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# If m, n, and p are three-digit integers such that m + n = p, what is

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If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 06:30
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50% (02:01) correct 50% (02:02) wrong based on 89 sessions

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Hello all—
Another new (original) problem for your enjoyment and pleasure.

__

If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 06:50
Are we sure this is a correct question.

For statement 1 - If n and p have equal tens digits then m<10, and the tens digit is zero. That seems to be sufficient.
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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Updated on: 03 Aug 2017, 20:03
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RonPurewal wrote:
Hello all—
Another new (original) problem for your enjoyment and pleasure.

__

If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

We are calculating the tens digit of m.
(1)Tens digit of n and p are equal.
m + n = p and the tens digit of n and p are equal.
It could be possible in two ways.

Case1: tens place of m is 0.

If m = 301 and n= 513, m + n = 814=p.
Tens digit of n and p are equal and the tens digit of m here is 0.

If m = 301 and n= 523, m + n = 824=p.
Tens digit of n and p are equal and the tens digit of m here is 0.

Case2: tens place of m=9 and there is a carry over from the addition of the units digit of m and n.

If m=196 and n=246, m+n= 442 = p.
Tens digit of n and p are equal and the tens digit of m here is 9.

Clearly statement 1 is not sufficient.

(2) Units digit of n is greater than the units digit of p.

For the units digit of n to be greater than that of p, there should definitely be a carry from the units digit addition.
If m=336 and n = 255. m+n= 591 =p; Tens digit of m is 3.
If m = 326 and n = 255, m + n = 571; Tens digit of m is 2.
Since we are getting multiple answers, the statement is not alone sufficient.

Now if we combine both the statements, we already know from the second statement that there should be a carry from the units digit addition.
From the first statement, we know that if there is carry, then for units digit of n and p to be equal, tens place of m should be 9.
: Sufficient.

So after combining, we get a definite answer. So answer should be

Originally posted by sarathgopinath on 03 Aug 2017, 07:02.
Last edited by sarathgopinath on 03 Aug 2017, 20:03, edited 3 times in total.
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 07:09
sarathgopinath, you have the right idea overall — but, you should definitely double-check some of your results.

For instance:

Quote:
If m = 301 and n= 513, m + n = 814=p.
Tens digit of n and p are equal and the tens digit of m here is 1.
However, we can easily get a different value if we give another value for n.
If m = 301 and n= 523, m + n = 824=p.
Tens digit of n and p are equal and the tens digit of m here is 2.

^^ In both of these examples, the tens digit of m is 0 (NOT 1 or 2).

Quote:
If m=196 and n=246, m+n= 442 = p.
Tens digit of n and p are equal and the tens digit of m here is 1.

^^ Here, none of the tens digits is 1. (The tens digits of m, n, and p, respectively, are 9, 4, and 4.) So, I'm honestly not sure where you're getting "tens digit = 1".

Etc.

Always use due diligence!
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 07:14
RonPurewal wrote:
sarathgopinath, you have the right idea overall — but, you should definitely double-check some of your results.

For instance:

Quote:
If m = 301 and n= 513, m + n = 814=p.
Tens digit of n and p are equal and the tens digit of m here is 1.
However, we can easily get a different value if we give another value for n.
If m = 301 and n= 523, m + n = 824=p.
Tens digit of n and p are equal and the tens digit of m here is 2.

^^ In both of these examples, the tens digit of m is 0 (NOT 1 or 2).

Quote:
If m=196 and n=246, m+n= 442 = p.
Tens digit of n and p are equal and the tens digit of m here is 1.

^^ Here, none of the tens digits is 1. (The tens digits of m, n, and p, respectively, are 9, 4, and 4.) So, I'm honestly not sure where you're getting "tens digit = 1".

Etc.

Always use due diligence!

That was a careless mistake that I made while typing.
Thank you for correcting me Sir
I'll edit and make it right.
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 07:20
sarathgopinath wrote:
RonPurewal wrote:
Hello all—
Another new (original) problem for your enjoyment and pleasure.

__

If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

We are calculating the tens digit of m.
(1)Tens digit of n and p are equal.
m + n = p and the tens digit of n and p are equal.
It could be possible in two ways.

Case1: tens place of m is 0.

If m = 301 and n= 513, m + n = 814=p.
Tens digit of n and p are equal and the tens digit of m here is 0.

If m = 301 and n= 523, m + n = 824=p.
Tens digit of n and p are equal and the tens digit of m here is 0.

Case2: tens place of m=9 and there is a carry over from the addition of the units digit of m and n.

If m=196 and n=246, m+n= 442 = p.
Tens digit of n and p are equal and the tens digit of m here is 9.

Clearly statement 1 is not sufficient.

(2) Units digit of n is greater than the units digit of p.

For the units digit of n to be greater than that of p, there should definitely be a carry from the units digit addition.
If m=336 and n = 255. m+n= 591 =p; Tens digit of m is 3.
If m = 326 and n = 255, m + n = 571; Tens digit of m is 2.
Since we are getting multiple answers, the statement is not alone sufficient.

Now if we combine both the statements, we already know from the second statement that there should be a carry from the units digit addition.
From the first statement, we know that if there is carry, the for units digit of n and p to be equal, tens place of m should be 9.
: Sufficient.

So after combining, we get a definite answer. So answer should be

I think you are mistaken, the question is asking about the tens digit of m. The digits you have mentioned i.e 1 and 2 and the tens digit of n.

