What is the probability that the month of May will have five Tuesdays?

Question

(A) 2/3
(B) 2/5
(C) 3/5
(D) 3/7
(E) 3/8

Nidzo · Answer

31 days in May. 31/7 = 4 weeks with 3 days remaining. For there to be a 5th Tuesday, then the month must start on either Sunday, Monday or Tuesday. 3/7 of the days of the week.

Answer D

dec2023 · Answer

What is the fastest way to identify the month must start on Sun, Mon, Tues? I am able to find if I test all cases Mon-Sun, but it takes too long

egmat · Answer

dec2023

Looking at your doubt, I can see you understand the concept but need a more efficient approach. Here's the  fastest method  to solve this type of problem:

The Key Pattern Recognition: 
For any 31-day month, remember:  31 = 28 + 3 = 4 	imes 7 + 3

This means May has exactly 4 complete weeks  plus 3 extra days . These 3 extra days are critical – they're the  only  days that appear 5 times instead of 4.

The Quick Rule:  In a 31-day month, the  first 3 consecutive days of the month  will appear 5 times. That's it!

Application to Your Problem:  For May to have 5 Tuesdays, Tuesday must be among the first 3 days:
 
 If May starts on  Sunday  → Days 1, 2, 3 are Sun, Mon,  Tue  ✓ 
 If May starts on  Monday  → Days 1, 2, 3 are Mon,  Tue , Wed ✓ 
 If May starts on  Tuesday  → Days 1, 2, 3 are  Tue , Wed, Thu ✓ 
 If May starts on Wednesday or later → Tuesday is NOT in the first 3 days ✗  
 
Result:  3 favorable outcomes out of 7 possible starting days 
 Probability:   \frac{3}{7}

Time-Saving Strategy for Test Day: 
 
 Identify extra days:  	ext{Month days} - 28   
 Those extra consecutive days (starting from day 1) appear 5 times  
 
 Count how many starting days include your target day in this range

Quick Check Method:

For 30-day months → 2 extra days → smaller probability window 
For 31-day months → 3 extra days → larger probability window

This pattern works for  any  day of the week in  any  31-day month, cutting your solution time from testing 7 cases to instantly identifying the 3 favorable cases.

Answer: D   \left(\frac{3}{7}ight)

What is the probability that the month of May will have five Tuesdays?

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 Problem Solving (PS) Questions

What is the probability that the month of May will have five Tuesdays?

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