Of the N candies in a bag, some are peppermint and the rest are

Question

Of the N candies in a bag, some are peppermint and the rest are spearmint.What is the value of N?

(1) If 1 peppermint candy were removed from the N candies, 1/5 of the remaining candies would be peppermint.

(2) If 2 spearmint candies were removed from the N candies, 1/4 of the remaining candies would be peppermint.

ID 02716

mau5 · Accepted Answer

The number of Peppermint candies = x, Of Spearmint= N-x.

From F.S 1 , we have (N-1)/5 = (x-1)

or 5x - N = 4. Insufficient.

From F.S 2, we have (N-2)/4 = x

or N - 4x = 2. Insufficient.

Taken together, we can get a particular value for N. Sufficient.

C.

krrish · Answer

Stmt1: 2 unknowns one equation
stmt2 : 2 unknowns and one equation

combine both 2 equations and 2 unknowns so C

stne · Answer

can any body help me here, may be I am missing something but even with using both the statements I am not able to get the value of N

P +S= N

1)  \frac{1(N-1)}{5}= P-1 \rightarrow N= 5P-4

2)  \frac{1(N-2)}{4} = S-2 \rightarrow N= 4S-6

Now can anybody show me how to get N ?

Appreciate your help

Thanks

mau5 · Answer

The correct equation for the second fact statement would be:

\frac{1(N-2)}{4} = P

Hope this helps

stne · Answer

Thundering Typhoons! Cue for me to take a break.
Thank you +1

1)  \frac{1(N-1)}{5}= P-1 \rightarrow N= 5P- 4  ...1
2)  \frac{1(N-2)}{4} =P \rightarrow N= 4P+2  ...2

4P+2 =5P-4 
p=6 ( Put in 1 or 2 )

Then N= 26

erikvm · Answer

I put E for this question because I mismanaged to translate the word problem into math.

in (2) I couldnt get all the variables to match into one equation. Why is "S" never part of the equation?

minwoswoh · Answer

This problem can easily be solved by following the rule that states that to solve for a variable we need the same number of distinct, linear equations as variables.
I hope you find my approach "elegant"

Question (Given)  
N = p + s
N = ?
We have 3 variables and 1 equation

Statement 1  
(p - 1)/s = 1/4
When we combine this statement with the given info, we yield 3 variables and 2 equations. Insufficient

Statement 2  
(s - 2)/p = 3/1
When we combine this statement with the given info, we yield 3 variables and 2 equations. Insufficient

Therefore, we need to combine both statements to get 3 variables and 3 equations. Of course, no need to do the actual calculation.
 Correct Answer = C

Bonus Track : In case you REALLY want to know the value of variables: p = 6 and s = 20, thereby N = 26.

okay · Answer

I am having an issue translating Statement 2 for some reason. I am fine on S1

On Statement 2, could I not do  \frac{(s-2)}{(n-2)}  =  \frac{3}{4}  (in that 3/4 of remaining candies are Spearmint)?

chetan2u · Answer

yes you can.. it also leads to same..

\frac{(s-2)}{(n-2)}  =  \frac{3}{4} ..
now s-2=(n-2)-p..
substitute
 \frac{(s-2)}{(n-2)}=\frac{(n-2)-p}{n-2}=\frac{n-2}{n-2}-\frac{p}{n-2}=1-\frac{p}{n-2}=\frac{3}{4} ...
 \frac{p}{n-2}=1-\frac{3}{4}=\frac{1}{4} 
now these is same as the statement II

dabaobao · Answer

N = P + S = ?

1) (P - 1)/S = 1/4
4P - S = 4
Not Sufficient

2) P/(S-2) = 1/3
3P - S = -2
Not Sufficient

1+2)
2 equations and 2 unknowns. Can be solved to get P + S = 6 + 20 = 26
Sufficient

ANSWER: C

Basshead · Answer

N = P + S

(1) tells us  \frac{1}{5} (n-1) = P -1

INSUFFICIENT.

(2) tell us  \frac{1}{4} (n-2) = P

INSUFFICIENT.

(1&2) Combining the two equation above, we can solve for N. SUFFICIENT.

Answer is C.

adityasuresh · Answer

Of the N candies in a bag, some are peppermint and the rest are spearmint.What is the value of N?

(1) If 1 peppermint candy were removed from the N candies,1/5 of the remaining candies would be peppermint.

(2) If 2 spearmint candies were removed from the N candies, 1/4 of the remaining candies would be peppermint.

Total N = No of peppermint + No of Spearmint

Fact 1:  P - 1/N - 1  =  1/5  (Remaining are peppermint) N.S 1 Equation 2 variables
Fact 2:  P/N - 2  =  1/4  (Since there are only 2 quantities mentioned it makes things easier if we keep equations from the pov of peppermint, if 2 spearmint candies are removed it  implies that the no of peppermint candies is unchanged , as mentioned in the Fact 2 the remaining 1/4th are peppermint)
N.S same as 1
Combining F1 & F2
2 Equations 2 variables sufficient 
 C

Sa800 · Answer

Can someone provide a detailed explanation? I set the thing up like this for (1)

(Px-1/Sx) = (1x/5x)

i used the x because when you multiply the ratio P/S by x/x you will get the actual number of the candies instead of just a ratio….same with the 1/5

so px/Sx represents the actual number of peppermint and spearmint candies and when you simplify it, you end up with the original P/S ratio

any way

I dont arrive at the answer you guys arrive in. I dont get the 1/4

the problem clearly says 1/5

after solving the equation i get x = (1)/(5p-s)

what am i doing wrong?

Bunuel · Answer

You are using the ratio multiplier, which is not needed ihere. Check the esiest solution here: https://gmatclub.com/forum/of-the-n-can ... l#p1202968

Sa800 · Answer

another question… why do you guys write (P-1)=(1/5)(N-1)

for the first choice…

If we already deducted 1 candy from the peppermint then doesnt the (N-1) already account for it?

in other words, why isnt the equation P= (1/5)(N-1)…?

P= (1/5)(N-1)would suggest that if you take away one from the total then the fifth of the remaining is peppermint…right?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Of the N candies in a bag, some are peppermint and the rest are

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Of the N candies in a bag, some are peppermint and the rest are

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards