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

 It is currently 25 Apr 2019, 18:58

### 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

# What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Aug 2013
Posts: 96
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)
What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

14 Dec 2014, 00:41
1
6
00:00

Difficulty:

95% (hard)

Question Stats:

29% (01:33) correct 71% (01:36) wrong based on 149 sessions

### HideShow timer Statistics

What is the value of x ?

(1) 3^x X 5^y = 75
(2) 3^(x-1)(y-2) = 1
Senior Manager
Joined: 13 Jun 2013
Posts: 274
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

14 Dec 2014, 05:15
anceer wrote:
What is the value of x ?

(1) 3^x X 5^y = 75
(2) 3^(x-1)(y-2) = 1

Here we are not told whether x is an integer or not.

st.1 3^x.5^y = 75, if x and y both are integers, then x=1 and y=2. but if they are not, then x and y can take any non-integer value. for example say x=0, then we have
5^y=75

y=2.68

st.2 3^(x-1)(y-2)=1
(x-1)(y-2)=0

if x=1 then y can have any value. if y=2 then x can have any value.

hence insufficient

combining st.1 and st.2

we have a common solution of x=1.

Math Expert
Joined: 02 Sep 2009
Posts: 54544
What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

15 Dec 2014, 07:59
3
1
What is the value of $$xy$$?

Notice that we are not told that the $$x$$ and $$y$$ are integers.

(1) $$3^x*5^y=75$$ --> if $$x$$ and $$y$$ are integers then as $$75=3^1*5^2$$ then $$x=1$$ and $$y=2$$ BUT if they are not, then for any value of $$x$$ there will exist some non-integer $$y$$ to satisfy given expression and vise-versa (for example if $$y=1$$ then $$3^x*5^y=3^x*5=75$$ --> $$3^x=25$$ --> $$x=some \ irrational \ #\approx{2.9}$$). Not sufficient.

(2) $$3^{(x-1)(y-2)}=1$$ --> $$(x-1)(y-2)=0$$ --> either $$x=1$$ and $$y$$ is ANY number (including 2) or $$y=2$$ and $$x$$ is ANY number (including 1). Not sufficient.

(1)+(2) If from (2) $$x=1$$ then from (1) $$3^x*5^y=3*5^y=75$$ --> $$y=2$$ and if from (2) $$y=2$$ then from (1) $$3^x*5^y=3^x*25=75$$ --> $$x=1$$. Thus $$x=1$$ and $$y=2$$. Sufficient.

_________________
Senior Manager
Joined: 02 Dec 2014
Posts: 364
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

03 Mar 2015, 03:28
1
anceer wrote:
What is the value of x ?

(1) 3^x X 5^y = 75
(2) 3^(x-1)(y-2) = 1

Hi Bunuel!
Looks like you made a typo in your solution! There should be 3^(x-1)(y-2) = 1 not 5^(x-1)(y-2) = 1 as in your text. Yes?
_________________
"Are you gangsters?" - "No we are Russians!"
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

03 Mar 2015, 05:42
Konstantin1983 wrote:
anceer wrote:
What is the value of x ?

(1) 3^x X 5^y = 75
(2) 3^(x-1)(y-2) = 1

Hi Bunuel!
Looks like you made a typo in your solution! There should be 3^(x-1)(y-2) = 1 not 5^(x-1)(y-2) = 1 as in your text. Yes?

Yes. Typo edited. Thank you.
_________________
Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 305
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

28 Jun 2016, 00:32

-> Going by the numbers manpreetsingh86 has picked up, where x=0, there will be no combination of 5^y that will yield *exactly* 75. (I spent a lot of time with the calculator trying different numbers for y and went down to y=2.682606-2.682607). I agree we will have an approximate 75 but not an integer 75.

->Neither does Bunuel 's numbers fit in.

I had picked A because both 3 and 5 are prime numbers and any non-integer exponent will yield a non-integer to us. It will only yield an integer if we pick integer exponents. What scenario am I missing from my analysis?
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

28 Jun 2016, 05:24
AmoyV wrote:

-> Going by the numbers manpreetsingh86 has picked up, where x=0, there will be no combination of 5^y that will yield *exactly* 75. (I spent a lot of time with the calculator trying different numbers for y and went down to y=2.682606-2.682607). I agree we will have an approximate 75 but not an integer 75.

->Neither does Bunuel 's numbers fit in.

I had picked A because both 3 and 5 are prime numbers and any non-integer exponent will yield a non-integer to us. It will only yield an integer if we pick integer exponents. What scenario am I missing from my analysis?

You are missing the scenario with irrational numbers.

$$3^x*5^y=75$$. If $$y=1$$ then $$3^x*5^y=3^x*5=75$$ --> $$3^x=25$$ --> $$x=some \ irrational \ #\approx{2.9}$$). So, there is some irrational number x, for which 3^x = 25.
_________________
Current Student
Joined: 28 Nov 2014
Posts: 840
Concentration: Strategy
Schools: Fisher '19 (M\$)
GPA: 3.71
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

01 Jul 2016, 02:16
Bunuel wrote:
AmoyV wrote:

-> Going by the numbers manpreetsingh86 has picked up, where x=0, there will be no combination of 5^y that will yield *exactly* 75. (I spent a lot of time with the calculator trying different numbers for y and went down to y=2.682606-2.682607). I agree we will have an approximate 75 but not an integer 75.

->Neither does Bunuel 's numbers fit in.

I had picked A because both 3 and 5 are prime numbers and any non-integer exponent will yield a non-integer to us. It will only yield an integer if we pick integer exponents. What scenario am I missing from my analysis?

You are missing the scenario with irrational numbers.

$$3^x*5^y=75$$. If $$y=1$$ then $$3^x*5^y=3^x*5=75$$ --> $$3^x=25$$ --> $$x=some \ irrational \ #\approx{2.9}$$). So, there is some irrational number x, for which 3^x = 25.

Bunuel - Can we safely assume that there will an irrational number which will make 3^x equal to 25. Indeed, I too could not locate any number till 5 decimal places.
Is it safe to make such an assumption?
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

01 Jul 2016, 03:14
Keats wrote:
Bunuel wrote:
AmoyV wrote:

-> Going by the numbers manpreetsingh86 has picked up, where x=0, there will be no combination of 5^y that will yield *exactly* 75. (I spent a lot of time with the calculator trying different numbers for y and went down to y=2.682606-2.682607). I agree we will have an approximate 75 but not an integer 75.

->Neither does Bunuel 's numbers fit in.

I had picked A because both 3 and 5 are prime numbers and any non-integer exponent will yield a non-integer to us. It will only yield an integer if we pick integer exponents. What scenario am I missing from my analysis?

You are missing the scenario with irrational numbers.

$$3^x*5^y=75$$. If $$y=1$$ then $$3^x*5^y=3^x*5=75$$ --> $$3^x=25$$ --> $$x=some \ irrational \ #\approx{2.9}$$). So, there is some irrational number x, for which 3^x = 25.

Bunuel - Can we safely assume that there will an irrational number which will make 3^x equal to 25. Indeed, I too could not locate any number till 5 decimal places.
Is it safe to make such an assumption?

This is not an assumption: 3^x = 25 has a solution for x: $$x=\frac{2log(5)}{log(3)} \approx 2.929947...$$
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 10639
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1  [#permalink]

### Show Tags

16 Jul 2017, 00:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: What is the value of x ? (1) 3^x X 5^y = 75 (2) 3^(x-1)(y-2) = 1   [#permalink] 16 Jul 2017, 00:27
Display posts from previous: Sort by