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

It is currently 21 Oct 2019, 03:06

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The product of integers w, x, y, and z is 210, and w > x > y > z > 0.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58423
The product of integers w, x, y, and z is 210, and w > x > y > z > 0.  [#permalink]

Show Tags

New post 29 Aug 2017, 23:50
1
1
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

53% (02:30) correct 47% (02:21) wrong based on 116 sessions

HideShow timer Statistics

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
The product of integers w, x, y, and z is 210, and w > x > y > z > 0.  [#permalink]

Show Tags

New post 30 Aug 2017, 00:00
2
210 when prime factorized is 2*3*5*7

The various options for w,x,y,z are as follows:
Given that w > x > y > z > 0, therefore they are all positive

---------w-----y-----x-----q
---------2-----3-----5------7(sum is 17)
---------1-----2-----3-----35(sum is 41)
---------1-----2-----7-----15(sum is 25)
---------1-----5-----6------7(sum is 19)
---------1-----3-----7-----10(sum is 21)

The only possibility(from the answer options)
that's still missing for the sum of w,x,y, and z is 31(Option D)
_________________
You've got what it takes, but it will take everything you've got
Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 603
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Reviews Badge
Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0.  [#permalink]

Show Tags

New post 30 Aug 2017, 00:16
1
Bunuel wrote:
The product of integers w, x, y, and z is 210, and w > x > y > z > 0. Which of the following could NOT be the sum w + x + y + z?

A. 17
B. 19
C. 21
D. 31
E. 41


210 = 2*3*5*7 =Sum 17
1*6*5*7= Sum 19
1*3*10*7 = Sum 21
1*2*3*35 = Sum 41

But
1*1*14*15 = Sum 31 but w > x > y > z > 0
D
_________________
We must try to achieve the best within us


Thanks
Luckisnoexcuse
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0.  [#permalink]

Show Tags

New post 02 Sep 2017, 07:18
Bunuel wrote:
The product of integers w, x, y, and z is 210, and w > x > y > z > 0. Which of the following could NOT be the sum w + x + y + z?

A. 17
B. 19
C. 21
D. 31
E. 41


Let’s break down 210 as a product of two positive integers:

210 = 1 x 210 = 2 x 105 = 3 x 70 = 5 x 42 = 6 x 35 = 7 x 30 = 10 x 21 = 14 x 15

For each of the expressions except 1 x 210, we can write each factor as the product of two distinct factors. For example:

210 = 2 x 105 = (1 x 2) x (3 x 35) = (1 x 2) x (5 x 21) = (1 x 2) x (7 x 15)

From the above, we see that the sum w + x + y + z could be 41, 29, and 25, respectively. Thus, we can eliminate choice E.

Now let’s use 210 = 3 x 70:

210 = 3 x 70 = (1 x 3) x (2 x 35) = (1 x 3) x (5 x 14) = (1 x 3) x (7 x 10)

From the above, we see that the sum w + x + y + z could be 41, 23, and 21, respectively. Thus, we can eliminate choice C.

Now let’s use 210 = 5 x 42:

210 = 5 x 42 = (1 x 5) x (2 x 21) = (1 x 5) x (3 x 14) = (1 x 5) x (6 x 7)

From the above, we see that the sum w + x + y + z could be 29, 23, and 19, respectively. Thus, we can eliminate choice B.

Now let’s use 210 = 6 x 35:

210 = 6 x 35 = (1 x 6) x (5 x 7) = (2 x 3) x (1 x 35) = (2 x 3) x (5 x 7)

From the above, we see that the sum w + x + y + z could be 19, 41, and 17, respectively. Thus, we can eliminate choice A.

We can stop here since we’ve eliminated choices A, B, C, and E. Thus, D is the correct answer.

Answer: D
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
avatar
S
Joined: 24 Sep 2018
Posts: 137
Premium Member
Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0.  [#permalink]

Show Tags

New post 06 Oct 2018, 11:34
Quote:
The product of integers w, x, y, and z is 210, and w > x > y > z > 0. Which of the following could NOT be the sum w + x + y + z?

A. 17
B. 19
C. 21
D. 31
E. 41


When you're factoring any number that ends in 0, a good first rule is to break that number into something-times-10. 210 therefore becomes 21×10.

From there, you'll want to break each of 21 and 10 even further. 21 = 3×7, and 10 = 2×5. Since those are prime numbers, you're done factoring there.

The prime factors of 210 are 2, 3, 5, and 7.

If you sum 2 + 3 + 5 + 7, you get 17, so you can confidently say that choice A is incorrect, as 17 could be the sum of four factors of 210.

How are the other choices formed? Recognize that 1 is a factor of all integers, so you can include 1 in the factorization, too. In order to do that and have exactly four integers w, x, y, and z, however, you will need to combine two of the other primes. For example, if you combined 2 and 3 to multiply to 6, your terms would be:

1×(2×3)×5×7. This is then 1×6×5×7 = 210, so you can sum 1 + 6 + 5 + 7 to see that 19 is also a possible sum. Choice B is also then eliminated.

Going further, you can combine 2 and 5 as a single term, making the factorization 1×3×(2×5)×7, or 1×3×10×7 = 210, and the sum of those terms is 1 + 3 + 10 + 7, which is 21. Choice C is also eliminated.

Choice E is eliminated by combining larger prime factors. If you take 1×2×3×(5x7), you get 1×2×3×35 = 210, and the sum 1 + 2 + 3 + 35 = 41. So choice E is eliminated, leaving only choice D.

Choice D is therefore correct.
_________________
Please award :thumbup: kudos, If this post helped you in someway. :student_man:
GMAT Club Bot
Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0.   [#permalink] 06 Oct 2018, 11:34
Display posts from previous: Sort by

The product of integers w, x, y, and z is 210, and w > x > y > z > 0.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne