• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

A bowl contains pecans, cashews, and almonds in a ratio of 6

This topic has 3 expert replies and 1 member reply

A bowl contains pecans, cashews, and almonds in a ratio of 6

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



A bowl contains pecans, cashews, and almonds in a ratio of 6 : 10 : 15, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?

i. 1 : 2 : 3

ii. 2 : 3 : 4

iii. 4 : 7 : 10


A. I only

B. II only

C. III only

D. I and III only

E. II and III only

OA A

Source: Manhattan Prep

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
BTGmoderatorDC wrote:
A bowl contains pecans, cashews, and almonds in a ratio of 6 : 10 : 15, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?

i. 1 : 2 : 3

ii. 2 : 3 : 4

iii. 4 : 7 : 10


A. I only

B. II only

C. III only

D. I and III only

E. II and III only

OA A

Source: Manhattan Prep
We are given that the ratio of pecans to cashews to almonds is 6 : 10 : 15. We are also given that some of the nuts of one of the three types are removed. Let p, c and a be the leftover nuts of pecans, cashews and almonds, respectively, if some of them are removed.

If some of the pecans are removed, we have p : 10 : 15 or (p/5)x : 2x : 3x for some positive integer x.

Notice that if x = 1, then the ratio 1 : 2 : 3 in Roman numeral I is possible if p = 5. Since 5 < 6, then the ratio is definitely possible (notice that 5 : 10 : 15 = 1 : 2 : 3).

Similarly, if some of the cashews are removed, we have 6 : c : 15 or 2y : (c/3)y : 5y for some positive integer y.

Notice that if y = 2, then the ratio 4 : 7 : 10 in Roman numeral III is possible if c = 10.5 (notice that (10.5/3)*2 = 7). However, since 10.5 > 10 in the original ratio, the ratio 4 : 7 : 10 is not possible.

Lastly, if some of the almonds are removed, we have 6 : 10 : a or 3z : 5z : (a/2)z for some positive integer z. However, none of the given ratios in the Roman numerals can be equate to 3z : 5z : (a/2)z for any positive integer z.

Therefore, the only possible ratio is the one in Roman numeral I.

Answer: A

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
BTGmoderatorDC wrote:
A bowl contains pecans, cashews, and almonds in a ratio of 6 : 10 : 15, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?

i. 1 : 2 : 3

ii. 2 : 3 : 4

iii. 4 : 7 : 10


A. I only

B. II only

C. III only

D. I and III only

E. II and III only
Original ratio values:
P.................................................C...............................................A
6x<---distance of 4x--->10x<---distance of 5x--->15x

Options for the new ratio:
I) 1 : 2 : 3
I) 2 : 3 : 4
III) 4 : 7 : 10

The ratio values in each option are EVENLY SPACED.
Implication:
By removing some of one type of nut, we must yield a ratio composed of EVENLY SPACED VALUES.
Two cases are possible:

Case 1: The value for P decreases by x units (from 5x to 4x)
P.................................................C...............................................A
5x<---distance of 5x--->10x<---distance of 5x--->15x
Yielded ratio:
5:10:15 = 1:2:3

Case 2: The value for A decreases by x units (from 15x to 14x)
P.................................................C...............................................A
6x<---distance of 4x--->10x<---distance of 4x--->14x
Resulting ratio:
6:10:14 = 3:5:7

Of options I, II, and III, only option I is possible.

The correct answer is A.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

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

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
BTGmoderatorDC wrote:
A bowl contains pecans, cashews, and almonds in a ratio of 6 : 10 : 15, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?

i. 1 : 2 : 3
ii. 2 : 3 : 4
iii. 4 : 7 : 10

A. I only
B. II only
C. III only
D. I and III only
E. II and III only

Source: Manhattan Prep
$$?\,\,\,:\,\,\,p:c:a\,\,{\text{possible}}\,\,\left( {{\text{when}}\,\,{\text{some}}\,\,{\text{nuts}}\,\,{\text{of}}\,\,{\text{one}}\,\,{\text{type}}\,\,{\text{removed}}} \right)$$

$$p:c:a = 6:10:15\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ \matrix{
\,p = 6k \hfill \cr
\,c = 10k \hfill \cr
\,a = 15k \hfill \cr} \right.\,\,\,\,\,\,\left( {k > 0\,\,{\mathop{\rm int}} \left( * \right)} \right)$$

$$\left( * \right)\,\,\left\{ \matrix{
\,{\mathop{\rm int}} - {\mathop{\rm int}} = a - c = 15k - 10k = 5k\,\,{\mathop{\rm int}} \hfill \cr
\,{\mathop{\rm int}} - {\mathop{\rm int}} = p - 5k = 6k - 5k = k\,\,\,{\mathop{\rm int}} \hfill \cr} \right.$$

$$\left( {\text{I}} \right)\,\,\,p:c:a = 1:2:3\,\,\,\, \Rightarrow \,\,\,{\text{possible}}\,\,\left( {k = 1,\,\,{\text{take}}\,\,1\,\,{\text{pecan}}\,\,{\text{nut}}\,\,{\text{out}}\,\,\,\, \Rightarrow \,\,\,\,\left( {p,c,a} \right) = \left( {5,10,15} \right)} \right)$$
$$\,\,\, \Rightarrow \,\,\,\,\,{\text{refute}}\,\,\left( {\text{B}} \right),\left( {\text{C}} \right),\left( {\text{E}} \right)$$

$$\left( {{\text{III}}} \right)\,\,p:c:a = 4:7:10\,\,\,\,\mathop \Rightarrow \limits^{\left( {\text{below}} \right)} \,\,\,{\text{impossible:}}\,\,\,$$
$${\rm{some}}\,\,p\,\,{\rm{out}}\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,\left( {p,c,a} \right) = \left( {6k - {\rm{some}},10k,15k} \right) \hfill \cr
\,{2 \over 3} = {{10k} \over {15k}} = {c \over a} \ne {7 \over {10}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,k,{\rm{some}}\,\, > 0\,} \right]$$
$${\rm{some}}\,\,c\,\,{\rm{out}}\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,\left( {p,c,a} \right) = \left( {6k,10k - {\rm{some}},15k} \right) \hfill \cr
\,{4 \over 7} = {p \over c} = {{6k} \over {10k - {\rm{some}}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,40k - 4 \cdot {\rm{some}} = 42k\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\, \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,k,{\rm{some}}\,\, > 0\,} \right]$$
$${\rm{some}}\,\,a\,\,{\rm{out}}\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,\left( {p,c,a} \right) = \left( {6k,10k,15k - {\rm{some}}} \right) \hfill \cr
\,{4 \over 7} = {p \over c} = {{6k} \over {10k}} = {3 \over 5}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\, \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,k,{\rm{some}}\,\, > 0\,} \right]$$


The correct answer is (A).

(Note that (II) does not need to be evaluated!)



We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag
Post
I don’t know the standard approach for this sum, but I just tried number plugin method
6:10:15
Which means 6x,10x,15x
So probably 6,10,15
12,20,30
18,30,45
24,40,60
Now we try to fit with answer 6,10, 15 to be fitted with
1:2:3 ( 2 & 3 direct fits when we multiply 5), reduce 6 by one number 5
5, 10 15 (1:2:3)
So A works

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts