It is currently 19 Feb 2018, 11:29

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain store sold pens for $0.35 each and pencils for$0.

Author Message
TAGS:

### Hide Tags

Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 514
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
A certain store sold pens for $0.35 each and pencils for$0. [#permalink]

### Show Tags

24 Oct 2013, 08:57
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:35) correct 28% (01:48) wrong based on 216 sessions

A certain store sold pens for $0.35 each and pencils for$0.25 each. If a customer purchased both pens and pencils from the store for a total of $2.50, what total number of pens and pencils did the customer purchase? (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 GH-04.05.13 - OE to follow [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 43810 Re: A certain store sold pens for$0.35 each and pencils for $0. [#permalink] ### Show Tags 24 Oct 2013, 09:04 2 This post received KUDOS Expert's post 1 This post was BOOKMARKED avohden wrote: A certain store sold pens for$0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of$2.50, what total number of pens and pencils did the customer purchase?

(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

GH-04.05.13 - OE to follow

$$0.35x+25y=2.5$$;
$$35x+25y=250$$;
$$7x+5y=50$$.

Since x and y must be positive integers, then only one solution exists: x=5 and y=3 --> x+y=8.

_________________
Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 514
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: A certain store sold pens for $0.35 each and pencils for [#permalink] ### Show Tags 27 Oct 2013, 09:41 1 This post received KUDOS Official Explanation Answer: A Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y However, that's the only equation we get, so we can't solve for x and y this way. There would be an infinite number of possible values of x and y. Instead, we must use an intelligent version of guessing and checking. Since at least one pencil and one pen is purchased, the customer must spend at least$2.25 ($2.50 minus$0.25) on pens. There are six possible numbers of pens that fit that requirement:

1 pen: $0.35 2 pens:$0.70
3 pens: $1.05 4 pens:$1.40
5 pens: $1.75 6 pens:$2.10

Many of those aren't applicable here, though. For instance, if the customer bought 6 pens, he would need to spend an additional $0.40 on pencils. At$0.25 per pencil, that's impossible. Consider each of the other 5:

1 pen: $2.15 on pencils 2 pens:$1.80 on pencils
3 pens: $1.45 on pencils 4 pens:$1.10 on pencils
5 pens: $0.75 on pencils Only the last of these works.$0.75 is 3 pencils for $0.25 each. That's 5 pens and 3 pencils for a total of 8 pens and pencils. Choice (A) is correct. Senior Manager Joined: 02 Dec 2014 Posts: 370 Location: Russian Federation Concentration: General Management, Economics GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications) Re: A certain store sold pens for$0.35 each and pencils for $0. [#permalink] ### Show Tags 10 Mar 2015, 02:16 A certain store sold pens for$0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of$2.50, what total number of pens and pencils did the customer purchase?

(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

If you don't want to pick up numbers here is one more solution.
Let x is a number of penc and y is a number of pencils, Then we have that 0.35x+0.25y=2.5 Multiply by 100 both parts to get 35x+25y=250 ==>7x+5y=50. Now let's factor out 5 ==>5((7/5)x+y)=50. Divide by 5 to get (7/5)x+y=10. Now since both x and y are integers it is clear that x is a multiple of 5. So we can pick numbers. Lets start with x=5 ==> y=3 and x+y=8. Looks good but let's try x=10. Now we have y=-4 which is impossible. Hence x=5,y=3 and answer is A. Hope it is clear
_________________

"Are you gangsters?" - "No we are Russians!"

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2181
Location: United States (CA)
Re: A certain store sold pens for $0.35 each and pencils for$0. [#permalink]

### Show Tags

09 Oct 2017, 16:54
avohden wrote: