Question no.1:
3.2@#6 : If @ and # each represent single digits in the given decimal, what digit does @ represent?
(1) When the decimal is rounded to the nearest tenth, 3.2 is the result.
(2) When the decimal is rounded to the nearest hundredth, 3.24 is the result.
Question no.2:
If p is a positive integer, what is the remainder when p is divided by 4?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.
Answer will be posted in 24 hrs time
Thanks,
Quant-Master
Thursday, August 6, 2009
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Q1
ReplyDelete3.2@#6=3.2_3_7_6(a possible scenario using information in (2))
Therefore, @=3
and if this is a data sufficiency question, the answer is (B)
Q2
ReplyDeleteSince we get a remainder of 5 when p is divided by 8(from (1)), let us assume
p=8k+5(where k is any number)
p/4=(2k+1)+1/4
(2k+1) is an integer and the remainder, thus is 1.
The answer should thus be (A)
I don't think that we can deduce any information from (2), or can we?
I think Q1 answer is: E
ReplyDeleteFrom 1st condition, we can conclude: @<5
From 2nd condition, we can conclude: we cannot conclude anything, cos: 3.2@#6 cud be 3.2406 or 2.2396 and still be rounded to 3.24. So @=3 or 4.
Combine 1, 2:
2nd condition already deals with cases where @<5. So no new info results. Hence (E)
Solution to Question no.1:
ReplyDelete3.2@#6 : If @ and # each represent single digits in the given decimal, what digit does @ represent?
(1) When the decimal is rounded to the nearest tenth, 3.2 is the result.
(2) When the decimal is rounded to the nearest hundredth, 3.24 is the result.
Statement 1: If the number is rounded to 3.2 then @ has to be any number between 0-4. If @ is above 4 than the number will be rounded off to 3.3 which is not the case. This statement alone is insufficient as any number between 0-4 might be the possibility.
Statement 2: If the number is rounded to 3.24 than @ can be 3 or 4. Let’s say the number is 3.23#6 if # is above 5 than the number will be rounded off to 3.24. Let’s say the number is 3.24#6 if # is below 5 than the number will be rounded off to 3.24 Hence @ can be 3 or 4. Insufficient
Even after combining both the statements it is not possible to bet on the answer.
Hence E
Solution to Question no.2:
If p is a positive integer, what is the remainder when p is divided by 4?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.
Statement 1: This statement says that the number is of the form 8k+5. Now let’s divide this number by 4. 8k+5/4 = (8k/4)+(5/4)
When 8k is divided by 4 remainder is 0 and when 5 is divided by four remainder is 1. Hence the remainder when 8K+5 is divided by 4 will be 1. Statement 1 is sufficient
Statement 2: This statement alone is sufficient. You need not try different values. Since p is the sum of the square of two different numbers two different numbers can be both even, odd or one odd and one even. When both or even or odd the sum will be even hence the remainder can be 2 or 0. If one is even and one is odd the result will be odd hence the remainder will be 1 or 3. If you know this simple fact evaluating statement 2 is 10 secs job
Hence A
Let me know if you have any queries
Thanks,
Quant-Master