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B) 252 - 1 min
2-3-5-7 are primes
4*4=16 possible double digits(units+tens) in first 100 numbers
Since there are 15 hundreds, multiply that by 15 and get 240
For the numbers above 1500, just remove the possibilities of having units+tens prime (72-73-75-77) so 16-4=12
Add up and get 240+12=252
_________________

I certainly misunderstood the question : to me it is to count integers from 0 to 1570 with 1 prime tens digit or 1 prime units digit (nothing to do with this but makes me remember a possible mistake in the 8th challenge...)

from 0 > 999

tens digit prime : 10.4.6 = 240
units digit prime : 10.6.4 = 240

from 1000 > 1570

tens digit prime : 6.4.6 = 144
units digit prime : 6.4.4 = 96

You have tens and units digits T-U
T could be 2-3-5-7
U could be 2-3-5-7
Because you need both digits being prime, total possible combinations: 4*4=16
_________________

begin with 2 digits number : 16 numbers
then 3 digits number : 16*9 ways numbers
then 4 digits number until 1500 (but we know that the number can not begin by 2, 3, 4, ... because the biggest number is 1570 so we just need to consider 1 possibility for 4 digits) : 16*5 numbers
then 1500 -> 1571 : 12 numbers (22-23-25-27-32-33-35-37-52-53-55-57)

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

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15 Oct 2013, 13:25

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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

There are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.

So, in each hundred there are 16 such numbers. In 16 hundreds there will be 16*16=256 such numbers, but 4 out of them will be more than 1570, namely: 1572, 1573, 1575 and 1577. Which means that there are 256-4=252 numbers between 0 and 1570 which have a prime tens digit and a prime units digit.

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

There are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.

So, in each hundred there are 16 such numbers. In 16 hundreds there will be 16*16=256 such numbers, but 4 out of them will be more than 1570, namely: 1572, 1573, 1575 and 1577. Which means that there are 256-4=252 numbers between 0 and 1570 which have a prime tens digit and a prime units digit.

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

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19 Apr 2014, 18:00

Tried to solve it and can't quite understand the following:

you have the 4 digits: _ _ _ _ From right to left: 1*15*4*4 (since units and tens can take either four options: 2,3,5,7) and then you have 15 possibilities (from 1 to 15) to account for hundreds.

16*15 = 240

Yet, I don't get the part where you have to add up those 12 to reach 252, since you already took 15 into account (1500's) and those 16 for the 1500's are also multiplied (1500s + 16 options of tens and hundreds).

What I mean is: It seems to me that those 12 should not be added up since they're implied in the multiplication.

Tried to solve it and can't quite understand the following:

you have the 4 digits: _ _ _ _ From right to left: 1*15*4*4 (since units and tens can take either four options: 2,3,5,7) and then you have 15 possibilities (from 1 to 15) to account for hundreds.

16*15 = 240

Yet, I don't get the part where you have to add up those 12 to reach 252, since you already took 15 into account (1500's) and those 16 for the 1500's are also multiplied (1500s + 16 options of tens and hundreds).

What I mean is: It seems to me that those 12 should not be added up since they're implied in the multiplication.

As for your solution: 1570 is 15 "complete" hundreds and 70. The same way as 170 is 1 hundred and 70. So, 15*16 is not correct.

Next, we are doing 16*16 - 4: in each hundred there are 16 numbers, which have a prime tens digit and a prime units digit. So, in 16 hundreds there will be 16*16 such numbers. But the last "incomplete" hundred will not have 16 numbers, it will have only 16-4=12, because 1572, 1573, 1575 and 1577 are greater than 1570.

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

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20 Apr 2014, 04:35

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Bunuel wrote:

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

There are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.

So, in each hundred there are 16 such numbers. In 16 hundreds there will be 16*16=256 such numbers, but 4 out of them will be more than 1570, namely: 1572, 1573, 1575 and 1577. Which means that there are 256-4=252 numbers between 0 and 1570 which have a prime tens digit and a prime units digit.

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

There are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.

So, in each hundred there are 16 such numbers. In 16 hundreds there will be 16*16=256 such numbers, but 4 out of them will be more than 1570, namely: 1572, 1573, 1575 and 1577. Which means that there are 256-4=252 numbers between 0 and 1570 which have a prime tens digit and a prime units digit.

Answer: A.

Hope it's clear.

You mean Answer:B, not A right ?

Yes, 252 is B, not A. Edited the typo. Thank you.
_________________

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

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20 Apr 2014, 06:27

I tried solving it but it didn't come out right. Can someone see where the problem is with the logic?

For each of the 1's and 10's digits, there can be 4 options. so we have 16. For the hundreds we have 6 options. For the thousands we have 2 options. So it comes to 12*16 = 192. -> wrong!!

I tried solving it but it didn't come out right. Can someone see where the problem is with the logic?

For each of the 1's and 10's digits, there can be 4 options. so we have 16. For the hundreds we have 6 options. For the thousands we have 2 options. So it comes to 12*16 = 192. -> wrong!!

Can someone see the problem?

If the thousands digit is 0, then for hundreds we have 10 options not 6.
_________________

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

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29 Apr 2014, 23:24

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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.

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.

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

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01 May 2015, 23:55

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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04 May 2015, 15:03

Bunuel wrote:

shaderon 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.

Yes, your solution is correct.

Hello Bunuel and everyone else. I have been reading the answers and Im on the same page as everyone else but I got answer as 256 because 252 +4 , the 4 comes from single digit number 2,3,5, or 7 only. Hmmmm.... where Im going worng here. I would like kindly to ask for explanaion what others think on this issue

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