For how many of the integers from 10 to 99 is at least one of the two

Question

For how many of the integers from 10 to 99 is at least one of the two digits a 4 ?

A. 9
B. 10
C. 18
D. 19
E. 20

PS21197

BrentGMATPrepNow · Accepted Answer

Number of 2-digit integers with  at least  one 4  = (  total number of 2-digit integers  ) - (  number of 2-digit integers that have ZERO 4's  )

total number of 2-digit integers   
We want to count the number of integers from 10 to 99 inclusive
A nice rule says:   the number of integers from x to y inclusive equals y - x + 1  
So the number of integers from 10 to 99 inclusive = 99 - 10 + 1 =   90

number of 2-digit integers that have ZERO 4's   
Let's build some 2-digit integers that have ZERO 4's
The tens digit can be 1, 2, 3, 5, 6, 7, 8, or 9 (8 options)
The units digit can be 0, 1, 2, 3, 5, 6, 7, 8, or 9 (9 options)
So, the total number of 2-digit integers that have ZERO 4's = (8)(9) =   72

We get: 
Number of 2-digit integers with at least one 4 =   90   -   72   =  18

Answer: C

Cheers, 
Brent

yashikaaggarwal · Answer

The integers between 10 to 99,
With at least 1 of the two digits a four.

The no. With 4 as units digit :8 no. ------(1)(14,24,34,54,64,74,84,94)

The no. With 4 as tens digit : 9 no. -------(2)
(40,41,42,43,45,46,47,48,49)

The no. With 4 as both ones and tens digit = 1 -----(3) 
(44)

Total no. : 1+8+9=18
Answer is C

Posted from my mobile device

GMATinsight · Answer

FACT : 1 to 99 there are 19 numbers which include digit 4 and 20 times digit 4 is used

But we need to exclude one 4 that comes between 1 and 10

so total numbers with digit 4 used = 19-1 = 18

Answer: Option C

Archit3110 · Answer

total digits from 10 to 99 ; 99-10 +1 ; 90
and not with 4 we have ( 8*9= 72 terms ) 
so with 4 we have ; 90-72 ; 18 terms
OPTION C

EgmatQuantExpert · Answer

Solution

To find  
We need to determine
 • For how many of the integers from 10 to 99 is at least one of the two digits a 4

Approach and Working out  
 • Number of integers in which units digit is 4 = 9 {units digit can take any value from 1 to 9}
• Number of integers in which tens digit is 4 = 10 {units digit can take any value from 1 to 9}
• Number of integers in which both the digits are 4 = 1 {44}
• Thus, total number of such integers = 9 + 10 – 1 = 18

Thus, option C is the correct answer.

Correct Answer: Option C

bumpbot · Answer

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For how many of the integers from 10 to 99 is at least one of the two

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For how many of the integers from 10 to 99 is at least one of the two

Prep Toolkit

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