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

 It is currently 23 Oct 2019, 11:18

### 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

# If integers x, y and z are greater than 1 what is the value

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 11 May 2008
Posts: 502
If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

04 Aug 2008, 11:05
3
48
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:28) correct 47% (01:37) wrong based on 746 sessions

### HideShow timer Statistics

If x, y and z are integers greater than 1, what is the value of x + y + z?

(1) xyz = 70
(2) x/(yz) = 7/10
Senior Manager
Joined: 27 May 2008
Posts: 387
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

04 Aug 2008, 11:10
9
8
arjtryarjtry wrote:
) If x, y and z are integers greater than 1, what is the value of x + y + z?
1) xyz = 70
2) x/yz = 7/10

statement 1 : 70 = 2*5*7
x+y+z = 2+5+7 = 14 suff

statement 2 : x/yz = 7/10 = 14/20 = 21/30 ... not suff

option A
##### General Discussion
VP
Joined: 07 Nov 2007
Posts: 1317
Location: New York
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

04 Aug 2008, 11:11
1
2
arjtryarjtry wrote:
) If x, y and z are integers greater than 1, what is the value of x + y + z?
1) xyz = 70
2) x/yz = 7/10

1) xyz = 70 (suffcient)
= 2 * 5 * 7 ( is only combination which leads to 70)

2) x/yz = 7/10 (not suffcient)

x/yz = 7/10 ( x=7 y = 5 z=2)
x/yz = (7/10)*(k/k) also true for ( x=14 y = 10 z=2)

_________________
Smiling wins more friends than frowning
VP
Joined: 17 Jun 2008
Posts: 1015
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

05 Aug 2008, 19:15
arjtryarjtry wrote:
) If x, y and z are integers greater than 1, what is the value of x + y + z?
1) xyz = 70
2) x/yz = 7/10

Given : x,y,z are integers >1
(1)xyz=70 => xyz=5*7*2 => say 5,2,7 are values of x,y,z in any order
(2)x/yz =7/10 this can be any values for x,y,z say,
x=7,y=5,z=2 or x=14,y=5,z=4 hence x+y+z will change INSUFFI

IMO A
_________________
cheers
Its Now Or Never
Director
Joined: 30 Jun 2008
Posts: 856
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

22 Oct 2008, 11:58
2
2
rishi2377 wrote:
If integers x, y and z are greater than 1 what is the value of x + y + z ?

A. xyz = 70
B. x/yz = 7/10

I got this right. but with 2nd statement. I went to only 10x = 7yz
is that the end of 2nd statement or we can drive something with that?

x,y,z >1

(1) xyz = 70 = 2*5*7 so we can find x+y+z

(2) $$\frac{x}{yz} = \frac{7}{10}$$

this just means x is a multiple of 7 and the product yz is a multiple of 10. We have no info to determine values of x,y and z.

A
_________________
"You have to find it. No one else can find it for you." - Bjorn Borg
Manager
Joined: 07 Feb 2010
Posts: 114
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

05 Jan 2011, 08:29
xyz = 70
so the values could be 1 7 10
x+y+z = 18
if the values are 2 5 7
x+y+z =14
so a not sufficient
Math Expert
Joined: 02 Sep 2009
Posts: 58464
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

05 Jan 2011, 08:40
anilnandyala wrote:
xyz = 70
so the values could be 1 7 10
x+y+z = 18

if the values are 2 5 7
x+y+z =14
so a not sufficient

"If x, y and z are integers greater than 1 ..."

_________________
Intern
Joined: 29 Dec 2010
Posts: 27
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

01 Mar 2011, 15:45
Bunuel, if the question states that x, y and z are greater then 1... then is ok to say that one of thoes is 1? as I read it , none of them can be one " GREATER THEN 1"???
Math Expert
Joined: 02 Sep 2009
Posts: 58464
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

01 Mar 2011, 16:04
marijose wrote:
Bunuel, if the question states that x, y and z are greater then 1... then is ok to say that one of thoes is 1? as I read it , none of them can be one " GREATER THEN 1"???

Again: "If x, y and z are integers greater than 1 ..." So none of them is one.
_________________
Intern
Joined: 02 Oct 2012
Posts: 3
GMAT 1: 730 Q49 V41
GPA: 3.73
WE: Project Management (Military & Defense)
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

20 Oct 2013, 11:48
Bunuel,

The problem doesnt specifically state that the integers are unique or different. Is it possible for A to be insufficient as xyz to be 7*7*5 with a sum of 19 or the answer provided above with 2*5*7 and a sum of 14?

I'm assuming the variables need to be unique integer values, but this threw me off at first.
Math Expert
Joined: 02 Sep 2009
Posts: 58464
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

20 Oct 2013, 11:51
affalcon12 wrote:
Bunuel,

The problem doesnt specifically state that the integers are unique or different. Is it possible for A to be insufficient as xyz to be 7*7*5 with a sum of 19 or the answer provided above with 2*5*7 and a sum of 14?

