Last visit was: 13 Jul 2025, 07:24 It is currently 13 Jul 2025, 07:24
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
User avatar
cheapjasper
Joined: 19 Jan 2016
Last visit: 15 Mar 2016
Posts: 2
Own Kudos:
59
 [56]
Posts: 2
Kudos: 59
 [56]
2
Kudos
Add Kudos
54
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 13 Jul 2025
Posts: 11,295
Own Kudos:
41,713
 [11]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,295
Kudos: 41,713
 [11]
7
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
cheapjasper
Joined: 19 Jan 2016
Last visit: 15 Mar 2016
Posts: 2
Own Kudos:
59
 [3]
Posts: 2
Kudos: 59
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
avatar
vivekkumar987
Joined: 07 Mar 2015
Last visit: 05 Mar 2018
Posts: 97
Own Kudos:
57
 [1]
Given Kudos: 48
Location: India
Concentration: General Management, Operations
GMAT 1: 590 Q46 V25
GPA: 3.84
WE:Engineering (Energy)
GMAT 1: 590 Q46 V25
Posts: 97
Kudos: 57
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO : A

I don’t know the standard approach for this sum, but I just tried number plug in method
6:10:15
Which means 6x,10x,15x
So probably 6,10,15
12,20,30
18,30,45
24,40,60
No we try to fit with answer 6,10 ,15 to be fitted with
1:2:3 ( 2 & 3 direct fit when we multiply 5) , reduce 6 by one number 5
5, 10 15 (1:2:3)
So A works
Remaining I tried it doesn’t get fit
User avatar
LakerFan24
Joined: 26 Dec 2015
Last visit: 03 Apr 2018
Posts: 167
Own Kudos:
677
 [3]
Given Kudos: 1
Location: United States (CA)
Concentration: Finance, Strategy
WE:Investment Banking (Finance: Venture Capital)
Posts: 167
Kudos: 677
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
i managed to get this correct by implementing a shorter method. not sure if this can be applied to other/similar problems, so lmk what you think:

GIVEN-- 6:10:15:31
CONSTRAINT: can only remove nuts from ONE jar

i. 1 : 2 : 3

- 1:2:3:6 (total).
NOTICE YOU CAN MULTIPLY BY 5 (to get us as close to 31 as possible).
- Result: 5:10:15:30.
* We need to make the following adjustments: 1 (6 is missing 1, giving us "5" in this example. Therefore, only removing nut from ONE jar). 2:3 is the same proportion as 10:15. CORRECT.

ii. 2 : 3 : 4

- 2:3:4:9 (total).
NOTICE YOU CAN MULTIPLY BY 3 (to get us as close to 31 as possible).
- Result: 6:9:12:27.
* We need to make the following adjustments: (9 should be "10". 12 should be "15". Therefore, need to remove nuts from TWO jars). INCORRECT.

iii. 4 : 7 : 10

- 4:7:10:21
DO NOT NEED TO MULTIPLY BY ANYTHING B/C MULTIPLYING 2X WOULD GIVE YOU SAME DIFFERENCE (+/- 10)
- Result: same
* We need to make the following adjustments: (4 should be "5". 7 should be "10". 10 should be "15". Therefore, need to remove nuts from THREE jars). INCORRECT.

Again, please let me know your thoughts! If this was helpful, kudos please :)
avatar
Praveen123B
Joined: 25 Aug 2017
Last visit: 25 Aug 2017
Posts: 1
Own Kudos:
1
 [1]
Posts: 1
Kudos: 1
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
As always, get it from answer,

Given:
P:C:A = 6x:10x:15x
Some nuts removed from one of three types
Which of the following be the ratio?

i. 1 : 2 : 3

ii. 2 : 3 : 4

iii. 4 : 7 : 10

From the given ratio we need to get the above three answer,
NOTE: all the number should be divisible by common number(dividend)
Let's say some quantity removed from pecans, then we need to figure out the divisor divisible by common dividend

i) if removed 1 from 6 changes to 5 =>5:10:15 = 1:2:3
SATISFIED
ii) if anything removed from cashew, we not going to get divisor that is divisible by common dividend
NOT SATISFIED
iii) if removed a number we can able to solve,
OPTION 1:- 6:10:14 = 3:5:7
whatever may the number we get reduced still we gonna get same amount of peacans and cashew.
NOT SATISFIED

