Last visit was: 19 Nov 2025, 06:25 It is currently 19 Nov 2025, 06:25
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,388
Own Kudos:
778,226
 [73]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,388
Kudos: 778,226
 [73]
Juana mailed at least one letter on each day last week. Was the total 07 Aug 2023, 10:00
3
Kudos
Add Kudos
70
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

67% (01:13) correct 33% (01:33) wrong based on 1121 sessions

History

Date
Time
Result
Not Attempted Yet
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
SaquibHGMATWhiz
User avatar
GMATWhiz Representative
Joined: 23 May 2022
Last visit: 12 Jun 2024
Posts: 623
Own Kudos:
724
 [23]
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Expert
Expert reply
GMAT 1: 760 Q51 V40
Posts: 623
Kudos: 724
 [23]
Juana mailed at least one letter on each day last week. Was the total 14 Nov 2023, 10:29
17
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
Ittiphatkluayy
JeffTargetTestPrep
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.

The number of letters was positive on each day.

We need to answer the question:

Is ℓ₁ + ℓ₂ + ℓ₃ + ℓ₄ + ℓ₅ + ℓ₆ + ℓ₇ > 27 ?

Statement One Alone:

=> Juana mailed fewer than 8 letters on each of the 7 days.

Let’s imagine the daily numbers of letters in chronological order.

If {7, 7, 7, 7, 7, 7, 7}, then the answer is Yes.

Whereas, if {1, 1, 1, 1, 1, 1, 1}, then the answer is No.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Juana mailed a different number of letters on any two of the 7 days.

If {1, 2, 3, 4, 5, 6, 7}, then the sum is 28, and the answer is Yes. Since 28 is the least possible sum for different numbers of letters, we have a definite Yes answer.

Statement two is sufficient.

Answer: B

Could you explain more regarding the meaning of "on any two of the 7 days" in Statement (2)
Show more

Ittiphatkluayy Matsu12

The phrase "different number of letters on any two of the 7 days" means that Juana did not mail the same number of letters on any 2 days OR the number of letters she mailed in 7 days were all different

If she mails \(ℓ₁, ℓ₂, ℓ₃, ℓ₄, ℓ₅, ℓ₆\) and \(ℓ₇\) letters on seven days respectively, then \(ℓ₁≠ ℓ₂≠ ℓ₃≠ ℓ₄≠ ℓ₅≠ ℓ₆ ≠ ℓ₇\)

Hope this helps :)
User avatar
raianshul
User avatar
Joined: 25 Feb 2020
Last visit: 30 Oct 2023
Posts: 26
Own Kudos:
78
 [8]
Given Kudos: 81
Posts: 26
Kudos: 78
 [8]
Juana mailed at least one letter on each day last week. Was the total 07 Aug 2023, 10:34
3
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
Jauna can mail 1 letter each on 7 days, sum = 7
Jauna can mail 7 letters each on 7 days, sum = 49
so not sufficient.
(2) Juana mailed a different number of letters on any two of the 7 days.
Jauna has mailed at least one letter (given)
so minimum number of letters Jauna can sent = 1+2+3+4+5+6+7 =28 which is greater than 27, hence sufficient.

So B should be the Answer. IMO
General Discussion
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,977
Own Kudos:
8,389
 [2]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,977
Kudos: 8,389
 [2]
Juana mailed at least one letter on each day last week. Was the total 31 Aug 2023, 07:44
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.
Show more

The number of letters was positive on each day.

We need to answer the question:

Is ℓ₁ + ℓ₂ + ℓ₃ + ℓ₄ + ℓ₅ + ℓ₆ + ℓ₇ > 27 ?

Statement One Alone:

=> Juana mailed fewer than 8 letters on each of the 7 days.

Let’s imagine the daily numbers of letters in chronological order.

If {7, 7, 7, 7, 7, 7, 7}, then the answer is Yes.

Whereas, if {1, 1, 1, 1, 1, 1, 1}, then the answer is No.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Juana mailed a different number of letters on any two of the 7 days.

If {1, 2, 3, 4, 5, 6, 7}, then the sum is 28, and the answer is Yes. Since 28 is the least possible sum for different numbers of letters, we have a definite Yes answer.

Statement two is sufficient.

Answer: B
User avatar
Ittiphatkluayy
User avatar
Joined: 21 Nov 2020
Last visit: 15 Mar 2024
Posts: 1
Own Kudos:
3
 [3]
Posts: 1
Kudos: 3
 [3]
Juana mailed at least one letter on each day last week. Was the total 24 Sep 2023, 18:01
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JeffTargetTestPrep
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.

The number of letters was positive on each day.

We need to answer the question:

Is ℓ₁ + ℓ₂ + ℓ₃ + ℓ₄ + ℓ₅ + ℓ₆ + ℓ₇ > 27 ?

Statement One Alone:

=> Juana mailed fewer than 8 letters on each of the 7 days.

Let’s imagine the daily numbers of letters in chronological order.

If {7, 7, 7, 7, 7, 7, 7}, then the answer is Yes.

Whereas, if {1, 1, 1, 1, 1, 1, 1}, then the answer is No.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Juana mailed a different number of letters on any two of the 7 days.

If {1, 2, 3, 4, 5, 6, 7}, then the sum is 28, and the answer is Yes. Since 28 is the least possible sum for different numbers of letters, we have a definite Yes answer.

Statement two is sufficient.

Answer: B
Show more

Could you explain more regarding the meaning of "on any two of the 7 days" in Statement (2)
User avatar
sanebeyondone
User avatar
Joined: 22 Sep 2023
Last visit: 15 Mar 2025
Posts: 29
Own Kudos:
28
 [3]
Given Kudos: 143
Posts: 29
Kudos: 28
 [3]
Juana mailed at least one letter on each day last week. Was the total 27 Jan 2024, 01:25
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What if I say
"on any three of the 7 days"
Does this has any meaning?
or just the same as
"on any two of the 7 days"?

Posted from my mobile device
User avatar
GMATCoachBen
User avatar
Joined: 21 Mar 2017
Last visit: 18 Nov 2025
Posts: 465
Own Kudos:
2,719
 [4]
Given Kudos: 210
Status:Professional GMAT Trainer
Affiliations: GMAT Coach
Location: United States (WA)
GMAT Focus 1: 775 Q87 V90 DI88 (Online)
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
Expert
Expert reply
GMAT Focus 1: 775 Q87 V90 DI88 (Online)
GMAT 5: 780 Q51 V48
Posts: 465
Kudos: 2,719
 [4]
Juana mailed at least one letter on each day last week. Was the total 31 Mar 2024, 21:31
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
 
sanebeyondone
What if I say
"on any three of the 7 days"
Does this has any meaning?
or just the same as
"on any two of the 7 days"?

Posted from my mobile device
Show more
sanebeyondone ­No, "a different number on any three of the 7 days" has no meaning, and wouldn't be used on the GMAT or normal English.

(2) Juana mailed a different number of letters on any two of the 7 days.

@Matsu12  "a different number on ANY two ____" means that none of the numbers are the same. This has the same meaning as the wording we may see in other problems, "7 different integers are selected".

Therefore, the minimum possible sum is the evenly spaced set, 1+2+3+4+5+6+7, since the stem says she mailed "at least one letter on each day".
The fastest way to calculate a sum of consecutive integers is S = AN. 
For an evenly spaced set, A = Average = Median = ((First + Last) / 2)
N = the number of numbers
S = AN = 4*7 = 28, so statement (2) is sufficient.

 ­
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,993
 [2]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,993
 [2]
Juana mailed at least one letter on each day last week. Was the total 08 Apr 2024, 22:31
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
 
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.
Show more
­
Total letters mailed is more than 7 (at least 1 letter each day)
Question: Is Total > 27 ?

(1) Juana mailed fewer than 8 letters on each of the 7 days.

This means she mailed at most 7 letters each day. So max she mailed 49 letters total. We don't know whether total was less or more than 27.
Not Sufficient

(2) Juana mailed a different number of letters on any two of the 7 days.

So minimum number of letters she mailed is 1 + 2 + 3 +... + 7
Sum of n consecutive integers starting from 1 is given by \(\frac{n(n+1)}{2} = \frac{7*8}{2} = 28\)
So she mailed at least 28 letters. Sufficient to say that Yes, total is more than 27. 

Answer (B)
 
User avatar
Spoorthii
User avatar
Joined: 03 Apr 2023
Last visit: 09 Dec 2024
Posts: 17
Own Kudos:
3
Given Kudos: 125
Location: India
Schools: MIT '27
GPA: 4.0
Schools: MIT '27
Posts: 17
Kudos: 3
Juana mailed at least one letter on each day last week. Was the total 13 Apr 2024, 08:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
KarishmaB

Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.
­
Total letters mailed is more than 7 (at least 1 letter each day)
Question: Is Total > 27 ?

(1) Juana mailed fewer than 8 letters on each of the 7 days.

This means she mailed at most 7 letters each day. So max she mailed 49 letters total. We don't know whether total was less or more than 27.
Not Sufficient

(2) Juana mailed a different number of letters on any two of the 7 days.

So minimum number of letters she mailed is 1 + 2 + 3 +... + 7
Sum of n consecutive integers starting from 1 is given by \(\frac{n(n+1)}{2} = \frac{7*8}{2} = 28\)
So she mailed at least 28 letters. Sufficient to say that Yes, total is more than 27. 

Answer (B)

 
Show more
­Statement (2) - Any two of the 7 days could mean same number of letters for 5 days and different numbers for the rest of the days. Why is it different for all the days?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,993
 [3]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,993
 [3]
Juana mailed at least one letter on each day last week. Was the total 13 Apr 2024, 08:51
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Spoorthii

KarishmaB

Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.
­
Total letters mailed is more than 7 (at least 1 letter each day)
Question: Is Total > 27 ?

(1) Juana mailed fewer than 8 letters on each of the 7 days.

This means she mailed at most 7 letters each day. So max she mailed 49 letters total. We don't know whether total was less or more than 27.
Not Sufficient

(2) Juana mailed a different number of letters on any two of the 7 days.

So minimum number of letters she mailed is 1 + 2 + 3 +... + 7
Sum of n consecutive integers starting from 1 is given by \(\frac{n(n+1)}{2} = \frac{7*8}{2} = 28\)
So she mailed at least 28 letters. Sufficient to say that Yes, total is more than 27. 

Answer (B)



 
­Statement (2) - Any two of the 7 days could mean same number of letters for 5 days and different numbers for the rest of the days. Why is it different for all the days?
Show more
"­mailed a diferent number of letters on any two of the 7 days" means if you pick ANY 2 days of the 7, the number of letters will be different. Hence number of letters has to be different on all days. 

"mailed a diferent number of letters on two of the days" means that on some specific 2 days the number of letters was different. ­We don't know about other days.
User avatar
Aslamkhanshovon
User avatar
Joined: 22 Mar 2023
Last visit: 15 Oct 2025
Posts: 9
Own Kudos:
3
 [2]
Given Kudos: 387
Posts: 9
Kudos: 3
 [2]
Juana mailed at least one letter on each day last week. Was the total 08 Jun 2024, 11:02
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
any two of seven days means ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,388
Own Kudos:
778,226
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,388
Kudos: 778,226
Juana mailed at least one letter on each day last week. Was the total 08 Jun 2024, 11:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Aslamkhanshovon
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.

any two of seven days means ?
Show more
­The phrase "any two of the seven days" means that Juana mailed a different number of letters on each day, so no two days had the same count of mailed letters.
User avatar
ach12345
User avatar
Joined: 17 Jan 2025
Last visit: 08 May 2025
Posts: 2
Given Kudos: 1
Posts: 2
Kudos: 0
Juana mailed at least one letter on each day last week. Was the total 03 Apr 2025, 04:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.
Show more

My question here is why is (2) alone SUFF? Most responses focus on it being the least possible, but where in the question does it ask that?

Using (2):

(1,2,3,4,5,6,7,8) fulfills condition 2 and results in more than 27 letters sent; total is 28.
(2,3,4,5,6,7,8,9) fulfills condition 2 as well and results in more than 27 letters sent; total is 44

Here we get two different solutions which means two should not be sufficient!

Using both we can limit ourselves to the first solution and only get one answer for the total number of letters.
User avatar
sahilsehdev97
User avatar
Joined: 24 Aug 2024
Last visit: 18 Nov 2025
Posts: 12
Given Kudos: 3
Posts: 12
Kudos: 0
Juana mailed at least one letter on each day last week. Was the total 24 Jun 2025, 02:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It's the "different number of letters on any TWO of the 7 days" that is highly confusing to me. This was how I saw it:
1+2+3+4+5+6+7 = 28, YES because 28>27
1+2+3+4+5+3+2 = 20, NO, because 20>27 and it satisfies the fact that she mailed at least 1 letter.
Why are we assuming that the number of letters are different on each day for the other 5 days? What if Juana repeated the number of letters on a particular day. Nowhere does it say that Juana mailed different letters on each day.
This is very confusing, because some DS questions involve considering all possibilities in order to answer the question, but in this case we are just assuming that she is mailing a different number of letters on each day. I'm open to all explanations. Thanks :)

JeffTargetTestPrep
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.

The number of letters was positive on each day.

We need to answer the question:

Is l1 + l2 + l3 + l4 + l5 + l6 + l7 > 27 ?

Statement One Alone:

=> Juana mailed fewer than 8 letters on each of the 7 days.

Let’s imagine the daily numbers of letters in chronological order.

If {7, 7, 7, 7, 7, 7, 7}, then the answer is Yes.

Whereas, if {1, 1, 1, 1, 1, 1, 1}, then the answer is No.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Juana mailed a different number of letters on any two of the 7 days.

If {1, 2, 3, 4, 5, 6, 7}, then the sum is 28, and the answer is Yes. Since 28 is the least possible sum for different numbers of letters, we have a definite Yes answer.

Statement two is sufficient.

Answer: B
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,388
Own Kudos:
778,226
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,388
Kudos: 778,226
Juana mailed at least one letter on each day last week. Was the total 24 Jun 2025, 06:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ach12345
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.

My question here is why is (2) alone SUFF? Most responses focus on it being the least possible, but where in the question does it ask that?

Using (2):

(1,2,3,4,5,6,7,8) fulfills condition 2 and results in more than 27 letters sent; total is 28.
(2,3,4,5,6,7,8,9) fulfills condition 2 as well and results in more than 27 letters sent; total is 44

Here we get two different solutions which means two should not be sufficient!

Using both we can limit ourselves to the first solution and only get one answer for the total number of letters.
Show more

You're missing the point. We are not asked to find the exact number of letters. The question is whether the total is greater than 27. Statement (2) guarantees that the totals possible are 28 or more, so that's a definite Yes. That makes it sufficient.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,388
Own Kudos:
778,226
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,388
Kudos: 778,226
Juana mailed at least one letter on each day last week. Was the total 24 Jun 2025, 06:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sahilsehdev97
It's the "different number of letters on any TWO of the 7 days" that is highly confusing to me. This was how I saw it:
1+2+3+4+5+6+7 = 28, YES because 28>27
1+2+3+4+5+3+2 = 20, NO, because 20>27 and it satisfies the fact that she mailed at least 1 letter.
Why are we assuming that the number of letters are different on each day for the other 5 days? What if Juana repeated the number of letters on a particular day. Nowhere does it say that Juana mailed different letters on each day.
This is very confusing, because some DS questions involve considering all possibilities in order to answer the question, but in this case we are just assuming that she is mailing a different number of letters on each day. I'm open to all explanations. Thanks :)
Show more

Your doubt is addressed above, but here it is again. You're misunderstanding the wording. Statement (2) clearly says Juana mailed a different number of letters on any two of the 7 days, which means no two days had the same number. So repetition is not allowed.

That forces the 7 numbers to all be distinct, and since she mailed at least one each day, the smallest possible total is 1+2+3+4+5+6+7 = 28, which is greater than 27. So the answer is always Yes, making the statement sufficient.
User avatar
agnivakolay
User avatar
Joined: 15 Feb 2024
Last visit: 04 Sep 2025
Posts: 1
Given Kudos: 3
Location: India
Posts: 1
Kudos: 0
Juana mailed at least one letter on each day last week. Was the total 02 Aug 2025, 13:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It says different in ANY two of the days (NOT any 2 Consecutive days) . So randomly if you pick 2 days, they shouldn't have same no of letters
sahilsehdev97
It's the "different number of letters on any TWO of the 7 days" that is highly confusing to me. This was how I saw it:
1+2+3+4+5+6+7 = 28, YES because 28>27
1+2+3+4+5+3+2 = 20, NO, because 20>27 and it satisfies the fact that she mailed at least 1 letter.
Why are we assuming that the number of letters are different on each day for the other 5 days? What if Juana repeated the number of letters on a particular day. Nowhere does it say that Juana mailed different letters on each day.
This is very confusing, because some DS questions involve considering all possibilities in order to answer the question, but in this case we are just assuming that she is mailing a different number of letters on each day. I'm open to all explanations. Thanks :)

JeffTargetTestPrep
Bunuel
Juana mailed at least one letter on each day last week. Was the total number of letters that Juana mailed on the 7 days greater than 27?

(1) Juana mailed fewer than 8 letters on each of the 7 days.
(2) Juana mailed a different number of letters on any two of the 7 days.

The number of letters was positive on each day.

We need to answer the question:

Is l1 + l2 + l3 + l4 + l5 + l6 + l7 > 27 ?

Statement One Alone:

=> Juana mailed fewer than 8 letters on each of the 7 days.

Let’s imagine the daily numbers of letters in chronological order.

If {7, 7, 7, 7, 7, 7, 7}, then the answer is Yes.

Whereas, if {1, 1, 1, 1, 1, 1, 1}, then the answer is No.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Juana mailed a different number of letters on any two of the 7 days.

If {1, 2, 3, 4, 5, 6, 7}, then the sum is 28, and the answer is Yes. Since 28 is the least possible sum for different numbers of letters, we have a definite Yes answer.

Statement two is sufficient.

Answer: B
Show more
Moderators:
Bunuel
Math Expert
105388 posts
kingbucky
496 posts