If x,y, and z are three digit positive integers and if x= y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1. The tens digit of x is equal to the sum of the tens digits of y and z.
2. The units digit of x is equal to the sum of the units digits of y and z.
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Brent@GMATPrepNow
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Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?If x,y, and z are three digit positive integers and if x= y+z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1) The tens digit of x equal to the sum of the tens digits of y and z
2) The unit digit of x is equal to the sum of the units of y and z
Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308
Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
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Let y = 2BC, z = 2EF, and x = HTU, so that the addition looks as follows:oquiella wrote:If x,y, and z are three digit positive integers and if x= y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1. The tens digit of x is equal to the sum of the tens digits of y and z.
2. The units digit of x is equal to the sum of the units digits of y and z.
2BC
2EF
HTU
When will it be true that H ≠2+2?
When we have to CARRY A 1 FROM THE TENS PLACE TO THE HUNDREDS PLACE.
To illustrate:
259
249
508
Here, because we have to carry a 1 from the tens place to the hundreds place, H = 2+2+1 = 5.
Question rephrased:
ABC
DEF
HTU
In the addition problem above, do we have to a carry a 1 from the tens place to the hundreds place?
Statement 1: The tens digit of x is equal to the sum of the tens
digits of y and z.
Since T = B+E, there is no need to carry a 1 to the hundreds place.
SUFFICIENT.
Statement 2: The units digit of x is equal to the sum of the
units digits of y and z.
Since U = C+F, we do not need to carry a 1 from the UNITS PLACE to the TENS PLACE.
But it cannot be determined whether we have to carry a 1 from the TENS PLACE to the HUNDREDS PLACE.
If T = B+E = 0+0 = 0, then there is no need to carry a 1 to the hundreds place:
If T = B+E = 9+9 = 18, then we must carry a 1 to the hundreds place.
INSUFFICIENT.
The correct answer is A.
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Amrabdelnaby
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Brent,
I dont understand why in your approach you ruled out scenario one in statement one?
how did you assume that the hundreds digits of y and z don't add up to more than 9?
I dont understand why in your approach you ruled out scenario one in statement one?
how did you assume that the hundreds digits of y and z don't add up to more than 9?
Brent@GMATPrepNow wrote:Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?If x,y, and z are three digit positive integers and if x= y+z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1) The tens digit of x equal to the sum of the tens digits of y and z
2) The unit digit of x is equal to the sum of the units of y and z
Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308
Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
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Brent@GMATPrepNow
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Actually, I ruled our Scenario 1 BEFORE I examined the statements.Amrabdelnaby wrote:Brent,
I dont understand why in your approach you ruled out scenario one in statement one?
how did you assume that the hundreds digits of y and z don't add up to more than 9?
Brent@GMATPrepNow wrote:Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?If x,y, and z are three digit positive integers and if x= y+z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1) The tens digit of x equal to the sum of the tens digits of y and z
2) The unit digit of x is equal to the sum of the units of y and z
Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308
Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
If the hundreds digits of y and z add up to more than 9, then x would NOT be a 3-digit number. x would be a 4-digit number.Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Cheers,
Brent
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nasahtahir
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Hi,Brent@GMATPrepNow wrote:Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?If x,y, and z are three digit positive integers and if x= y+z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1) The tens digit of x equal to the sum of the tens digits of y and z
2) The unit digit of x is equal to the sum of the units of y and z
Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308
Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
If I may ask
if we take x = 500
Y=275
z=225
How exactly is statement one sufficient when according to both your scenarios 1 & 2 we got different answers, which technically contradicts '1) The tens digit of x equal to the sum of the tens digits of y and z '
Please forgive me as I am just a beginner
regards,
Hash
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Brent@GMATPrepNow
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If you're suggesting that x = 500, y=275 and z=225 satisfies statement 1, then that it not correct.nasahtahir wrote: Hi,
If I may ask
if we take x = 500
Y=275
z=225
How exactly is statement one sufficient when according to both your scenarios 1 & 2 we got different answers, which technically contradicts '1) The tens digit of x equal to the sum of the tens digits of y and z '
Please forgive me as I am just a beginner
regards,
Hash
With those particular values, the tens digit of x in not equal to the sum of the tens digits of y and z
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nasahtahir
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Exactly my point kind sir,Brent@GMATPrepNow wrote:If you're suggesting that x = 500, y=275 and z=225 satisfies statement 1, then that it not correct.nasahtahir wrote: Hi,
If I may ask
if we take x = 500
Y=275
z=225
How exactly is statement one sufficient when according to both your scenarios 1 & 2 we got different answers, which technically contradicts '1) The tens digit of x equal to the sum of the tens digits of y and z '
Please forgive me as I am just a beginner
regards,
Hash
With those particular values, the tens digit of x in not equal to the sum of the tens digits of y and z
Both these scenarios 'Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308 '
ARE NOT SUFFICIENT if I'm not mistaken.
What I'm tying to ask from you is How!
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nasahtahir
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Jeff@TargetTestPrep
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We are given that x, y, and z are three-digit positive integers. We are also given that x = y + z. We must determine whether the hundreds digit of x is equal to the sum of the hundreds digits of y and z.oquiella wrote:If x,y, and z are three digit positive integers and if x= y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
1. The tens digit of x is equal to the sum of the tens digits of y and z.
2. The units digit of x is equal to the sum of the units digits of y and z.
Statement One Alone:
The tens digit of x is equal to the sum of the tens digits of y and z.
In order for statement one to be true, the sum of the tens digits of y and z must be less than 10. Let's test some convenient numbers to illustrate this idea.
y = 143
z = 132
x = 275
Since 4 + 3 = 7, the tens digit of x is equal to the sum of the tens digits of y and z.
Since 1 +1 = 2, we also see that the hundreds digit of x is equal to the sum of the hundreds digits of y and z.
The concept here is:
Since x = y + z, the sum of the hundreds digits of y and z must be no more than 9 and there cannot be a 1 carrying over to the thousands place, because x is only 3 digits. In other words, the sum of the hundreds digits of y and z will be equal to the hundreds digit of x UNLESS there is a 1 carrying over from the sum of the tens digits of y and z to the hundreds place. However, we see from the example shown above that if the sum of the tens digits of y and z is equal to the tens digit of x, the sum of the tens digits of y and z will be no more than 9. And if the sum of the tens digits of y and z is no more than 9, there will not be a 1 carrying over to the hundreds place. Therefore, the sum of the hundreds digits of y and z indeed will be equal to the hundreds digit of x.
Thus, we see that statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Note: Notice that if we selected numbers in which the sum of the tens digit of y and z was 10 or higher, those numbers would not have fulfilled the information in statement one.
y = 143
z = 172
x = 315
Notice that 4 + 7 ≠1. In other words, the tens digit of x IS NOT equal to the sum of the tens digits of y and z. Thus, we cannot use numbers in which the sum of the tens digits of y and z is 10 or higher.
Statement Two Alone:
The units digit of x is equal to the sum of the units digits of y and z.
From the work we did in statement one, we can see that knowing only that the units digit of x is equal to the sum of the units digits of y and z is not enough information to determine whether the hundreds digit of x is equal to the sum of the hundreds digits of y and z.
Case #1
y = 143
z = 172
x = 315
In this case 1 + 1 ≠3, so the hundreds digit of x IS NOT equal to sum of the hundreds digits of y and z.
Case #2
y = 143
z = 132
x = 275
In this case 1 + 1 = 2, so the hundreds digit of x is equal to sum of the hundreds digits of y and z.
Statement two alone is not sufficient to answer the question.
Answer: A
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