A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives a $4 plus one half of what remains. Next, Bob receives $4 plus one third of what remains. Finally, Chloe receives the remaining $32. How much money did Bob receive?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 52
I got 20, but I am confused about the methodology. Can someone help me out (in details) here?
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Word Problem - seems difficult
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muhtasimhassan
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Note: we don't need to consider Ann's portion in the solution.muhtasimhassan wrote:A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives a $4 plus one half of what remains. Next, Bob receives $4 plus one third of what remains. Finally, Chloe receives the remaining $32. How much money did Bob receive?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 52
Let K = the money remaining AFTER Ann has received her portion and then go from there.
We're told that, once we remove Bob's portion, we have $32 for Chloe.
So, we get K - Bob's $ = 32
Bob receives $4 plus one-third of what remains
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives 4 + (K-4)/3
So, our equation becomes: K - [4 + (K-4)/3 ] = 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value into K - Bob's $ = 32 to get 52 - Bob's $ = 32
So, Bob's $ = 20
Answer: A
Cheers,
Brent
Solve for K (K=52) and then determine Bob's portion ($20).
The answer is, indeed, A
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Hi muhtasimhassan,
What is the source of this question? I ask because it does NOT follow any established GMAT patterns. Of the three people mentioned in the prompt, Ann (and the data that applies to Ann) is absolutely irrelevant to the question that is asked (meaning that it can be completely ignored). GMAT questions do NOT include "filler", so this question is NOT representative of what you'll see on Test Day, and you should be suspicious of whatever source this came from.
To answer the question, there are a couple of different approaches that you can use. You might find the algebra to be fairly straight-forward:
We're told that Bob receives $4 plus 1/3 of whatever money remains (re: exists). We're told that after Bob receives his money, Chloe receives the remaining $32.
Working backwards from this information, the 1/3 of the money that Bob received was based on a total that included Chloe's $32. Since Bob got 1/3 of what remained, Chloe got 2/3 of what remained:
(2/3)(X) = $32
X = $48
So, Bob received 1/3 of $48 + $4
Bob = $16 + $4 = $20
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
What is the source of this question? I ask because it does NOT follow any established GMAT patterns. Of the three people mentioned in the prompt, Ann (and the data that applies to Ann) is absolutely irrelevant to the question that is asked (meaning that it can be completely ignored). GMAT questions do NOT include "filler", so this question is NOT representative of what you'll see on Test Day, and you should be suspicious of whatever source this came from.
To answer the question, there are a couple of different approaches that you can use. You might find the algebra to be fairly straight-forward:
We're told that Bob receives $4 plus 1/3 of whatever money remains (re: exists). We're told that after Bob receives his money, Chloe receives the remaining $32.
Working backwards from this information, the 1/3 of the money that Bob received was based on a total that included Chloe's $32. Since Bob got 1/3 of what remained, Chloe got 2/3 of what remained:
(2/3)(X) = $32
X = $48
So, Bob received 1/3 of $48 + $4
Bob = $16 + $4 = $20
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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Let R = what remains after Ann takes her share and Bob takes $4.muhtasimhassan wrote:A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives a $4 plus one half of what remains. Next, Bob receives $4 plus one third of what remains. Finally, Chloe receives the remaining $32. How much money did Bob receive?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 52
Since, Bob receives (1/3)R, Chloe receives (2/3)R.
Since Chloe receives 32:
(2/3)R = 32
R = 48.
Since Bob receives 1/3 of what remains plus $4:
B = (1/3)*48 + 4 = 20.
The correct answer is A.
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Brent@GMATPrepNow
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Hey Rich,
I created this question, based on a math contest question I quite enjoyed. The question isn't part of our GMAT prep course. That said, I don't agree with your assertion that it isn't a GMAT-style question.
Sure, we need not use the information about Ann to solve the question, but we COULD use it. In fact, if you check the original post (https://www.beatthegmat.com/tough-word-p ... 27218.html), you'll see that several people used the information about Ann to answer the question.
The fact that the question can be solved without using the "filler" information about Ann, doesn't mean it's not a GMAT-style question.
Consider question #172 from the OG13 (and the OG2015)
So, the fact that we need not use the formula to answer the question does not make it less GMAT-like.
Cheers,
Brent
I created this question, based on a math contest question I quite enjoyed. The question isn't part of our GMAT prep course. That said, I don't agree with your assertion that it isn't a GMAT-style question.
Sure, we need not use the information about Ann to solve the question, but we COULD use it. In fact, if you check the original post (https://www.beatthegmat.com/tough-word-p ... 27218.html), you'll see that several people used the information about Ann to answer the question.
The fact that the question can be solved without using the "filler" information about Ann, doesn't mean it's not a GMAT-style question.
Consider question #172 from the OG13 (and the OG2015)
Here, we're given a formula for finding the sum of the first n positive integers. Do we need that formula to answer the question? No. If you check this thread https://www.beatthegmat.com/og13-q172-ps ... tml#624461, you'll find 3 different solutions, and ONLY 1 solution used the given formula.For any positive integer n, the sum of first n positive integer equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?
A) 10,100
B) 20,200
C) 22,650
D) 40,200
E) 45,150
So, the fact that we need not use the formula to answer the question does not make it less GMAT-like.
