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

 It is currently 18 Jun 2019, 20:10

### 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

# Ralph is giving out Valentine’s Day cards to his friends.

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

### Hide Tags

Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 464
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 02:24
3
7
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:44) correct 48% (02:05) wrong based on 176 sessions

### HideShow timer Statistics

Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

_________________
Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 55670
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 02:52
6
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.

Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: $$\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}$$.

(2) says that: $$\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}$$ --> $$\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}$$, thus $$\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}$$.

Does this make sense?
_________________
##### General Discussion
Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 464
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 02:27
1
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.
_________________
Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9330
Location: Pune, India
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 02:47
2
1
honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.

I think your interpretation of statement 2 is not correct.

(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

This means if the number of friends is doubled, the number of cards would be less than the number of friends. That is, each friend will not get at least 1 card. You will not be able to distribute the cards such that each friend gets one card.
So we cannot have 7 people and 21 cards.
Say we have 10 friends and 20 cards. If you double the number of friends, the number of friends is 20 and each friend can still get a card. So this is not the case. You must have had 20 friends if you have 20 cards/ 30 friends if you have 30 cards, 40 friends if you have 40 cards etc.

So the question is: was the number of cards received by each friend more than one? Answer: No. Each friend got only one card. Statement II alone is sufficient

Answer (B)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 464
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 02:55
Bunuel wrote:
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.

Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: $$\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}$$.

(2) says that: $$\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}$$ --> $$\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}$$, thus $$\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}$$.

Does this make sense?

Yes, Veritas questions have high degree of analytical challenge, I believe they have the best questions among so many brands in the market. I mis interpreted statement B, I have jotted down this question, explanation is amazing.
_________________
Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html
Math Expert
Joined: 02 Sep 2009
Posts: 55670
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 03:02
honchos wrote:
Bunuel wrote:
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.

Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: $$\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}$$.

(2) says that: $$\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}$$ --> $$\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}$$, thus $$\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}$$.

Does this make sense?

Yes, Veritas questions have high degree of analytical challenge, I believe they have the best questions among so many brands in the market. I mis interpreted statement B, I have jotted down this question, explanation is amazing.

Yes, I do agree. VeritasPrep questions are very good.
_________________
Intern
Joined: 28 Mar 2012
Posts: 4
Location: Yugoslavia
Concentration: Accounting, Finance
GPA: 3.75
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

16 Sep 2013, 04:23
1
In my opinion the best way to solve this is to draw --- for example there are 3 friends and 6 cards (once you draw you can see that even if the number of friends doubles everyone still gets one card).

However, if there are 3 friends and 3 cards, if you double the number of friends there are three friends left without any cards.

So if we remember the statement that everyone has the same number of cards we can conclude that "B" gives us enough information

Hope this helps
Manager
Joined: 28 Sep 2013
Posts: 81
GMAT 1: 740 Q51 V39
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

03 Jan 2014, 06:00
honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.

What is the source of such questions?
_________________
Richa Champion | My GMAT Journey - 470 720 740

Target 760+

Not Improving after Multiple attempts. I can guide You.
Contact me richacrunch2@gmail.com
Math Expert
Joined: 02 Sep 2009
Posts: 55670
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

03 Jan 2014, 06:04
1
crunchboss wrote:
honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.

However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.

What is the source of such questions?

This is VeritasPrep question as indicated here:
It's also mentioned in the posts above.
_________________
Senior Manager
Joined: 06 Aug 2011
Posts: 329
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

03 Jan 2014, 12:45
Nice question...

Statement 1... Its very easy to eliminate this choice. because we dont have information of friends.

Statement 2 .. very tricky.. bt i tuk around 3 mints to manipulate this choice because i was sure there is smthing is this choice that will make it sufficient..My sixth sense

My explantion for option b.. If we double the number and no any friends will get atleast one card, and question stem said that they all have same number of cards, so that means, no anyone has 2 card now.. How ? if each person wud have 2 cards , and if we double the friends still they cud get atleast one.. So this statement is sufficient. Ans is B.

This thing force me to choose option B..
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

22 Oct 2015, 13:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

There are 2 variables (no. of friends, no. of cards given), and 2 equations are given, so there is high chance (C) will be our answer. If we combine the 2 conditions,
the answer to the question becomes 'yes' as 40=8*5 (8 friends get 5 cards each), but 'no' for 40=40*1. Therefore the conditions are insufficient, and the answer becomes (E). The question is weird here...
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Senior Manager
Joined: 12 Aug 2015
Posts: 283
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

06 Dec 2015, 10:16
great algebraic solution by Bunuel, plenty of kudos to you, guru
_________________
KUDO me plenty
Manager
Joined: 10 Apr 2015
Posts: 178
GPA: 3.31
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

06 Apr 2017, 22:42
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
Clearly NS as there is no mention of no. of friends.

(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.
Surely there are less cards than friends if no of friends is doubled.
So, certainly each friend got one card each.

B

_________________
In case you find my posts helpful, give me Kudos. Thank you.
Manager
Status: The darker the night, the nearer the dawn!
Joined: 16 Jun 2018
Posts: 96
Re: Ralph is giving out Valentine’s Day cards to his friends.  [#permalink]

### Show Tags

04 Apr 2019, 01:22
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

Let's say there are 7 Friends and each one gets an equal number of cards: Total #Cards MUST be >= 7.

Now, if we double the friends, i.e., from 7 to 14: NOT everyone will get at least one card ---> Someone will be WITHOUT any card.
Thus, the range of cards MUST be in between 7(including) and 14(excluding), i.e.,
Anything from the set: {7, 8, 9, 10, 11, 12, 13} - Considering JUST the 1st range of possible cards
Another possible set can be {14, 15, 16, 17, 18, 19, 20}

The role of this vital sentence comes in the picture:
Each friend gets the same number of cards and NO cards were leftover.

Since the number of cards received by each of the friends is the SAME since the beginning, the number of cards need to be MULTIPLE of the number of friends.
ELSE, the number of cards received by each of the friends will NOT be the SAME.

Thus, B is sufficient to answer.
_________________
---------------------------------------------------------------------------------
“The trouble is, you think you have time.” – Buddha
Giving Kudos is the best way to encourage and appreciate people.
Re: Ralph is giving out Valentine’s Day cards to his friends.   [#permalink] 04 Apr 2019, 01:22
Display posts from previous: Sort by

# Ralph is giving out Valentine’s Day cards to his friends.

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

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