Can anyone pls the solution
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 07:23
srikanth9502 wrote:
sarathgopinath wrote:
RonPurewal wrote:
Hello all—
Another new (original) problem for your enjoyment and pleasure.

__

If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

We are calculating the tens digit of m.
(1)Tens digit of n and p are equal.
m + n = p and the tens digit of n and p are equal.
It could be possible in two ways.

Case1: tens place of m is 0.

If m = 301 and n= 513, m + n = 814=p.
Tens digit of n and p are equal and the tens digit of m here is 0.

If m = 301 and n= 523, m + n = 824=p.
Tens digit of n and p are equal and the tens digit of m here is 0.

Case2: tens place of m=9 and there is a carry over from the addition of the units digit of m and n.

If m=196 and n=246, m+n= 442 = p.
Tens digit of n and p are equal and the tens digit of m here is 9.

Clearly statement 1 is not sufficient.

(2) Units digit of n is greater than the units digit of p.

For the units digit of n to be greater than that of p, there should definitely be a carry from the units digit addition.
If m=336 and n = 255. m+n= 591 =p; Tens digit of m is 3.
If m = 326 and n = 255, m + n = 571; Tens digit of m is 2.
Since we are getting multiple answers, the statement is not alone sufficient.

Now if we combine both the statements, we already know from the second statement that there should be a carry from the units digit addition.
From the first statement, we know that if there is carry, the for units digit of n and p to be equal, tens place of m should be 9.
: Sufficient.

So after combining, we get a definite answer. So answer should be

I think you are mistaken, the question is asking about the tens digit of m. The digits you have mentioned i.e 1 and 2 and the tens digit of n.

Can anyone pls the solution

I think I have done it right and have calculated the tens digit of m. Could you please tell me where I am wrong by quoting that part?
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 07:29
1
RonPurewal wrote:
Hello all—
Another new (original) problem for your enjoyment and pleasure.

__

If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) talone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

(1) The tens digits of n and p are equal.
When tens digit of m is 0
m = 100
n = 288
p = 388

But when m = 199
n = 189
p = 388
So here the ten's digit of m is 9 .

Not sufficient since we get 2 different values of tens digit of m

(2) The units digit of n is greater than the units digit of p.

m = 126
n = 235
p = 361

Tens digit of m is 2

m = 136
n = 235
p = 371
Tens digit of m is 3
Not sufficient

Combining 1 and 2, we get since units digit of n is greater than the units digit of p, so there is a carry over of 1 from units to tens digit. Also , from statement one since
tens digit of n and p are equal , then tens digit of m+ 1(carry over ) should be equal to 10 . So tens digit of m should be 9

But when m = 199
n = 189
p = 388
So here the tens digit of m is 9 .

Sufficient
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 08:05
Quote:
If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

Great question. Thanks for sharing Ron!

M = ABC
N = DEF
---------
P = XYZ
---------

1) E = Y
This can happen if B = 0, or if B = 9 and there is carry over from the Sum of (C + F)

M = 192 M = 105
N = 249 N = 254
------- --------
P = 441 P = 359
------- --------
B = 0 or 9. Hence, Insufficient.

2) F>Z
This statement basically means there has to be carry over from the units digit to the ten's digit. Otherwise Z will always be greater than F

M = 255 M = 278
N = 255 N = 202
-------- ----------
P = 510 P = 480
-------- ----------
B = 5 or 7. Hence, Insufficient.

1+2)
M = ABC
N = DEF
---------
P = XYZ
---------
E = Y and F > Z
=> B has to be equal to 9. Sufficient.

M = 192
N = 249
-------
P = 441
-------

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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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03 Aug 2017, 10:52
mcm2112 wrote:
Are we sure this is a correct question.

For statement 1 - If n and p have equal tens digits then m<10, and the tens digit is zero. That seems to be sufficient.

294 + 157 = 451

^^ Here, the tens digits of n and p are equal, but the tens digit of m is not zero.
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Re: If m, n, and p are three-digit integers such that m + n = p, what is  [#permalink]

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21 Aug 2017, 01:25
RonPurewal wrote:
Hello all—
Another new (original) problem for your enjoyment and pleasure.

__

If m, n, and p are three-digit integers such that $$m + n = p$$, what is the tens digit of m ?

(1) The tens digits of n and p are equal.

(2) The units digit of n is greater than the units digit of p.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Digits of M are abc
Digits of N are pqr
Digits of P are xyz

M + N = P
a b c (M)
+ q q r (N)
-------
x y z (P)

(1) The tens digits of n and p are equal.

q = y
This does not talk about the unit digits of M and N
if c = 1, r = 2 then z = 3
but
if c = 8, r = 9 then z = 7 (with 1 carry over) this will add 1 to expected value of y
so, we can't determine value of y

(2) The units digit of n is greater than the units digit of p.
r > z
again we can’t determine value of y (Tens digit of P)

Combining two statements,
if r > z then, c must be such that the unit digit of c + r < r
r = 5
c has to be 6, 7, 8, 9 so, z will be 1, 2, 3, 4 which are less than r.
basically c + r has to carry over.
now when we do this, there will be carry over 1 to total of b and q.
if q = y so, 1 + b = y so, b = 0 and y will always be 1.

ans: C
Re: If m, n, and p are three-digit integers such that m + n = p, what is   [#permalink] 21 Aug 2017, 01:25
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