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# x and y are 2-digt integers. What is the difference between

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Director
Joined: 25 Oct 2006
Posts: 635
x and y are 2-digt integers. What is the difference between [#permalink]

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08 Jun 2007, 14:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

x and y are 2-digt integers. What is the difference between two tens' digit?
1). x-y=27
2). Units' digit of x minus the units' digit of y is greater than 3.

Any template or thoughts on how to attack this kinda problem.

Director
Joined: 12 Jun 2006
Posts: 532

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08 Jun 2007, 15:13
priyankur_saha@ml.com wrote:
x and y are 2-digt integers. What is the difference between two tens' digit?
1). x-y=27
2). Units' digit of x minus the units' digit of y is greater than 3.

Any template or thoughts on how to attack this kinda problem.

I'd have to go with C. I picked #s
1 and 2 insufficient.
While picking #s it seemed that the difference b/w the units digit of x and y was either negative 3 or +ve 7. When the difference b/w the units digit was -ve the diff b/w the tens was 3. When the diff b/w the units digit was 7 the diff b/w the tens was 2. Anyone have a better method?
Director
Joined: 26 Feb 2006
Posts: 899

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08 Jun 2007, 17:02
priyankur_saha@ml.com wrote:
x and y are 2-digt integers. What is the difference between two tens' digit?
1). x-y=27
2). Units' digit of x minus the units' digit of y is greater than 3.

Any template or thoughts on how to attack this kinda problem.

suppose if
if x = 49 and y = 22, x - y = 27 and the difference between tens digits of x and y is 2.
if x = 40 and y = 13, x - y = 27 and the difference between tens digits of x and y is 3.

I got E. did i miss anything????????????/
Manager
Joined: 18 Apr 2007
Posts: 120

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08 Jun 2007, 17:19
I agree with Himalaya... I got E.

From stmt [1] we know that the difference between the tens digit can only be 3 or 2. Insufficient.

Stmt [2] tells us nothing because we already know that the units digit of x minus the units digit of y is 7, which is greater than 3. Insufficient.

Putting both together gives us nothing.

Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

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09 Jun 2007, 17:36
go with C

st1 - either 2 or 3 INSUFF

st2 - Insuff by itself

st1 and st2 - only 2 is poss SUFF
CEO
Joined: 17 May 2007
Posts: 2950

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09 Jun 2007, 19:26
lets say x = AB y = CD

According to 1)

AB
-CD
-----
27

We have to find A - C
Now there two possibilities 3 and 2.

So A is insufficient

According to 2

B-D > 3 which is excellent news. Because it tells us that there is no carry over from the A to B in order to subtract D. Thus It is sufficient to know that A-C = 2.

Director
Joined: 25 Oct 2006
Posts: 635

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09 Jun 2007, 22:16
In my copy I've got the answer E, but not sure whether it's OA!! Thanks for the discussion....
Manager
Joined: 23 Dec 2006
Posts: 134

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09 Jun 2007, 22:42
Alternatively, let 10u+t and 10m+n denote our two numbers

1) says 10u+t - (10m+n) = 27

2) says t-n > 3

expand 1: 10(u-m) + (t - n) = 27

27-10(u-m) = t - n

27-10(u-m) > 3

24 > 10(u-m)

Now, we only know that 10(u-m) needs to be LARGER than 24, but we don't have an upper bound. Therefore, E.
Director
Joined: 25 Oct 2006
Posts: 635

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10 Jun 2007, 15:01
sludge wrote:
Alternatively, let 10u+t and 10m+n denote our two numbers

1) says 10u+t - (10m+n) = 27

2) says t-n > 3

expand 1: 10(u-m) + (t - n) = 27

27-10(u-m) = t - n

27-10(u-m) > 3

24 > 10(u-m)

Now, we only know that 10(u-m) needs to be LARGER than 24, but we don't have an upper bound. Therefore, E.

Thanks, I proceeded in this way...
Manager
Joined: 07 May 2007
Posts: 178

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10 Jun 2007, 16:52
Let x=10m+n
and y=10p+q

From 1, x-y = 10(m-p)+(n-q) = 27
This can be expressed as 10*3-3 or as 10*2+7

So, the diff of units digits can be 7 or -3
Diff of tens digits can be 2 or 3

Second stmt says diff is greater than 3. So it has to be 7.
So Diff of tens digits should be 2

Answer is both together are suff
VP
Joined: 10 Jun 2007
Posts: 1438

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10 Jun 2007, 17:11
x and y are 2-digt integers. What is the difference between two tens' digit?
1). x-y=27
2). Units' digit of x minus the units' digit of y is greater than 3

______________________________________________________
Set:
x = AB
Y = CD

1) Stated that X-Y = 27; thus, we know that B-D=7. Therefore, the possible values for (B,D) are (0,3) (7,0) (8,1) (9,2). If (B,D) = (0,3), then we know that we have to subtract 1 from A. If (B,D) = (7,0) OR (8,1) OR (9,2), we do not substract 1 from A. This means that we cannot determine A-C. This statement is INSUFFICIENT.

2) Stated that B-D > 3. We only know the unit digit substraction, we don't know the tens digits; thus, INSUFFICIENT.

Together, we know that B-D > 3. This eliminate the possible value of (B,D) = (0,3). Since (B,D) not equal to (0,3), we know that we don't have to substract one from A; thus, A-C must be 2. SUFFICIENT.

Let me know if there is any mistake.
I got C   [#permalink] 10 Jun 2007, 17:11
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