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Bunuel
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Set A comprises all 3-digit positive integers that are multiples of 6. 13 Jan 2021, 10:15
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65% (hard)

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68% (03:10) correct 32% (02:38) wrong based on 220 sessions

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Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?

A. 38
B. 225
C. 263
D. 265
E. 300
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A
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Krishnahelps
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Set A comprises all 3-digit positive integers that are multiples of 6. 01 Mar 2021, 04:06
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Bunuel
Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?

A. 38
B. 225
C. 263
D. 265
E. 300
Show more

Total 3 digit number= 900

numbers that are multiples of all (LCM of 6,4,8 ) =24 = 900/24 = 37

numbers that are multiples of 6 & 4 (LCM 6 and 4) =12 = 900/12 = 75

numbers that are common to both A and B= 75-37= 38

Hence, option A is the correct answer.
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Set A comprises all 3-digit positive integers that are multiples of 6. 13 Jan 2021, 13:30
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Bunuel
Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?

A. 224
B. 225
C. 263
D. 265
E. 300
Show more

Total 3 digit number 900
n(A) =numbers multiple of 6 = 900/6 =150
numbers multiple of 4 = 900/4 = 225
numbers multiple of 8 = 900/8 = 112.5
n(B) = 225-112.5 = 112.5 = 113 (as we don't need numbers are multiple to 8)
numbers which are multiple of all (LCM of 6,4,8 ) =24 = 900/24 = 37.5 =38

so final result = 150 + 113 - 38 = 225
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Set A comprises all 3-digit positive integers that are multiples of 6. 13 Jan 2021, 18:50
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HinalAmin24
Bunuel
Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?

A. 224
B. 225
C. 263
D. 265
E. 300

Total 3 digit number 900
n(A) =numbers multiple of 6 = 900/6 =150
numbers multiple of 4 = 900/4 = 225
numbers multiple of 8 = 900/8 = 112.5
n(B) = 225-112.5 = 112.5 = 113 (as we don't need numbers are multiple to 8)
numbers which are multiple of all (LCM of 6,4,8 ) =24 = 900/24 = 37.5 =38

so final result = 150 + 113 - 38 = 225
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Isn't the question asking for how many elements are common in A and B. Wouldn't this be the value for total no. of elements? I was stuck coz of this part.
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Set A comprises all 3-digit positive integers that are multiples of 6. Updated on: 13 Mar 2021, 01:03
Originally posted by TarunKumar1234 on 14 Jan 2021, 02:12.
Last edited by TarunKumar1234 on 13 Mar 2021, 01:03, edited 1 time in total.
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Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?

Given, set A= {102,108, 114, 120, 126, 132,...., 996}, n(A)= (996-102)/6 +1 = 150;
set B = {100,104, 108...., 996}- {104, 112...., 992} = {100, 108, 116, 124,...., 996}, n(B)= (996-100)/4 +1 - (992-104)/8 -1= 225-112 = 113.

Set A and B have common terms = {108,132,.....}, So, 24n + 108 <999, n<37.12, n(A⋂B)= 37+1 =38

So, I think A. :)
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Set A comprises all 3-digit positive integers that are multiples of 6. 15 Jan 2021, 09:59
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manasi05
HinalAmin24
Bunuel
Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?

A. 224
B. 225
C. 263
D. 265
E. 300

Total 3 digit number 900
n(A) =numbers multiple of 6 = 900/6 =150
numbers multiple of 4 = 900/4 = 225
numbers multiple of 8 = 900/8 = 112.5
n(B) = 225-112.5 = 112.5 = 113 (as we don't need numbers are multiple to 8)
numbers which are multiple of all (LCM of 6,4,8 ) =24 = 900/24 = 37.5 =38

so final result = 150 + 113 - 38 = 225

Isn't the question asking for how many elements are common in A and B. Wouldn't this be the value for total no. of elements? I was stuck coz of this part.
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You are right I guess. Lets see how others reply on the same.
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Set A comprises all 3-digit positive integers that are multiples of 6. 27 Feb 2021, 01:24
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Answer should be A,
Question stem asks for common elements between A & B, The number of common elements has to be less than or equal to the number of elements in the set that contains least number of elements.

SET A has 150 elements, all other options are so far off, A is the only option under 150
Hence A is the right choice,
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Set A comprises all 3-digit positive integers that are multiples of 6. 01 Jan 2024, 06:59
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Bunuel
Set A comprises all 3-digit positive integers that are multiples of 6. Set B comprises all 3-digit positive integers that are multiples of 4 but are not multiples of 8. How many elements does set A and B have in common?
A. 38
B. 225
C. 263
D. 265
E. 300
Show more

1) Method-1:
For Set A:
    Count the number for three-digit multiples of 6 in set A first.
    The lowest three digit multiple of 6 is 102 and the highest is 996.
    Total number of elements in the set would be :  (996-102)/6+1 = 150

As we have to find the intersection of set A and B, it can't be more than 150. Only Answer-A is lower than 150.
Option-A

2) Method-2:
To find a exact number of 3 digit numbers which are multiple of 6 and 4 but not-8:
a) For a number to be a multiple of 6 and 4 together, it should be a multiple of its LCM - LCM(6,4) = 12
Lowest 3 digit multiple of 12 is : 108 and the highest is 996
Therefore, Total no. of such elements are : (996-108)/12+1 = 75
b) As every 2nd such number will be a multiple of 8 e.g. 108 is a multiple of 4 but not 8, whereas, 112 (108+4) is multiple of 4 and 8 both and so on.
Also, the last number 996 is a multiple of 4 but not 8,.
Therefore intersection of set A and B is 38 (38 multiple of 4 alone + 37 multiple of 4 and 8)
Option-A
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Set A comprises all 3-digit positive integers that are multiples of 6. 24 Jul 2025, 21:12
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