OG Quant Diag problems

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fangtray: Master | Next Rank: 500 Posts; Posts: 273; Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members; Thanked: 5 times

by fangtray » Mon Apr 02, 2012 2:28 am

Hello,

I am wondering if an expert could help me with some quick solutions for these problems that i either got incorrect, or went way over the time allotment.

11. Of 3 digit integers greater than 700, how many have 2 digits that are equal to each other and the remaining digit different from the other 2?

a. 90
b. 82
c. 80
d. 45
e. 36

13. if s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?

a. 2
b. 4
c. 8
d. 20
e. 45

I am wondering for this one if the equation s/t = Q(quotient) + (R(remainder)/t) will help?

thanks.

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Source: Beat The GMAT — Problem Solving | Mon Apr 02, 2012 2:28 am

Pharo: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Jan 18, 2010 11:09 pm; Thanked: 8 times

by Pharo » Mon Apr 02, 2012 3:04 am

Q11:

For 700 range:

You can have any number in the form of 7xx where x can not be 7. This will give you 9. (since there are a total of 10 digits and 7 cannot be here). However, since we are looking for greater than 700; you have to subtract 1 from 9 (for when x =0 ; 700 is not greater than 700); hence 8 different values here.

You can also have a number in the form of 7x7; 9 possibilities. OR you can have 77x; again 9 possibilities. (9 possibilities since 10 digits; but 7 cannot be one of them)

So a total of (3*9) - 1 = 26 possible values.

For 800 and 900 ranges: Same as above (but of course we do not substract 1; since 800 and 900 are acceptable). Hence 27 + 27 = 54 here.

Total makes 26 + 54 = 80

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klmehta03: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Sun Sep 05, 2010 3:11 pm; Thanked: 3 times

by klmehta03 » Mon Apr 02, 2012 3:45 am

13. if s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?

a. 2
b. 4
c. 8
d. 20
e. 45

IMO C
OA pls?

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Pharo: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Jan 18, 2010 11:09 pm; Thanked: 8 times

by Pharo » Mon Apr 02, 2012 4:17 am

Q13:

s = 64t + 0.12t ;

This means i will always have 64 as quotient and 0.12t as remainder. Checking the choices, i know that my remainder should be an integer.

Now the question is; how can i make 0.12t an integer? Or in other words; if i divide the choices by .12; will i get an integer?

let's write 0.12 in a more friendly manner ..

0.12 = 12/100 = 3/25

Which means remainder = 3t/25 ; which in turns means my remainder must be have 3 as a multiplier in it.

Only choice divisible by 3 is 45. Hence the answer is E

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Apr 02, 2012 4:38 am

fangtray wrote:Hello,

I am wondering if an expert could help me with some quick solutions for these problems that i either got incorrect, or went way over the time allotment.

11. Of 3 digit integers greater than 700, how many have 2 digits that are equal to each other and the remaining digit different from the other 2?

a. 90
b. 82
c. 80
d. 45
e. 36

thanks.

Required number = (Number of 3 digit integers greater than 700) - (Number of 3 digit integers greater than 700 with 3 same digit) - (Number of 3 digit integers greater than 700 with different digits)

Number of 3 digit integers greater than 700 = (999 - 700) = 299
Number of 3 digit integers greater than 700 with 3 same digit = 3 (Namely 777, 888 and 999)
Number of 3 digit integers greater than 700 with different digits = 3*9*8 = 216

Thus required number = (299 - 216 - 3) = 80

The correct answer is C.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Apr 02, 2012 4:39 am

fangtray wrote:Hello,

I am wondering if an expert could help me with some quick solutions for these problems that i either got incorrect, or went way over the time allotment.

13. if s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?

a. 2
b. 4
c. 8
d. 20
e. 45

I am wondering for this one if the equation s/t = Q(quotient) + (R(remainder)/t) will help?

thanks.

We know that dividend = quotient * divisor + remainder
Here, let us assume that quotient = q and remainder = r. Given, dividend = s and divisor = t
So, s = q * t + r or s/t = q + r/t, where 0 â‰¤ r/t < 1
So, 64.12 = 64 + 12/100
or 64.12 = 64 + 3/25
This implies r/t = 3/25 or 25r = 3t, where r should be a multiple of 3 so that the remainder evenly divides 3t. From the given answer choices, 45 is the only integer that is a multiple of 3.

The correct answer is E.

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fangtray: Master | Next Rank: 500 Posts; Posts: 273; Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members; Thanked: 5 times

by fangtray » Tue Apr 03, 2012 3:22 am

Anurag@Gurome wrote:
fangtray wrote:Hello,

I am wondering if an expert could help me with some quick solutions for these problems that i either got incorrect, or went way over the time allotment.

11. Of 3 digit integers greater than 700, how many have 2 digits that are equal to each other and the remaining digit different from the other 2?

a. 90
b. 82
c. 80
d. 45
e. 36

thanks.

Required number = (Number of 3 digit integers greater than 700) - (Number of 3 digit integers greater than 700 with 3 same digit) - (Number of 3 digit integers greater than 700 with different digits)

Number of 3 digit integers greater than 700 = (999 - 700) = 299
Number of 3 digit integers greater than 700 with 3 same digit = 3 (Namely 777, 888 and 999)
Number of 3 digit integers greater than 700 with different digits = 3*9*8 = 216

Thus required number = (299 - 216 - 3) = 80

The correct answer is C.

where is the 3*9*8 from?

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fangtray: Master | Next Rank: 500 Posts; Posts: 273; Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members; Thanked: 5 times

by fangtray » Tue Apr 03, 2012 3:38 am

Anurag@Gurome wrote:
fangtray wrote:Hello,

I am wondering if an expert could help me with some quick solutions for these problems that i either got incorrect, or went way over the time allotment.

13. if s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?

a. 2
b. 4
c. 8
d. 20
e. 45

I am wondering for this one if the equation s/t = Q(quotient) + (R(remainder)/t) will help?

thanks.
We know that dividend = quotient * divisor + remainder
Here, let us assume that quotient = q and remainder = r. Given, dividend = s and divisor = t
So, s = q * t + r or s/t = q + r/t, where 0 â‰¤ r/t < 1
So, 64.12 = 64 + 12/100
or 64.12 = 64 + 3/25
This implies r/t = 3/25 or 25r = 3t, where r should be a multiple of 3 so that the remainder evenly divides 3t. From the given answer choices, 45 is the only integer that is a multiple of 3.

The correct answer is E.

could you please explain further the part where r/t = 3/25 or 25r/3t and how r should be a multiple of 3? i'm not sure i understand.

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Pharo: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Jan 18, 2010 11:09 pm; Thanked: 8 times

by Pharo » Tue Apr 03, 2012 4:47 am

Remainder = (3 * t)/25 ; rewrite it
Remainder = 3 * (t/25) ;

All the answer choices are integers. That means (t/25) should be an integer as well (since the only way to get an integer from a multiplication of two numbers (where one of the multiplicands is an integer) is to have the second number an integer as well.

Checking the answer choices we see that the only choice that is in form of (3*(an integer)) is E.

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