GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Dec 2018, 02:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51301
If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

12 Jun 2015, 02:34
1
8
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:57) correct 33% (02:03) wrong based on 328 sessions

### HideShow timer Statistics

If x, y, and z are integers and $$2^x*5^y*z = 6.4*10^6$$, what is the value of xy?

(1) z = 20
(2) x = 9

Kudos for a correct solution.

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

12 Jun 2015, 03:31
1
3
Bunuel wrote:
If x, y, and z are integers and $$2^x*5^y*z = 6.4*10^6$$, what is the value of xy?

(1) z = 20
(2) x = 9

Kudos for a correct solution.

CONCEPT: Such Questions always require Prime factorization on both side of the equation to compare the exponent of the same base values

Given: $$2^x*5^y*z = 6.4*10^6$$
i.e. $$2^x*5^y*z = 64*10^5$$
i.e. $$2^x*5^y*z = 2^{11}*5^5$$

Question : xy = ?

Statement 1: z = 20
i.e $$2^x*5^y*20 = 2^{11}*5^5$$
i.e $$2^{x+2}*5^{y+1} = 2^{11}*5^5$$
i.e. x+2 = 11 and y+1 = 5
i.e. x = 9 and y = 4

Hence, SUFFICIENT

Statement 2: x = 9
i.e $$2^9*5^y*z = 2^{11}*5^5$$
i.e. z must a multiple of $$2^2$$ for the exponent of 2 to be equal on both sides of the equation
But y still remains unknown

Hence, NOT SUFFICIENT
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 28 Jan 2013
Posts: 31
Location: United States
GPA: 3.1
WE: Information Technology (Consulting)
If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

Updated on: 15 Jun 2015, 07:31
1
1
If x, y, and z are integers and $$2^x$$∗$$5^y$$∗z=6.4∗10^6, what is the value of xy?

(1) z = 20

$$2^x$$∗$$5^y$$∗20 = $$2^5$$*$$10^4$$*20
$$2^x$$*$$5^y$$ = $$2^9$$*$$5^4$$

x=9,y=4
xy=36
Sufficient

(2) x = 9

$$2^9$$*$$5^y$$*z=$$2^6$$*$$10^5$$
$$2^9$$*$$5^y$$*z=$$2^{11}$$*$$5^5$$
if y=5 then z=4
if y=4 then z=20
if y=3 then z=100

So y can take any value ranging from 0 to 5.

Insufficient

Ans : A

Originally posted by ManojReddy on 12 Jun 2015, 03:54.
Last edited by ManojReddy on 15 Jun 2015, 07:31, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51301
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

15 Jun 2015, 04:42
Bunuel wrote:
If x, y, and z are integers and $$2^x*5^y*z = 6.4*10^6$$, what is the value of xy?

(1) z = 20
(2) x = 9

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Express both sides of the equation in terms of prime numbers. $$2^x*5^y*z = 6.4*10^6=2^{11}*5^5$$.

The right side of the equation is composed of only 2's and 5's. The left side of the equation has x number of 2's and y number of 5's along with some factor z. This unknown factor z must be composed of only 2's and/or 5's, or it must be 1 (i.e. with no prime factors).

If z = 1, then x = 11 and y = 5.
If z = 2^?*5^?, where the exponents are not 0, then x and y will depend on the value of those exponents.

The rephrased question is thus “How many factors of 2 and 5 are in z?”

(1) SUFFICIENT: If $$z = 20 = 2^2*5^1$$, then we have the answer to our rephrased question. Incidentally,this implies that $$2^x*5^y(2^2*5^1) = 2^{11}*5^5$$, so x = 9 and y = 4, making xy = 36.

(2) INSUFFICIENT: If x = 9, then

$$2^x*5^y*z = 2^{11}*5^5$$

$$2^9*5^y*z = 2^{11}*5^5$$

$$z=2^2*5^{5-y}$$

While this tells us the number of 2's among z's factors, we still do not know how many factors of 5 are in z.

_________________
Director
Joined: 31 Oct 2013
Posts: 901
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If x,y and z are integers and 2^x 5^y z = 6.4*10^6 , what is the value  [#permalink]

### Show Tags

22 Apr 2018, 06:10
If x,y and z are integers and $$2^x 5^y z = 6.4*10^6$$ , what is the value of xy?

1.z=20
2.x=9
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
If x,y and z are integers and 2^x 5^y z = 6.4*10^6 , what is the value  [#permalink]

### Show Tags

22 Apr 2018, 06:28
selim wrote:
If x,y and z are integers and $$2^x 5^y z = 6.4*10^6$$ , what is the value of xy?

1.z=20
2.x=9

$$2^x 5^y z = 6.4*10^6=>64*10^5$$

$$2^x 5^y z = 2^{10}5^5$$. Hence to know the value of $$xy$$, we need to know the value of $$z$$

