Pls Explain
If K is an integer and (0.0025)(0.025)(0.00025)*10^k is an integer, what is the least possible value of K?
A. –12
B. –6
C. 0
D. 6
E. 12
Thanks a lot!
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least possible value of k
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satyasharma321
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0.0025)(0.025)(0.00025)*10^ksatyasharma321 wrote:Pls Explain
If K is an integer and (0.0025)(0.025)(0.00025)*10^k is an integer, what is the least possible value of K?
A. –12
B. –6
C. 0
D. 6
E. 12
Thanks a lot!
= 25/10^4 * 25/10^3 * 25^5/10^5 *10^k
= 25*25*25 * 10^k/10^12
least of value of k should 12 to make it integer.
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komati_anusha
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K = Integer
25x10^(-4) x 25x10^(-3) x 25x10(-5) x 10^k
25^3 x 10^(-12) x 10^k
25^3 x 10^(k-12)
I could not think after this step and ended up least value for k is -12
Rich, can you help me what mistake I have done. Thank you.
25x10^(-4) x 25x10^(-3) x 25x10(-5) x 10^k
25^3 x 10^(-12) x 10^k
25^3 x 10^(k-12)
I could not think after this step and ended up least value for k is -12
Rich, can you help me what mistake I have done. Thank you.
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GMATGuruNY
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(0.0025)(0.025)(0.00025) × 10^kIf k is an integer and (0.0025)(0.025)(0.00025) * 10^k is an integer, what is the least possible value of k?
(A) -12
(B) -6
(C) 0
(D) 6
(E) 12
= (25)(10ˉ�)(25)(10ˉ³)(25)(10ˉ�)(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(10ˉ²�).
B: 25³(10ˉ¹²)(10ˉ�) = 25³(10ˉ¹�).
C: 25³(10ˉ¹²)(10�) = 25³(10ˉ¹²).
D: 25³(10ˉ¹²)(10�) = 25³(10ˉ�).
E: 25³(10ˉ¹²)(10¹²) = 25³(10�) = 25³.
Only E yields an integer value
The correct answer is E.
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Brent@GMATPrepNow
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Another approach is to convert everything to fractions.If k is an integer and (0.0025)(0.025)(0.00025) × 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) × 10^k is an integer
So, (25/10,000)(25/1,000)(25/100,000) × 10^k is an integer
Simplify to get: (25³/1,000,000,000,000) × 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
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Once you get to your last step, rewrite everything askomati_anusha wrote:K = Integer
25x10^(-4) x 25x10^(-3) x 25x10(-5) x 10^k
25^3 x 10^(-12) x 10^k
25^3 x 10^(k-12)
I could not think after this step and ended up least value for k is -12
Rich, can you help me what mistake I have done. Thank you.
25³ * 10� / 10¹²
or
(25³ / 10¹²) * 10�
or
(1 / (2� * 10�)) * 10�
or
10� / (2� * 10�)
For that to be an integer, you need to cancel everything in the denominator. That will be six 10s from 10�, and six more to erase the six 2s in 2�. That means we need at least twelve 10s, and k ≥ 12.
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We are given the expression:satyasharma321 wrote:Pls Explain
If K is an integer and (0.0025)(0.025)(0.00025)*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 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 result of 0.0025 x 0.025 x 0.00025 will have 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, making it an integer.
Answer: E
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Hi komati_anusha,komati_anusha wrote:K = Integer
25x10^(-4) x 25x10^(-3) x 25x10(-5) x 10^k
25^3 x 10^(-12) x 10^k
25^3 x 10^(k-12)
I could not think after this step and ended up least value for k is -12
Rich, can you help me what mistake I have done. Thank you.
Your work was perfect, but you lost sight of the question that was ASKED. We want the LEAST possible value of K that will make that product into an INTEGER.
25^3 is an integer (we don't actually have to calculate it though) and we know that we're going to multiply that number by 10^(K-12). If (K-12) ends up being anything negative (meaning that K is any integer less than or equal to 11), then that value will be a fractional value (and the overall product will NOT be an integer). So K MUST be greater than 11 - looking at the answers, there's only one that fits...
Final Answer: E
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