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A “palindromic integer” is an integer that remains the same when its

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A “palindromic integer” is an integer that remains the same when its  [#permalink]

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New post 24 Sep 2015, 22:48
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A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 400,000?

(A) 200
(B) 216
(C) 300
(D) 400
(E) 2,500


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A “palindromic integer” is an integer that remains the same when its  [#permalink]

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New post 25 Sep 2015, 07:17
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Bunuel wrote:
A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 400,000?

(A) 200
(B) 216
(C) 300
(D) 400
(E) 2,500


Kudos for a correct solution.


first digit=last digit=4 or 6 or 8 so three possiblities..
second =fifth= any of ten digits
third =fourth= any of ten digits..
so total integers=3*10*10=300
C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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A “palindromic integer” is an integer that remains the same when its  [#permalink]

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New post 27 Sep 2015, 11:25
2
Bunuel wrote:
A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 400,000?

(A) 200
(B) 216
(C) 300
(D) 400
(E) 2,500


Kudos for a correct solution.


Gmatprepnow Official Solution:

Can we take the task of “building” 6-digit palindromic integers and break it into individual stages? Yes!

Let’s say that our 6-digit integer takes the form XYZZYX. Once we choose values for X, Y and Z, we can be assured that the resulting 6-digit integer is palindromic.

From here, we can define the stages as follows:

Stage 1: Choose a value for X

Stage 2: Choose a value for Y

Stage 3: Choose a value for Z

Once we complete all 3 stages, we will have “built” our 6-digit palindromic integer. So, at this point, we must determine the number of ways to accomplish each stage.

Stage 1: Choose a value for X: In how many ways can we choose a value for X? Since the resulting 6-digit integer must be both even AND greater than 400,000, X must equal 4, 6 or 8. So, Stage 1 can be accomplished in 3 different ways.

Stage 2: Choose a value for Y: Since there are no restrictions on the value of Y, we can choose any of the ten digits {0,1,2,3,4,5,6,7,8,9}. So, Stage 2 can be accomplished in 10 different ways.

Stage 3: Choose a value for Z: Since there are no restrictions on the value of Z, we can choose any of the ten digits {0,1,2,3,4,5,6,7,8,9}. So, Stage 3 can be accomplished in 10 different ways.

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create an even, 6-digit palindromic number that’s greater than 400,000) in 3 × 10 × 10 ways (300 ways). So, the answer to the original question is C.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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