Statement 1: provides the value of $$z$$. Sufficient

For the sake of calculation, $$2^x 5^y*20 = 2^{10}5^5=>2^{x+2}*5^{y+1}=2^{10}5^5$$

$$=>x+2=10=>x=8$$

$$=>y+1=5=>y=4$$. Hence $$xy=8*4=32$$

Statement 2: nothing can be said about the value of y & z. Insufficient

Option A
Math Expert
Joined: 02 Sep 2009
Posts: 51301
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

22 Apr 2018, 20:47
selim wrote:
If x,y and z are integers and $$2^x 5^y z = 6.4*10^6$$ , what is the value of xy?

1.z=20
2.x=9

Merging topics.

Similar question to practice: https://gmatclub.com/forum/if-x-y-and-z ... 88182.html
_________________
Director
Joined: 02 Oct 2017
Posts: 731
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

08 May 2018, 23:01
I) 2^x*5^y=32*10^4

So y=4 and x=9
To make up equality of eqn so sufficient

II) we know x but we don't know z
Z=1 or z=5 or 10
Can result in different values of xy
So insufficient

Posted from my mobile device
_________________

Give kudos if you like the post

CEO
Joined: 11 Sep 2015
Posts: 3243
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

24 Jun 2018, 05:12
Top Contributor
Bunuel wrote:
If x, y, and z are integers and $$2^x*5^y*z = 6.4*10^6$$, what is the value of xy?

(1) z = 20
(2) x = 9

Target question: What is the value of xy?

Given: x, y, and z are integers and (2^x)(5^y)(z) = (6.4)(10^6)
Since the left side of the given equation has been factored by primes, let's find the prime factorization of (6.4)(10^6)
(6.4)(10^6) = (6.4)(10^1)(10^5)
= (64)(10^5)
= (2^6)(10^5)
= (2^6)(2^5)(5^5)
= (2^11)(5^5)

So, we have: (2^x)(5^y)(z) = (2^11)(5^5)

Statement 1: z = 20
Take (2^x)(5^y)(z) = (2^11)(5^5) and replace z with 20...
We get: (2^x)(5^y)(20) = (2^11)(5^5)
Rewrite 20 as follows: (2^x)(5^y)(2^2)(5) = (2^11)(5^5)
Divide both sides of the equation by 2^2 to get: (2^x)(5^y)(5) = (2^9)(5^5)
Divide both sides of the equation by 5 to get: (2^x)(5^y) = (2^9)(5^4)
At this point, we can see that x = 9 and y = 4, so xy = (9)(4) = 36
So, the answer to the target question is xy = 36
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 9
Take (2^x)(5^y)(z) = (2^11)(5^5) and replace x with 9...
We get: (2^9)(5^y)(z) = (2^11)(5^5)
Divide both sides of the equation by 2^9 to get: (5^y)(z) = (2^2)(5^5)
From here, we can see that there are several values of x and z that satisfy the equation (5^y)(z) = (2^2)(5^5) .
Here are two possible cases:
Case a: y = 5 and z = 2^2. We already know that x = 9, so the answer to the target question is xy = (9)(5) = 45
Case b: y = 4 and z = (2^2)(5). We already know that x = 9, so the answer to the target question is xy = (9)(4) = 36
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

26 Jun 2018, 17:11
Bunuel wrote:
If x, y, and z are integers and $$2^x*5^y*z = 6.4*10^6$$, what is the value of xy?

(1) z = 20
(2) x = 9

Notice that 6.4 * 10^6= 64 * 10^5 = 2^6 * 2^5 * 5^5 = 2^11 * 5^5

Statement One Alone:

z = 20

Thus we have:

2^x + 5^y * 20 = 2^11 * 5^5

2^x + 5^y * 2^2 * 5 = 2^11 * 5^5

2^(x+2) + 5^(y+1) = 2^11 * 5^5

Since x and y are integers, x + 2 = 11 and y + 1 = 5. So x = 9 and y = 4 and xy = 9(4) = 36. Statement one alone is sufficient.

Statement Two Alone:

x = 9

Thus we have:

2^9 * 5^y * z = 2^11 * 5^5

5^y * z = 2^2 * 5^5

However, we can’t determine a unique value for y. For example, if z = 4, then y = 5. On the other hand, if z = 20, then y = 4. Statement two alone is not sufficient.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 22 Sep 2017
Posts: 19
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu  [#permalink]

### Show Tags

27 Jun 2018, 04:14
math revolution
how to apply variable approach here..??
Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu &nbs [#permalink] 27 Jun 2018, 04:14
Display posts from previous: Sort by