SAT-81: The "Plugging In Numbers" Tactic

SAT-81: The "Plugging In Numbers" Tactic

Description: When a problem is full of variables and the answer choices are also in variables, you can replace the letters with your own simple numbers, work out a real value, and then see which choice matches. This turns scary algebra into easy arithmetic — and it is one of the most powerful SAT tactics.

When to use it

• The question says "in terms of x" (or any variables) and the answer choices contain variables.
• The problem feels abstract and you're not sure how to start the algebra.
• There are percentages or fractions "of some number" with no actual number given.

(Oʻzbekcha: javoblar ham harflar bilan berilgan boʻlsa, harflar oʻrniga oddiy sonlar qoʻyib hisoblang.)

The steps

1. Pick simple, easy numbers for the variables (avoid 0 and 1, which can hide differences).
2. Work the problem with those numbers to get a single target number.
3. Plug the same numbers into every answer choice.
4. The choice that equals your target is the answer. (If two match, pick new numbers and re-test those two.)

(Oʻzbekcha: 0 va 1 dan qoching — ular farqni yashirishi mumkin.)

Worked Example 1 — answer in terms of x

If a number is x, what is "3 more than twice the number"? Choices: (A) 2x + 3 (B) 3x + 2 (C) 2(x + 3) (D) 3x.

• Let x = 4. "Twice the number" = 8; "3 more" = 11. Target = 11.
• Test each with x = 4: (A) 2(4)+3 = 11 ✓; (B) 14; (C) 14; (D) 12. Only (A) hits 11 → (A).

Worked Example 2 — percentages with no number

A price is increased by 20%, then decreased by 50%. The final price is what percent of the original?

• Let the original = 100 (the easiest number for percents).
• After +20%: 120. After −50%: 60. So the final is 60% of the original.

(Oʻzbekcha: foiz masalalarida boshlangʻich qiymatni 100 deb oling — eng qulayi.)

Worked Example 3 — choosing safe numbers

If y = 2x, which is larger, 3y or 5x? Try x = 3.

• x = 3 → y = 6. Then 3y = 18 and 5x = 15. So 3y is larger.
• (Here picking x = 0 would make both 0 and hide the answer — that's why we avoid 0.)

Tip: numbers like 2, 3, 4, 5, or 10 are usually best. For percent problems, 100 is king. (Oʻzbekcha: 2, 3, 4, 5 yoki 10 — eng qulay sonlar; foizlar uchun 100.)

Worked Example 4 — when a relationship is given

If a + b = 10, what is the value of 2a + 2b + 5? Choices: (A) 15 (B) 20 (C) 25 (D) 30.

• Pick numbers that fit the relationship: let a = 6 and b = 4 (they sum to 10).
• 2(6) + 2(4) + 5 = 12 + 8 + 5 = 25 → (C). (Any a, b summing to 10 gives the same result.)

(Oʻzbekcha: shart berilgan boʻlsa (a + b = 10), shartga mos sonlarni tanlang.)

The one safety check

Plugging in can rarely produce a "false match" — a wrong choice that happens to equal your target for the specific numbers you picked. That's why, if two choices both match, you re-test only those two with a different set of numbers; the impostor will fail the second round. Choosing slightly unusual numbers (like 3 and 7 instead of 5 and 5) also makes false matches less likely. (Oʻzbekcha: ikki variant mos kelsa, ularni boshqa sonlar bilan qayta tekshiring — soxta moslik yoʻqoladi.)

Practice 1

The sum of three consecutive integers is, in terms of the smallest integer n, which expression? (A) 3n (B) 3n + 3 (C) 3n + 1 (D) n + 3.

Practice 2

A shirt costs d dollars. It is marked up 25%. In terms of d, the new price is? (A) 1.25d (B) 0.25d (C) d + 25 (D) 1.025d.

Key words — Kalit soʻzlar

• Plug in — qiymat qoʻyish
• Variable — oʻzgaruvchi
• In terms of — ... orqali ifodalangan
• Target number — maqsadli son
• Answer choices — javob variantlari
• Substitute — oʻrniga qoʻyish
• Consecutive — ketma-ket
• Simple number — oddiy son
• Match — mos kelishi

Summary

• Use when variables appear in both the question and the choices.
• Pick simple numbers (avoid 0 and 1), get a target number, test every choice.
• For percent problems, start the original at 100.
• If two choices tie, re-test just those with new numbers.