Hi, can somebody help me in solving this DS question..."in easy way"??
if x, y, and z are three-digit positive integers and if x = y+z, is the hundreds digits 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 z is equal to the sum f the units digits of y and z.
OG
A
PLEASE HELP!
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When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.
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
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 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.
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:If x, y, and z are three-digit positive integers and if x = y+z, is the hundreds digits 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 z is equal to the sum f 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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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