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What is the number of integers that are not divisible by 7 in the rang

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Bunuel
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What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   17 Jun 2019, 23:43
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What is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A. 70
B. 71
C. 426
D. 427
E. 428
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D
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What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   17 Jun 2019, 23:49
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Total number of integers from 3 to 500 = 498

Number of multiples of 7 between 3 and 500 = (497-7)/7 + 1 = 71

Number of integers in the range 3 to 500 that are not divisible by 7 = 498 - 71 = 427

Answer is (D)
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Re: What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   18 Jun 2019, 00:24
Bunuel wrote:
What is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A. 70
B. 71
C. 426
D. 427
E. 428


No. of integers divisible by seven in till 500 is 500/7=71.some so 71 integers.
Total number of integers in 3 to 500 (inclusive)=500-3+1=498
So Not divisible is = 498-71=427 IMO D
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Re: What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   18 Jun 2019, 02:48
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Bunuel wrote:
What is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A. 70
B. 71
C. 426
D. 427
E. 428



Total number of integers from 3 to 500 = 500 - 3 + 1 = 498

Lets calculate the number of integers that are divisible by 7 from 3 to 500
--> 7, 14, 21, 28, . . . . . . . . . 497
The above series is in AP. To find number of terms use Last term
--> Last term = a + (n - 1)d
--> 497 = 7 + (n - 1)7
--> 490 = (n - 1)7
--> n - 1 = 490/7 = 70
--> n = 71

So, Numbers that are NOT divisible by 7 from 3 to 500 = 498 - 71 = 427

IMO Option D

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Re: What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   18 Jun 2019, 05:05
Bunuel wrote:
What is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A. 70
B. 71
C. 426
D. 427
E. 428


upto 500 ; 71 integers are divisible by 7
from 3 to 500 ; 498 integers so 498-71 ; 427
IMO D
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Re: What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   23 Jun 2019, 19:22
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Bunuel wrote:
What is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A. 70
B. 71
C. 426
D. 427
E. 428



First, let’s determine the total number of integers from 3 to 500 that are divisible by 7. We see that the largest multiple of 7 in this range is 497, and the smallest multiple of 7 is 7. Thus, the number of integers that are divisible by 7 is:

(497 - 7)/7 + 1 = 71

The total number of integers from 3 to 500, inclusive, is 500 - 3 + 1 = 498.

Thus, the number of integers that are not divisible by 7 is 498 - 71 = 427.

Answer: D
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Re: What is the number of integers that are not divisible by 7 in the rang [#permalink] New post   24 Mar 2024, 11:44
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Re: What is the number of integers that are not divisible by 7 in the rang [#permalink]
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