Cheers,
Brent
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Mathsbuddy
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Could someone please see what is flawed in this solution:
(Many thanks)
S = A + B + C
Ann: A = 4 + (S-4)/2] = 2 + S/2
Remainder1 = S - (2 +_ S/2) = S/2 - 2
Bob: B = 4 + (S/2 - 2 - 4)/3 = 2 + S/6
Remainder2 = S - (2 + S/6) = 5S/6 - 2
Chloe: C = 32
So 5S/6 - 2 = 32
5S/6 = 34
S/6 = 204/5 = 40.80
So B = 2 + 40.80 = 42.80
(Many thanks)
S = A + B + C
Ann: A = 4 + (S-4)/2] = 2 + S/2
Remainder1 = S - (2 +_ S/2) = S/2 - 2
Bob: B = 4 + (S/2 - 2 - 4)/3 = 2 + S/6
Remainder2 = S - (2 + S/6) = 5S/6 - 2
Chloe: C = 32
So 5S/6 - 2 = 32
5S/6 = 34
S/6 = 204/5 = 40.80
So B = 2 + 40.80 = 42.80
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Matt@VeritasPrep
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Not true at all - plenty of questions contain superfluous information. I had a few inference questions on test day that didn't require most of the prompt, and heck, red herrings are the essence of data sufficiency, which is all about testing a student's ability to determine which statements are necessary, which are sufficient, and which are needless.[email protected] wrote:GMAT questions do NOT include "filler", so this question is NOT representative of what you'll see on Test Day, and you should be suspicious of whatever source this came from.
IMO, students are better off being suspicious of posters who have not been designated as experts by BTG.
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Matt@VeritasPrep
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Mathsbuddy, here's how I'd do it:Mathsbuddy wrote:Could someone please see what is flawed in this solution:
(Many thanks)
S = A + B + C
Ann: A = 4 + (S-4)/2] = 2 + S/2
Remainder1 = S - (2 +_ S/2) = S/2 - 2
Bob: B = 4 + (S/2 - 2 - 4)/3 = 2 + S/6
Remainder2 = S - (2 + S/6) = 5S/6 - 2
Chloe: C = 32
So 5S/6 - 2 = 32
5S/6 = 34
S/6 = 204/5 = 40.80
So B = 2 + 40.80 = 42.80
Total = x
Ann = 4 + (x - 4)/2
Remainder 1 = x - (4 + (x-4)/2) = x - 4 - (x-4)/2 = (x - 4)/2
Bob = 4 + ((x-4)/2 - 4)/3
At this point, we know that Chloe gets $32, so we can say that Ann + Bob + Chloe = x, or
4 + (x-4)/2 + 4 + ((x-4)/2 - 4)/3 + 32 = x
which gives x = 108. From there, find Ann's portion, since it's easier to compute ($56). Since Ann gets $56 and Chloe gets $32, Bob must get what's left ($20).
I like this solution better, since it doesn't require students to notice that Ann's portion is irrelevant. (That's not an easy deduction with time constraints, or even without them!)
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I'll add that the sole objective of many/most Integrated Reasoning questions is to wade through an A LOT of information (most of which is fluff/filler) and extract the key piece(s) of information needed to answer the question.Matt@VeritasPrep wrote:Not true at all - plenty of questions contain superfluous information. I had a few inference questions on test day that didn't require most of the prompt, and heck, red herrings are the essence of data sufficiency, which is all about testing a student's ability to determine which statements are necessary, which are sufficient, and which are needless.[email protected] wrote:GMAT questions do NOT include "filler", so this question is NOT representative of what you'll see on Test Day, and you should be suspicious of whatever source this came from.
IMO, students are better off being suspicious of posters who have not been designated as experts by BTG.
Cheers,
Brent
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Matt@VeritasPrep
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Absolutely! Taking it that way, RC is also full of unhelpful fluff.Brent@GMATPrepNow wrote:I'll add that the sole objective of many/most Integrated Reasoning questions is to wade through an A LOT of information (most of which is fluff/filler) and extract the key piece(s) of information needed to answer the question.
Nice question, Brent: I like that it has a plodding solution (mine) and a poetic one (yours), as any good tricky standardized test question should.
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Mathsbuddy
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Thanks Matt,Matt@VeritasPrep wrote:Mathsbuddy, here's how I'd do it:Mathsbuddy wrote:Could someone please see what is flawed in this solution:
(Many thanks)
S = A + B + C
Ann: A = 4 + (S-4)/2] = 2 + S/2
Remainder1 = S - (2 +_ S/2) = S/2 - 2
Bob: B = 4 + (S/2 - 2 - 4)/3 = 2 + S/6
Remainder2 = S - (2 + S/6) = 5S/6 - 2
Chloe: C = 32
So 5S/6 - 2 = 32
5S/6 = 34
S/6 = 204/5 = 40.80
So B = 2 + 40.80 = 42.80
Total = x
Ann = 4 + (x - 4)/2
Remainder 1 = x - (4 + (x-4)/2) = x - 4 - (x-4)/2 = (x - 4)/2
Bob = 4 + ((x-4)/2 - 4)/3
At this point, we know that Chloe gets $32, so we can say that Ann + Bob + Chloe = x, or
4 + (x-4)/2 + 4 + ((x-4)/2 - 4)/3 + 32 = x
which gives x = 108. From there, find Ann's portion, since it's easier to compute ($56). Since Ann gets $56 and Chloe gets $32, Bob must get what's left ($20).
I like this solution better, since it doesn't require students to notice that Ann's portion is irrelevant. (That's not an easy deduction with time constraints, or even without them!)
I like what you have said; I fully understand and agree.
However, Remainder 2 must also equal Chloe's total of $32.
If I am not mistaken then
5S/6 - 2 = 32 which gives
b = 42.80
If this is not incorrect, then the question would be flawed for allowing 2 different answers.
Can you see my error, or am I right?
Thanks.
