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\(\frac{J}{B}\)=\(\frac{7}{3}\)
3J=7B

\(\frac{(J-15)}{(B+15)}\)=\(\frac{3}{2}\)
2J-30=3B+45

solve for either J or B-- substitute into equation 1
J= 105
B= 45
After switch:
J=105-15=90
B=45+15=60
Answer: 30
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Yes, +1 for B. Straight forward question.

30 cards will be more.

Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90

Kudos for a correct solution.
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Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90

Kudos for a correct solution.


Old ratio 7:3
new ratio after xfer of 15 cards. 3:2 or 6:4 . so basically a movement of 15 caused 7units to 6units and 3units to 4units..
that means old ratio=7×15/3×15 and new ratio is 6×15/4×15 .
answer 90-60=30
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shriramvelamuri
Yes, +1 for B. Straight forward question.

30 cards will be more.

Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90

Kudos for a correct solution.
ditto, I came up with pretty much same thing, the only difference is that I prefer X and Y as variables.
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Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90

Kudos for a correct solution.

J/B = 7/3
-> 3J = 7B
-> 6J = 14 B

(J-15)/ (B+15) = 3/2
-> 2J-30 = 3B +45
-> 2J = 3B +75
-> 6J = 9 B + 225
-> 14 B = 9 B +225
-> 5B = 225
-> B = 45

J = (7/3) * 45 = 105

So, after gift, difference between John and bills card = (J-15) - (B+15) = (105 - 15) - (45 +15) = 90 - 60 = 30

Answer B
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There is a shortcut of solving such questions: lookout for the Percentages of either John or Bill

Let the asked which is John had how many more baseball cards than Bill= X

So if I take the percentage for John in 7:3 then 70% of cards are with John

after John can 15 cards then john:Bill are in ratio of 3:2 .So John now has 60% of the total cards.

it means than (70%-60%)(total cards)=15

which means total cards=150

so for calculating the asked value which is 20% of the total(calculating the ratio from 3:2 which could be written into 60:40)

and 20% of 150=30


See....easy...peasy

This way of solving with percentages would help in solving ratio and proportion questions in which solution or water is involved


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Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90
My head is spinning from the OA explanation (Veritas is great, but this time, seriously?) and GMATOak 's impressive but NOT easy-peasy looking method. Think I'll stick to one measly variable, x, and a couple of ratios. They served just fine. Contrary to OA's prediction, I took just 1:40 with double checking.

\(\frac{J}{B}\) = \(\frac{7x}{3x}\)

\(\frac{7x - 15}{3x +\\
15}\) = \(\frac{3}{2}\)

2(7x - 15) = 3(3x + 15)

14x - 30 = 9x + 45

5x = 75

x = 15 --> that's the multiplier for the original ratio.

John had 7*15 = 105 cards, he gave 15 away, now he has 90.

Bill had 3*15 = 45 cards, he received 15 more, now he has 60.

90 - 60 = 30. John has 30 more cards than Bill.

Answer B
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Algebra was simple but some how i got stuck and then tried this approach and it seems to have worked.

I plugged in a value from answer choice and arrived at the correct answer through elimination. The calculations are simple so it did not take much time.

Let us pick the middle from the given answer choices=45

Therefore John has 45 more caps than bill.

Let bill have X caps than john will have X+45 caps. Set up the equation-Take 2nd ratio.
J/B=X+45/X=3/2
X(Bill)=90.
No of caps John has is 90+45=135
The earlier ratio will be J+15/B-15=150/75=2 so this is wrong since earlier ratio is 7/2

Next plugin=30
Equation=X+30/X=3/2
X(Bill)=60
J=60+30=90

Earlier Ratio=J/B=105/45=7/3
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Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90

Kudos for a correct solution.

We can let the original number of baseball cards John and Bill had be 7x and 3x, respectively. So we can create the equation:

(7x - 15)/(3x + 15) = 3/2

2(7x - 15) = 3(3x + 15)

14x - 30 = 9x + 45

5x = 75

x = 15

Therefore, John and Bill originally had 105 and 45 cards, respectively. After John gave Bill 15 cards, John now had 90 cards and Bill had 60 cards. So John had 30 more cards than Bill.

Answer: B
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Bunuel
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

A. 15
B. 30
C. 45
D. 60
E. 90

Kudos for a correct solution.




Could someone tell me what is wrong with this calculation?

7J/3B=(3J/2B)+15

(7J/3B)-(3J/2B)=15

(14J/6B)-(9J/6B)=15

5J/6B=15

5J=75B

J=15B

Then I am unsure. I tried substituting B for 2, obtaining the solution by coincidence.

Posted from my mobile device
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NOTE: Total number of cards before-after doesn't change.
Before:
7/10 : 3/10
After:
3/5 : 2/5 = 6/10 : 4/10
Let's consider J only. After giving 15 cards, the before-after GAP in his share is:
7/10 - 6/10 = 1/10
=> 15 cards = 1/10
=> total cards = 150
=> After, J has 90 cards, B has 60 cards.
=> 90-60 = 30 cards GAP between them.
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