Only satisfied option is 1

Answer will be 'A'
User avatar
Will2020
User avatar
Current Student
Joined: 24 Jan 2017
Last visit: 04 Mar 2022
Posts: 139
Own Kudos:
50
 [2]
Given Kudos: 1,120
Location: Brazil
Concentration: Entrepreneurship, Strategy
GPA: 3.2
WE:Consulting (Healthcare/Pharmaceuticals)
Products:
Posts: 139
Kudos: 50
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
cheapjasper
Official Answer on Manhattanprep.

To solve this question, it’s necessary to understand that if only one kind of nut is removed, the ratio of the two remaining nuts must remain unchanged. That means our correct answers must have a ratio of two nuts that corresponds to one of the nut to nut ratios we started with.

i. The ratio 2 : 3 is the same as the given ratio 10 : 15. If one pecan were removed, the new ratio would be 5 : 10 : 15, or 1 : 2 : 3.

ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.

iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.

The correct answer is (A).

Your answer is incomplete. Here is the Manhattan complete explanation:

To solve this question, it’s necessary to understand that if only one kind of nut is removed, the ratio of the two remaining nuts must remain unchanged. In other words, correct answers must have a ratio of two nuts that corresponds to one of the original nut to nut ratios.

Case 1: The number of pecans and cashews stay the same; almonds change.
6 : 10 : __
3 : 5 : __

Case 2: The number of pecans and almonds stay the same; cashews change.
6 : __ : 15
2 : __ : 5

Case 3: The number of cashews and almonds stay the same; pecans change.
__ : 10 : 15
__ : 2 : 3

Next, check to see whether any of the new ratios match.

I. The ratio of cashews to almonds of __ : 2 : 3 is the same as the ratio in Case 3 (pecans change). The ratio 1 : 2 : 3 would be equivalent to the ratio of 5 : 10 : 15. Because the original ratio was 6 : 10 : 15, this new ratio can be found by removing one pecan. Eliminate answer choices (B), (C), and (E).

Skip II. None of the remaining answer choices have roman numeral II as an option. However, note that none of the pairs of nuts currently have a ratio that matches any in this option.

III. The ratio 4 : __ : 10 is a multiple of the ratio 2 : __ : 5. Because the ratio of pecans to almonds must be in the ratio of 6 : 15 and 4 : 10, find a common multiple. The ratio 24 : __ : 60 would work for both.

Original New
6 : 10 : 15 4 : 7 : 10
24 : 40 : 60 24 : 42 : 60
The new ratio results from an increase in the number of cashews; eliminate choice (D).

The correct answer is (A).
avatar
cchen679
avatar
Current Student
Joined: 14 Jun 2017
Last visit: 20 Jul 2023
Posts: 14
Own Kudos:
Given Kudos: 193
Location: United States (MD)
Concentration: Technology, General Management
GMAT 1: 730 Q49 V40
GPA: 2.72
WE:General Management (Telecommunications)
GMAT 1: 730 Q49 V40
Posts: 14
Kudos: 39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For case #3 4:7:10 -- why does that not work? If each is multiplied by 1.5 and we remove from the middle, then it would match
User avatar
fskilnik
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,694
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cchen679
For case #3 4:7:10 -- why does that not work? If each is multiplied by 1.5 and we remove from the middle, then it would match
Hi cchen679 ,

In my solution (below) the reason for this impossibility will become explicit.

