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!
least possible value of k
This topic has expert replies
-
- Newbie | Next Rank: 10 Posts
- Posts: 5
- Joined: Fri Sep 26, 2008 8:04 am
-
- Newbie | Next Rank: 10 Posts
- Posts: 5
- Joined: Fri Sep 26, 2008 8:04 am
-
- Master | Next Rank: 500 Posts
- Posts: 258
- Joined: Thu Aug 07, 2008 5:32 am
- Thanked: 16 times
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.
-
- Junior | Next Rank: 30 Posts
- Posts: 17
- Joined: Thu Sep 19, 2013 9:50 pm
- Followed by:1 members
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.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
(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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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
Cheers,
Brent
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich