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Senior Manager  P
Joined: 27 Dec 2016
Posts: 303
Re: How many integers between 0 and 1570 have a prime tens digit  [#permalink]

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Hello there

I tried using the following approach. I did end up taking some time.

The numbers to be considered are 2,3,5 & 7.

For 2-digit numbers:
(4 PRIME numbers in the Ten's place)
(4 PRIME numbers in the Unit's place)

4*4 = 16 --- (1)

For 3-digit numbers:
(9 numbers in the Hundred's place i.e 1 to 9)
(4 PRIME numbers in the Ten's place)
(4 PRIME numbers in the Unit's place)

9*4*4 = 144 --- (2)

For 4-digit numbers (till 1500):
(1 number in the Thousand's place i.e. 1)
(5 numbers in the Hundred's place i.e. 0, 1, 2, 3, 4)
(4 PRIME numbers in the Ten's place i.e 2, 3, 5 & 7)
(4 PRIME numbers in the Unit's place i.e 2, 3, 5 & 7)

1*5*4*4 = 80 --- (3)

For 4-digit numbers (1501 to 1570):
(1 number in the Thousand's place i.e. 1)
(1 number in the Hundred's place i.e. 5)
(3 PRIME numbers in the Ten's place i.e 2, 3, 5)
(4 PRIME numbers in the Unit's place i.e 2, 3, 5 & 7)

1*1*3*4 = 12 --- (4)

Adding (1), (2), (3) & (4) ----> 252

Can an Expert evaluate the approach? I want to be sure that I considered the possibilities correctly.

Thanks in advance for the help.

Hi Bunuel,

I have followed a similar approach; however, I got a different answer. For 2-digit numbers, I got 16. For 3-digit numbers, I got 144. For 4-digit numbers, I had a different approach. My approach was to find integers from 1000 to 1569 for the 4 digit numbers. 1*6*4*4. First field: We only have one way to pick digit 1. Second field, we have 6 different ways to pick a digit between 0 and 5. Third & fourth field: we have 4 different ways of picking a prime number. Could you please explain where I went wrong in my approach? Would greatly appreciate it!
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Re: How many integers between 0 and 1570 have a prime tens digit  [#permalink]

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csaluja wrote:
Hello there

I tried using the following approach. I did end up taking some time.

The numbers to be considered are 2,3,5 & 7.

For 2-digit numbers:
(4 PRIME numbers in the Ten's place)
(4 PRIME numbers in the Unit's place)

4*4 = 16 --- (1)

For 3-digit numbers:
(9 numbers in the Hundred's place i.e 1 to 9)
(4 PRIME numbers in the Ten's place)
(4 PRIME numbers in the Unit's place)

9*4*4 = 144 --- (2)

For 4-digit numbers (till 1500):
(1 number in the Thousand's place i.e. 1)
(5 numbers in the Hundred's place i.e. 0, 1, 2, 3, 4)
(4 PRIME numbers in the Ten's place i.e 2, 3, 5 & 7)
(4 PRIME numbers in the Unit's place i.e 2, 3, 5 & 7)

1*5*4*4 = 80 --- (3)

For 4-digit numbers (1501 to 1570):
(1 number in the Thousand's place i.e. 1)
(1 number in the Hundred's place i.e. 5)
(3 PRIME numbers in the Ten's place i.e 2, 3, 5)
(4 PRIME numbers in the Unit's place i.e 2, 3, 5 & 7)

1*1*3*4 = 12 --- (4)

Adding (1), (2), (3) & (4) ----> 252

Can an Expert evaluate the approach? I want to be sure that I considered the possibilities correctly.

Thanks in advance for the help.

Hi Bunuel,

I have followed a similar approach; however, I got a different answer. For 2-digit numbers, I got 16. For 3-digit numbers, I got 144. For 4-digit numbers, I had a different approach. My approach was to find integers from 1000 to 1569 for the 4 digit numbers. 1*6*4*4. First field: We only have one way to pick digit 1. Second field, we have 6 different ways to pick a digit between 0 and 5. Third & fourth field: we have 4 different ways of picking a prime number. Could you please explain where I went wrong in my approach? Would greatly appreciate it!

Hi csaluja,

Your calculation includes 4 numbers that are GREATER than 1570 (re: 1572, 1573, 1575 and 1577). Those numbers are outside of the range defined by the question, so they should not be included.

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Re: How many integers between 0 and 1570 have a prime tens digit  [#permalink]

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hardworker_indian wrote:
How many integers between 0 and 1570 have a prime tens digit and a prime units digit?

(A) 295
(B) 252
(C) 236
(D) 96
(E) 76

Since 4 digits are prime digits (2, 3, 5, 7), if the number has 2 digits, then we have 4 x 4 = 16 such numbers. If the number has 3 digits, then we have 9 x 4 x 4 = 144 such numbers. If the number has 4 digits and it’s less than 1500, then we have 1 x 5 x 4 x 4 = 80 such numbers. Finally, if the number has 4 digits and it’s between 1500 and 1570 (inclusive), then we have 1 x 1 x 3 x 4 = 12 such numbers. Therefore, we have a total of 16 + 144 + 80 + 12 = 252 numbers between 0 and 1570 that have a prime tens digit and a prime units digit.

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