I'm assuming the variables need to be unique integer values, but this threw me off at first.

Notice that 7*7*5 = 245 not 70.
_________________
Intern
Joined: 02 Oct 2012
Posts: 3
GMAT 1: 730 Q49 V41
GPA: 3.73
WE: Project Management (Military & Defense)
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

20 Oct 2013, 11:55
Bunuel,
Yes, good correction. Obviously. For some reason I was thinking 7+7 = 14 and 14*5 = 70. Dumb mistake by me. Thank you!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15316
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

10 Jan 2015, 12:54
1
2
Hi All,

DS questions test a variety of skills, including the thoroughness of your thinking. In other words, do you notice when there's more than one possibility? Also, do you realize when enough "restrictions" exist to limit the number of possible answers to just one possibility? Those ideas are at the heart of this DS question.

Right from the beginning, we're given restrictions to work with:
X, Y and Z are INTEGERS
X, Y and Z are all > 1

We're asked for the value of X + Y + Z.

Fact 1: XYZ = 70

At first glance, many Test Takers would think that this was insufficient information since there are "so many" ways to get a product of 70. HOWEVER, we have to work with those initial restrictions (X, Y and Z are INTEGERS and they're ALL > 1). How many different sets of numbers will get us a product of 70 now?

With a bit of pattern-matching, you should notice that since 70 "ends in 0", one of the numbers MUST be a multiple of 5 and at least one of the numbers MUST be even. Prime-factorization can be used to quickly break the 70 "into pieces":

70 = (2)(5)(7)

A 2, a 5 and a 7 represent the ONLY possible numbers. Since the question asks us for the SUM of the 3 numbers, it doesn't matter which variable is which number. The final answer is 2 + 5 + 7 = 14.
Fact 1 is SUFFICIENT

Fact 2: X/YZ = 7/10

With the prior work form Fact 1, the Fact seems to have an obvious solution:
X = 7
Y and Z = 2 and 5
So X + Y + Z = 14

The "catch" here is that fractions can be reduced, so while X/YZ = 7/10 gave us this first outcome, X/YZ = 14/20 = 21/30 = 28/40 = etc. are ALSO possibilities that would lead to different answers.

For example:
X/YZ = 14/20
X = 14
Y = 2
Z = 10
So X + Y + Z now = 26 and we have a different answer.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 14 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

11 Jan 2015, 11:29
arjtryarjtry wrote:
If x, y and z are integers greater than 1, what is the value of x + y + z?

(1) xyz = 70
(2) x/yz = 7/10

We know x,y,z > 1

Read St.A --> xyz = 70 = 2*5*7
as x,y and z are greater than 1 we cant have (10,7,1), (70,1,1) or other combinations
Hence x+y+z = 2+5+7 = 14
A is sufficient

St. B --> x/yz = 7/10
now x is 7k, y is 2m and z is 5n
Hence x+y+z will be variable
Hence B is useless.

Only A is sufficient
Intern
Joined: 07 Mar 2014
Posts: 16
Location: India
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

26 Oct 2015, 02:40
1
$$X , Y , Z integers > 1$$

$$x + y + z = ?$$

Statement 1

$$xyz = 70$$

Prime factorizing 70 we get 2, 5 and 7 ( we can not take any value to be 1 because all integers are greater than 1)

so $$x + y + z = 14$$

No matter what value we take for x, y, z , sum will always be 14

Hence statement 1 is Sufficient

Statement 2

$$\frac{x}{yz} = \frac{7}{10}$$

here if $$x = 7$$ then y be 2 and z be 5 then $$x + y + z = 14$$

x can also be 14 , then y be 2 and z be 10 then $$x + y + z = 26$$

so clearly statement 2 is not sufficient.

Intern
Joined: 20 Aug 2018
Posts: 25
If integers x, y and z are greater than 1 what is the value  [#permalink]

### Show Tags

24 Nov 2018, 16:11
A video explanation can be found here:

Practically every GMAT will ask you a question that requires you to think about prime factorization, so always have than in the back of your mind.

70 = 2*5*7, so the sum of primes is 14. Statement (1) is sufficient

In statement (2) x, y and z COULD be 7, 2 and 5, but could also be a multiple of x and a multiple of y or z, such that the expression simplifies to 7/10 (for e.g. x = 14, y = 4, and z = 5), so (2) not sufficient
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13420
Re: If x, y and z are integers greater than 1, what is the value  [#permalink]

### Show Tags

17 Jul 2019, 21:58
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: If x, y and z are integers greater than 1, what is the value   [#permalink] 17 Jul 2019, 21:58
Display posts from previous: Sort by