that k should be more than or equal to 12. So the smallest number is 12.

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    GMAT/MBA Expert

    Post Fri Oct 30, 2015 12:40 am
    My approach:

    We have 25/10000 * 25/1000 * 25/100000. To get rid of the denominators, we need 1000 * 10,000 * 100,000 in the numerator, or 10³ * 10⁴ * 10⁵. Adding those exponents gives us (3 + 4 + 5), or 12, so we need 10 to the 12th power.

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    jmacym Newbie | Next Rank: 10 Posts
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    Posted:
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    Post Tue Oct 18, 2016 10:33 am
    But there are they getting 25 ^ 3?????

    GMAT/MBA Expert

    Max@Math Revolution Legendary Member
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    Post Thu Oct 20, 2016 4:28 pm
    jmacym wrote:
    But there are they getting 25 ^ 3?????
    From 25^3=5^6, if there is no 2, it can't turn into 10, which is meaningless.
    That is, no matter how many 5 there are, it can't be 10 if there is no 2.
    Hence, it is omitted.

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    fiza gupta Master | Next Rank: 500 Posts
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    Post Thu Oct 20, 2016 6:04 pm
    (0.0025)(0.025)(0.00025) X 10^k

    = [(25)(10ˉ⁴)(25)(10ˉ³)(25)(10ˉ⁵)](10^k)

    = 25³(10ˉ¹²)(10^k)
    K >=12
    SO E

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    Post Sat Oct 22, 2016 5:33 am
    Azizakaria wrote:
    67. If k is an integer and (0.0025)(0.025)(0.00025) X 10^k is an integer, what is the
    least possible value of k?
    (A) -12
    (B) -6
    (C) 0
    (D) 6
    (E) 12
    We are given the expression:

    0.0025 x 0.025 x 0.00025 x 10^k = integer

    To determine the least possible value of k, we want to use our rules of multiplication with decimals. When multiplying decimals, the final product has an equal number of decimal places to the decimal places of the numbers being multiplied. Let’s start by counting the number of decimal places.

    0.0025 has 4 decimal places

    0.025 has 3 decimal places

    0.00025 has 5 decimal places

    Thus, the product of 0.0025 x 0.025 x 0.00025 has 12 decimal places.

    In order for 0.0025 x 0.025 x 0.00025 x 10^k = integer, k would have to be at least 12, since 10^12 times any number with 12 decimal places would move the decimal point of that number 12 places to the right.

    Answer:E

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