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Bunuel
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What is the total number of integers between 200 and 400 each of which 30 Jul 2021, 04:45
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C
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65% (hard)

Question Stats:

57% (01:34) correct 43% (01:43) wrong based on 247 sessions

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What is the total number of integers between 200 and 400, each of which either begins with 3 or ends with 3 or both ?

(A) 10
(B) 100
(C) 110
(D) 120
(E) 130
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C
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rajatchopra1994
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What is the total number of integers between 200 and 400 each of which 30 Jul 2021, 04:51
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Explanation:

200 - 400 - either begins with 3 or ends with 3 or both

203,213, _ _ _ , 293 - 10
300 to 399 - 100

Total = 100 + 10 = 110

IMO-C
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What is the total number of integers between 200 and 400 each of which 30 Jul 2021, 05:12
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200 to 299:
213,213,223...293 (10 terms)
300 to 400 (100 terms)
Total =110
Ans C

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What is the total number of integers between 200 and 400 each of which 30 Jul 2021, 07:25
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200-300 -->203,213...293--> 10
300-399--> 100

Total--> 110

IMO C
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What is the total number of integers between 200 and 400 each of which 28 Mar 2025, 02:03
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Hi Bunuel,

Just wanted to confirm one thing, as mentioned in the question begins OR ends OR both therefore shouldn't it contain 3 subsets and based in them 100 numbers which starts , 10 which and 10 that has both
Making it 120.

Please correct me if there is a flaw in the concept.
Bunuel
What is the total number of integers between 200 and 400, each of which either begins with 3 or ends with 3 or both ?

(A) 10
(B) 100
(C) 110
(D) 120
(E) 130
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What is the total number of integers between 200 and 400 each of which 28 Mar 2025, 02:15
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MuditKapoor
Hi Bunuel,

Just wanted to confirm one thing, as mentioned in the question begins OR ends OR both therefore shouldn't it contain 3 subsets and based in them 100 numbers which starts , 10 which and 10 that has both
Making it 120.

Please correct me if there is a flaw in the concept.
Bunuel
What is the total number of integers between 200 and 400, each of which either begins with 3 or ends with 3 or both ?

(A) 10
(B) 100
(C) 110
(D) 120
(E) 130
Show more
You're counting the third subset (i.e. both begin and end with 3) twice.

First subset: Begins with 3; 3 _ _ = 10 * 9 = 90 numbers (in this case we are omitting nos. ending with 3, since we will count those in third subset)

Second subset: Ends with 3; 2 _ 3 = 10 numbers (nos. will begin with 2, the ones that begin with 3, will end with 3 -> they will be counted in third subset)

Third subset: Both Begins and Ends with 3; 3 _ 3 = 10 numbers

Now adding all 3 subsets = 10 + 90 + 10 = 110

Hope it helps.
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MuditKapoor
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What is the total number of integers between 200 and 400 each of which 28 Mar 2025, 03:15
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Thanks Krunaal for again being a support.


Krunaal
MuditKapoor
Hi Bunuel,

Just wanted to confirm one thing, as mentioned in the question begins OR ends OR both therefore shouldn't it contain 3 subsets and based in them 100 numbers which starts , 10 which and 10 that has both
Making it 120.

Please correct me if there is a flaw in the concept.
Bunuel
What is the total number of integers between 200 and 400, each of which either begins with 3 or ends with 3 or both ?

(A) 10
(B) 100
(C) 110
(D) 120
(E) 130
You're counting the third subset (i.e. both begin and end with 3) twice.

First subset: Begins with 3; 3 _ _ = 10 * 9 = 90 numbers (in this case we are omitting nos. ending with 3, since we will count those in third subset)

Second subset: Ends with 3; 2 _ 3 = 10 numbers (nos. will begin with 2, the ones that begin with 3, will end with 3 -> they will be counted in third subset)

Third subset: Both Begins and Ends with 3; 3 _ 3 = 10 numbers

Now adding all 3 subsets = 10 + 90 + 10 = 110

Hope it helps.
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What is the total number of integers between 200 and 400 each of which 28 Mar 2025, 09:39
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Here from 200 to 299 there are 10 numbers ending in 3
From 300 to 399 total there are 100 numbers beginning with 3 and few also ending with 3
Hence total 110 Option C
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