Regards,
Fabio.
User avatar
fskilnik
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,694
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cheapjasper
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
\(?\,\,\,:\,\,\,p:c:a\,\,{\rm{possible}}\,\,\left( {{\rm{when}}\,\,{\rm{some}}\,\,{\rm{nuts}}\,\,{\rm{of}}\,\,{\rm{one}}\,\,{\rm{type}}\,\,{\rm{removed}}} \right)\)


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

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


\(\left( {\rm{I}} \right)\,\,\,p:c:a = 1:2:3\,\,\,\, \Rightarrow \,\,\,{\rm{possible}}\,\,\left( {k = 1,\,\,{\rm{take}}\,\,1\,\,{\rm{pecan}}\,\,{\rm{nut}}\,\,{\rm{out}}\,\,\,\, \Rightarrow \,\,\,\,\left( {p,c,a} \right) = \left( {5,10,15} \right)} \right)\)

\(\,\,\, \Rightarrow \,\,\,\,\,{\rm{refute}}\,\,\left( {\rm{B}} \right),\left( {\rm{C}} \right),\left( {\rm{E}} \right)\)


\(\left( {{\rm{III}}} \right)\,\,p:c:a = 4:7:10\,\,\,\,\mathop \Rightarrow \limits^{\left( {\text{below}} \right)} \,\,\,{\rm{impossible:}}\,\,\,\)

\({\rm{some}}\,\,p\,\,{\rm{out}}\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{\\
\,\left( {p,c,a} \right) = \left( {6k - {\rm{some}},10k,15k} \right) \hfill \cr \\
\,{2 \over 3} = {{10k} \over {15k}} = {c \over a} \ne {7 \over {10}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,k,{\rm{some}}\,\, > 0\,} \right]\)

\({\rm{some}}\,\,c\,\,{\rm{out}}\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{\\
\,\left( {p,c,a} \right) = \left( {6k,10k - {\rm{some}},15k} \right) \hfill \cr \\
\,{4 \over 7} = {p \over c} = {{6k} \over {10k - {\rm{some}}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,40k - 4 \cdot {\rm{some}} = 42k\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\, \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,k,{\rm{some}}\,\, > 0\,} \right]\)

\({\rm{some}}\,\,a\,\,{\rm{out}}\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{\\
\,\left( {p,c,a} \right) = \left( {6k,10k,15k - {\rm{some}}} \right) \hfill \cr \\
\,{4 \over 7} = {p \over c} = {{6k} \over {10k}} = {3 \over 5}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\, \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,k,{\rm{some}}\,\, > 0\,} \right]\)


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.
User avatar
mangamma
Joined: 25 Dec 2018
Last visit: 12 Jul 2023
Posts: 506
Own Kudos:
1,752
 [1]
Given Kudos: 994
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE:Engineering (Consulting)
Posts: 506
Kudos: 1,752
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cheapjasper
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


To solve this question, it’s necessary to understand that if only one kind of nut is removed, the ratio of the two remaining nuts must remain unchanged. In other words, correct answers must have a ratio of two nuts that corresponds to one of the original nut to nut ratios.

Case 1: The number of pecans and cashews stay the same; almonds change.
6 : 10 : __
3 : 5 : __

Case 2: The number of pecans and almonds stay the same; cashews change.
6 : __ : 15
2 : __ : 5

Case 3: The number of cashews and almonds stay the same; pecans change.
__ : 10 : 15
__ : 2 : 3

Next, check to see whether any of the new ratios match.

I. The ratio of cashews to almonds of __ : 2 : 3 is the same as the ratio in Case 3 (pecans change). The ratio 1 : 2 : 3 would be equivalent to the ratio of 5 : 10 : 15. Because the original ratio was 6 : 10 : 15, this new ratio can be found by removing one pecan. Eliminate answer choices (B), (C), and (E).

Skip II. None of the remaining answer choices have roman numeral II as an option. However, note that none of the pairs of nuts currently have a ratio that matches any in this option.

III. The ratio 4 : __ : 10 is a multiple of the ratio 2 : __ : 5. Because the ratio of pecans to almonds must be in the ratio of 6 : 15 and 4 : 10, find a common multiple. The ratio 24 : __ : 60 would work for both.

Original New
6 : 10 : 15 4 : 7 : 10
24 : 40 : 60 24 : 42 : 60
The new ratio results from an increase in the number of cashews; eliminate choice (D).

The correct answer is (A).
avatar
jamiedimonn
Joined: 12 Jul 2024
Last visit: 12 Jul 2025
Posts: 34
Own Kudos:
Given Kudos: 40
Posts: 34
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel, could you explain this in simpler way!!
Moderators:
Math Expert
102638 posts
PS Forum Moderator
690 posts