GMAT-30: Data Sufficiency — Word Problems
Matnli DS masalalari: avval kerakli nomaʼlumlar roʻyxati, foiz oʻzgarishida baza kerak emas, toʻplam, tezlik va foiz daromadi.
GMAT-30: Data Sufficiency — Word Problems
Data Sufficiency'ning eng biznesga yaqin turi — matnli masalalar: foiz oʻzgarishi, aralashma, tezlik, toʻplamlar, foiz daromadi. Quant'dagi barcha bilim shu yerda qayta ishlaydi, bitta farq bilan: masalani yechmaysiz, yechish uchun nima kerakligini aniqlaysiz. Shuning uchun eng kuchli qurol — maʼlumotlarni oʻqishdan oldin «menga nima kerak?» deb soʻrash.
Bu darsdan keyin siz
- maʼlumotlarni oʻqishdan oldin kerakli nomaʼlumlar roʻyxatini tuzasiz;
- foiz oʻzgarishida baza kerak emasligini koʻrasiz;
- toʻplam, tezlik va aralashma formulalarini DS ichida ishlatasiz;
- «foiz» va «son» farqini maʼlumotlarda tanib olasiz.
Avval «menga nima kerak?»
Foiz oʻzgarishi — baza kerak emas
Tezlik va ish
Exam English — savol qanday soʻraydi
- by what percent did … changenecha foizga oʻzgardi — baza kerak emas
- how many … in alljami nechta — haqiqiy son kerak
- working togetherbirgalikda — unumlar qoʻshiladi
- compounded annuallyhar yili kapitallashtiriladi
- marked up / discountedustama / chegirma
GMAT savollari
GMAT-style question · Data Sufficiency 60 s
By what percent did a store's revenue from a certain product change from 2024 to 2025?
(1) From 2024 to 2025 the product's price rose by 10% and the number of units sold fell by 10%.
(2) The store's revenue from the product in 2024 was $50,000.
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Yechimni koʻrish
Javob: A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1): 1.1 × 0.9 = 0.99 — 1% kamaydi, yetarli. (2): bitta yilning tushumi — oʻzgarishni bermaydi.
C — foiz oʻzgarishini topish uchun haqiqiy summa kerak deb oʻylagan javob.
GMAT-style question · Data Sufficiency 60 s
Of the 50 employees at a firm, how many speak both English and Korean?
(1) 30 of the employees speak English and 25 speak Korean.
(2) 5 of the employees speak neither English nor Korean.
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Yechimni koʻrish
Javob: C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1): «hech biri» nomaʼlum — kesishma 5 dan 25 gacha boʻlishi mumkin. (2): A va B nomaʼlum. Birga: 30 + 25 + 5 − 50 = 10.
E — formulani eslay olmagan yoki «hech biri» ni hisobga olmagan javob.
Matnli DS savolida uch qadam:
- savoldan formulani tanlang (toʻplam, tezlik, foiz, aralashma);
- formulada nima nomaʼlum — roʻyxat qiling;
- har bir maʼlumot roʻyxatni toʻldiradimi — shuni tekshiring.
Percent change asked → need the actual revenue
Percent change asked → the multipliers are enough
Foiz oʻzgarishi — nisbat; baza qisqarib ketadi.
«Ikkala unum ham bor» → hisoblashni boshlash
«Ikkala unum ham bor» → yetarli, keyingi savolga
Javobni topish — vaqt isrofi; yetarlilik soʻralgan.
Mashq
1 What was the price of a jacket before a discount? (1) The discount was 20%. (2) The discount was $16.
Javobni koʻrish
C — BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Birga: 0.2 × narx = 16 → $80.
2 How many units must a company sell to break even? (1) Its fixed costs are $9,000, and each unit sells for $18 more than it costs to make. (2) Each unit sells for $30.
Javobni koʻrish
A — Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (1): 9,000 ÷ 18 = 500.
3 What was a van's average speed for a whole trip? (1) It drove 120 km in 2 hours and then 180 km in 3 hours. (2) The trip covered 300 km in 5 hours in total.
Javobni koʻrish
D — EACH statement ALONE is sufficient. Ikkalasi ham 300 ÷ 5 beradi.
4 How much interest does a deposit earn in 2 years at 10% compounded annually? (1) The deposit is $10,000. (2) After 1 year the balance is $11,000.
Javobni koʻrish
D — EACH statement ALONE is sufficient. (2) dan deposit 11,000 ÷ 1.1 = 10,000.
5 Did a store make a profit on a lamp? (1) The lamp's price was marked up 50% above its cost. (2) The lamp was sold at 40% off its marked price.
Javobni koʻrish
C — BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Birga: 1.5 × 0.6 = 0.9 — aniq «yoʻq».
Kalit soʻzlar
- word problemmatnli masala
- percent changefoiz oʻzgarishi
- basebaza
- ratetezlik, unum
- overlapping setskesishuvchi toʻplamlar
- break evenzararsiz ishlamoq
- depositomonat
- what you neednima kerak
Esda qoldiring
- Maʼlumotlarni oʻqishdan oldin formulani tanlang va nomaʼlumlarni yozing.
- Foiz soʻralsa — koʻpaytuvchilar yetarli; son soʻralsa — haqiqiy son kerak.
- Toʻplam: jami = A + B − ikkalasi + hech biri.
- Ish: ikkala unum kerak; tezlik: umumiy masofa va umumiy vaqt.
- Yetarli ekanini bilsangiz — hisoblamang, keyingi savolga oʻting.