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655-705 (Hard)|   Mixture Problems|                                          
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sriharsha4444
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Material A costs $3 per kilogram, and Material B costs $5 per kilogram 01 Jan 2024, 22:43
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Bunuel
Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x >y?

    Given: x + y = 10.
    Question: is x > y ?

(1) y > 4.

Clearly insufficient: if (y = 4.5) < (x = 5.5), the answer will be YES but if (y = 6) > (x = 4), the answer will be NO.

(2) The cost of the 10 kilograms of material K is less than $40:

    3x + 5y < 40

Since y = 10 - x then we'd have:

    3x + 5(10 - x) < 40;
    2x > 10;
    x > 5, so x > y.

Sufficient.

Answer: B.
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hey Bunuel, but the question doesn't say that 10 kilograms of material K consists of ONLY x kilograms of material A and y kilograms of material B. So how can we assume that x+y = 10? If that were the case, then we can assume so.
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Material A costs $3 per kilogram, and Material B costs $5 per kilogram 01 Jan 2024, 23:53
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sriharsha4444
Bunuel
Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x >y?

    Given: x + y = 10.
    Question: is x > y ?

(1) y > 4.

Clearly insufficient: if (y = 4.5) < (x = 5.5), the answer will be YES but if (y = 6) > (x = 4), the answer will be NO.

(2) The cost of the 10 kilograms of material K is less than $40:

    3x + 5y < 40

Since y = 10 - x then we'd have:

    3x + 5(10 - x) < 40;
    2x > 10;
    x > 5, so x > y.

Sufficient.

Answer: B.



hey Bunuel, but the question doesn't say that 10 kilograms of material K consists of ONLY x kilograms of material A and y kilograms of material B. So how can we assume that x+y = 10? If that were the case, then we can assume so.
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It does. The statement "material K consists of x kilograms of material A and y kilograms of material B" implies that material K is made entirely of these two ingredients, so x and y together make up 100% of material K.

P.S. Also, your doubt has been addressed twice previously in this thread. For example, here: https://gmatclub.com/forum/material-a-c ... l#p2989296 Please, read entire topic before posting. Thank you!
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Material A costs $3 per kilogram, and Material B costs $5 per kilogram 02 Jan 2024, 14:26
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Video solution here (2:41):


 ­
Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP
 
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Material A costs $3 per kilogram, and Material B costs $5 per kilogram 24 Jun 2025, 01:08
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A = 3/Kg
B = 5/Kg

X + Y = 10 Kg
Question is X>Y?

1. Y > 4?
So What? It Could be 4.5, 5, 5.5, | We can't say if X>Y?

2. Cost of 10Kgs of K is Less than 40.
Means Cost of 1 Kg is Less than 4


Now...If the Average is closer to X Means X is more than Y.

3--------4-------5

Average is Less than 4..Means X is is more in quantity... So Sufficient.
Answer B





alltimeacheiver
Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B, is x > y ?

(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40.
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Material A costs $3 per kilogram, and Material B costs $5 per kilogram 01 May 2026, 01:06
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1) y > 4

👉 Total = 10 → x=10−y

Test quickly (DS style):

If y=6 → x=4 → x<y ❌
If y=4.5 → x=5.5 → x>y ✅

👉 Both possible

❌ Not sufficient

(2) Total cost < 40

👉 Avg price < 4
👉 Tending toward cheaper (A = $3)

Think of it in alligation way
<40, means less than 4 means tending towards 4 means more weight of a means >3

👉 So more A than B → x > y

✅ Sufficient
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