Word Problems

[RiyaR]

How many integers n greater than 10 and less than 100 are there such that, if the digits of n are reversed the resulting integer is n + 9?
A) 5
B) 6
C) 7
D) 8
E) 9

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Hi RiyaR,

Sometimes Quant questions on the GMAT require a bit of experimentation on your part. By "playing" with the question a bit, you're more likely to find any hidden patterns within it (and solve the problem).

Here, we're asked to take a 2-digit number, reverse its digits and end up with a number that is +9 greater than what we started with.

Let's try....

n = 13
The reverse would be 31
31 is "18 more" than 13, so this is NOT what were looking for. We need the 2 digits to be "closer" together.

Now let's try...

n = 12
The reverse would be 21
21 IS "9 more" than 12, so this IS an example of exactly what we're looking for.

From the answer choices, we know that there are at least 5 (and at most 9) possibilities so let's find them....

12 and 21
23 and 32
Notice the pattern....?

34 and 43
45 and 54
56 and 65
67 and 76
78 and 87
89 and 98

Final Answer: D - 8 integers

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

How many integers n greater than 10 and less than 100 are there such that, if the digits of n are reversed the resulting integer is n + 9?
A) 5
B) 6
C) 7
D) 8
E) 9

Alternate approach:

Let T = the tens digit and U = the units digit.

Original integer = 10T + U.
To illustrate:
53 = 10(5) + 3.

The original integer with the digits reversed = 10U + T.

Since the reversed integer is 9 more than the original integer, we get:
10U + T = (10T + U) + 9
9U = 9T + 9
U = T+1.

Implication:
The units digit must be 1 more than the tens digit, yieding the following options:
12, 23, 34, 45, 56, 67, 78, 89.
Total options = 8.

The correct answer is D.