The figure above shows the circular cross section of a concrete water

Statement 1: The ratio of t - r to r is 0.15 and t - r is equal to 0.3 foot
(t - r)/r = 0.15 & (t - r) = 0.3
==> r = 2 --- Sufficient

Statement 2: The area of the concrete in the cross section is 1.29π square feet
π (t - r)^2 = 1.29π -- Insufficient

Answer A

Stmt 1: t-r =.3 ft; t-r/r = .15 => r = 2ft - sufficient
stmt 2: πt^2 - πr^2 = 1.29π - Not sufficient as we cannot find either t or t-r from this

A
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St-1: \(\frac{(t-r)}{r}\) = 0.15 --> \(\frac{0.3}{r}\) = 0.15 . r can be calculated. Sufficient
St-2: π(t^2 - r^2) = 1.29π. Two unknowns. Not sufficient

Ans - A

Hi Bunuel...

Eventhough I found out the answer to be A.

Doubt :-

At what point of time I should stop plugging in the values? t^2-r^2 = 1.29....After sometime I got tired and didnt plug in values because nothing
was getting satisfied?? How should I approach this types of problem, when in actual GMAT there might be one such question where one particular value will do the trick.

Is it necessary that if the answer yields result as D, both the answers should be same in numerical problems. Generally I ve found them same\
whenever the answer is D. So is it safe to solve easy one first? and try hit and trial for the second option and if I am not finding any particular result by using option B.. I should see whether the result is getting satisfied if I plug in the asnwer value obtained from A. Can 2 options A and B yield contradicting results yet be correct? (I am talking about numerical problems)

On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem (no matter whether the answer is A, B, C, D, or E).
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Statement 1: t-r/r=5/2 --> t-r=7/2 and t-r=0,3 foot --> 7x-2x=3/10 --> we can calculate x, thus we can calculate r. Sufficient.

Statement 2 π(t+r)(t-r)=1,29/π we cannot solve this equation

Answer A.
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the Answer is A...

Statement 1) : the ratio of t-r to t is 0.15 & t-r is 0.3

this means that t-r/r =0.15 OR : if we separate variables from each other we have ; t/r- r/r = 0.15 (as we know r/r is 1 ) so we have: t/r-1 =0.15 OR : t/r= 0.15 + 1 = 1.15

from this point we can take t= 1.15*r ... On the other hand we have t-r = 0.3 and we should replace 1.15r instead of t in the equation and get : 1.15 r - r = 0.3 or 0.15 r = 0.3


so we have : r = 0.3 / 0.15 = 2 so this statement is sufficient


statement 2 ) ONLY gives the whole area and we can not obtain r from this info . so this is clearly insufficient


so , answer is A....

I think 'D' should be the right answer as from 2 we have t^2-r^2=1.29;
(t-r)*(t+r)=1.29 only such factors of 1.29 are 4.3 & 0.3 (since 43 is prime).
Substituting t+r=4.3 & t-r = 0.3 gives us r = 2.
And statement 1 also gave the same answer, hence the correct option should be D.
If not, pls help me understand. TIA.

not that Tough and Tricky, LOL

VeritasKarishma Bunuel ScottTargetTestPrep

In sums like these, especially stat 2, we get (t+r)(t-r)= 1.29
Now I assumed that various numbers can fulfill the condition, so insuff.
But, on some DS problems, it turns out that statements like these sometimes have only one set of correct value.

So under time pressure, how to decide whether to mark insuff and move on or try plugging a few different values and check?

Chitra657

When you have no constraints on the values the variables can take, an equation with two or more variables will give you multiple solutions.

Say a + b = 10
a can be 9.1 so b will be 0.9
a can be 11 so b will be -1
a can be 5 so b will be 5
and so on...
There will be infinite values.

But what if you are given that a and b must be positive integers. Then you have limited solutions: a = 1, b = 9; a = 2, b = 8 ... till a = 9, b = 1.
Now what if you are given further than a < b? Then you have still fewer solutions: a = 1, b = 9; a = 2, b = 8; a = 3, b = 7, a = 4, b = 6
Now what if you are given that a and b both are perfect squares too? Then there is only one solution a = 1, b = 9

Hence, when trying to figure out whether an equation in multiple variables has a unique solution or many solutions, you need to look at the other constraints mentioned.

Check this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -of-thumb/
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There are indeed many DS questions where you have an equation with more than one unknown, but there is only one possibility for a solution (commonly when the unknowns are required to be integers). The first advice I can give you is to be super careful and always check the constraints on the unknowns.

That said, there are actually more than one value of r to satisfy that equation, so your answer was correct. However, unless you are running very short on time, it is a good idea to verify this. For this equation, it is not very difficult. I'd rather use the non-factored form t² - r² = 1.29 to do that.

First, we can let r = 0.1. Then, r² = 0.01 and t² = 1.28. We don't need to actually calculate the value of t, we just need to see that it is a reasonable number (for this question, it just means that it is positive) and notice that this set of r and t satisfies the equation t² - r² = 1.29. Thus, r = 0.1 is one possibility. Next, let r = 0.2 or some other number you want. You can follow the same steps as above and see that we can again find a positive value of t to satisfy the equation t² - r² = 1.29. Since we have more than one possible value for r, statement two is not sufficient to answer the question.
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